Optical, vibrational, thermal, electrical, damage, and phase-matching properties of lithium thioindate

Fossier et al. Vol. 21, No. 11 /November 2004 /J. Opt. Soc. Am. B 1981

Optical, vibrational, thermal, electrical, damage,and phase-matching properties of lithium

thioindate

Sandrine Fossier, Sophie Salaun, Jacques Mangin, and Olivier Bidault

Laboratoire de Physique de l’Universite de Bourgogne (Unite Mixte de Recherche 5027, Centre National de laRecherche Scientifique 5027), 9 avenue A. Savary, F-21078 Dijon, France

Isabelle Thenot and Jean-Jacques Zondy*

BNM-SYRTE, Observatoire de Paris (Unite Mixte de Recherche 8630, Centre National de la Recherche Scientifique8630), 61 avenue de l’Observatoire, F-75014 Paris, France

Weidong Chen

Laboratoire de Physicochimie de l’Atmosphere (Unite Mixte de Recherche 8101, Centre National de la RechercheScientifique 8101), Universite du Littoral Cote d’Opale, 145 Avenue Maurice Schumann, F-59140 Dunkerque,

France

Fabian Rotermund† and Valentin Petrov

Max-Born Institute for Nonlinear Optics and Ultrafast Spectroscopy, 2A Max-Born Strasse, D-12489 Berlin,Germany

Plamin Petrov and Jes Henningsen

Danish Institute of Fundamental Metrology, B 307 Matematiktorvet, DK-2800, Lyngby, Denmark

Alexander Yelisseyev, Ludmila Isaenko, and Sergei Lobanov

Design and Technological Institute for Monocrystals Siberian Branch of Russian Academy of Sciences, 43 RusskayaStreet, RU-630058, Novosibirsk, Russia

Ona Balachninaite,‡ Gintas Slekys,‡ and Valdas Sirutkaitis‡

Altechna Co. Ltd, Ukmerges 41A-203, LT-2004, Vilnius, Lithuania

Received January 28, 2004; Revised manuacript received June 15, 2004; accepted June 28, 2004

Lithium thioindate (LiInS2) is a new nonlinear chalcogenide biaxial material transparent from 0.4 to 12 mmthat has been successfully grown in large sizes and with good optical quality. We report on new physical prop-erties that are relevant for laser and nonlinear optics applications. With respect to AgGaS(e)2 ternary chal-copyrite materials, LiInS2 displays a nearly isotropic thermal expansion behavior, a 5-times-larger thermalconductivity associated with high optical damage thresholds, and an extremely low-intensity-dependent ab-sorption, allowing direct high-power downconversion from the near-IR to the deep mid-IR. Continuous-wavedifference-frequency generation (5–11 mm) of Ti:sapphire laser sources is reported for the first time to ourknowledge. © 2004 Optical Society of America

OCIS codes: 160.4330, 160.6000, 170.5660, 190.2620, 190.4970, 120.4530.

1. INTRODUCTIONThe intensive search for new nonlinear materials for thegeneration of coherent tunable radiation in the mid-IR(2–20 mm), a spectral range of importance for molecularspectroscopy, atmospheric sensing, and various opto-electronic devices, remains a continuing challenge. Incontrast with the oxides (with IR transmission range notexceeding ;5 mm) that attracted much attention lately,such deep mid-IR materials cannot be grown by well mas-tered hydrothermal, flux, or Czochralski methods. In-

0740-3224/2004/111981-27$15.00 ©

stead, the more complex Bridgman–Stockbarger growthtechnique in sealed (high-pressure) ampoules, with vola-tile and chemically reactive starting components, is theonly method used to produce large-size single-domaincrystals, and this certainly hampered their developmentall the more in that special postgrowth treatments areneeded to restore stoichiometry and improve their opticalquality.

To date, only a few suitable nonlinear crystals combin-ing an extended transparency from the visible/near-IR to

2004 Optical Society of America

1982 J. Opt. Soc. Am. B/Vol. 21, No. 11 /November 2004 Fossier et al.

the deep mid-IR and large-enough birefringence to allowphase matching over the whole transparency range areavailable. The majority of these compounds belong to theternary chalcogenide semiconductors of the AIBIIIC2

VI

family, where A 5 Cu, Ag; B 5 Al, Ga, In; C 5 S, Se,Te.1 Except for AgInS2 , which can exist in both the te-tragonal and orthorhombic phases,2 these crystallize inthe chalcopyrite (CuFeS2) structure with the I42d spacegroup and tetragonal symmetry (class) 42m but only afew of them possess sufficient birefringence. Most of thecommercially available nonlinear crystals (AgGaS2 orAGS, AgGaSe2 or AGSe, ZnGeP2 or ZGP; GaSe and CdSe)or more confidential ones (HgGa2S4, Ag3AsS3 or prous-tite, and Tl3AsSe3) have their advantages anddrawbacks.3 Despite their higher nonlinearity comparedwith the oxides, one limitation stems from their low-energy bandgap, which prevents the use of pump lasersbelow 1 mm owing to severe linear and two-photon absorp-tion and associated thermal effects. ZGP has a high non-linearity (72 pm/V) and thermal conductivity but requirespump wavelength above 2 mm owing to its residual ab-sorption in the near-IR. The noble-metal compounds(AGS, AGSe) have the lowest residual absorption, buttheir poor thermal conductivity owing to a low-energyphonon spectrum limits their performance, especially incw applications.4–7 Furthermore, their thermal expan-sion is anisotropic along the direction parallel and per-pendicular to the optic axis, which is a source of thermo-mechanical stresses. CdSe’s transparency extends up to18 mm, but its low birefringence and nonlinearity limit itsphase-matching capability. GaSe is a soft, cleaving com-pound that cannot be cut at directions different from theoptical axis; further, its large birefringence results in se-vere walk-off limitations.

Two new materials belonging to the AIBIIIC2VI chalco-

genide family, where the metal cations are replaced withthe lighter alkali metal (A 5 Li), can now be added tothis limited list: LiInS2 or lithium thioindate (LIS) andLiInSe2 or lithium selenoindate (LISe). They wereshown to crystallize with the b-NaFeO2 structure (ortho-rhombic Pna21 [ C2v

9 symmetry, point group mm2),which is a distorted superstructure of the wurtzite type,as early as 1965.8 Hence, contrary to the other mid-IRcompounds, these new materials are biaxial and isostruc-tural to, e.g., KTiOPO4 (KTP). The linear and nonlinearproperties of LIS were briefly studied by Boyd and co-workers in the early 1970s, using small and poor qualitysamples,9 but very few works (mainly focused on its opti-cal bandgap characterization and photoluminescencespectra10–15) have followed since until recently owing toproblems associated with its reliable growth in largersizes allowing design of good optical quality single-domain elements for practical applications.16 Thin filmsof LiInS2 on glass and silicon substrates were alsocharacterized.17 The growth problems, associated withthe high chemical activity of Li, were solved recently,18

and large crystals (up to 20 mm in length) of high opticalquality became available for practical nonlinear opticalapplications.19–21 To our knowledge, there is only oneother group that has succeeded previously in synthesizingthis material with comparable size,22 but this work wasalso stopped recently. While only non-phase-matched

second-harmonic generation (SHG) was used by Boyd andco-workers to determine the nonlinear properties of LIS,9

the first phase-matched SHG experiment using the tun-able output of a pulsed LiNbO3-optical parametric oscil-lator (OPO) near 2.5 mm was reported only recently.19

The range of fundamental wavelengths was extended to 6mm using the radiation from a free-electron laser andZGP frequency doubler,20 and rough estimation of the ef-fective nonlinear coefficients was extracted from thosemeasurements. Direct parametric downconversion inthe range 4.8–9 mm, using a femtosecond (200 fs) Ti:sap-phire amplifier as the pump source, was simultaneouslyreported with an upper-bound value of the two-photon ab-sorption (TPA) at 800 nm of b50.04 cm/GW,21 owing tothe high bandgap energy of LIS.13,14,22,23 Such a value isabout 100 times less than the value for AGS or 1000 timesless than for AGSe at 1.32 mm.24

These preliminary experiments allowed assessment ofthe potential of LIS over the existing mid-IR materials,and justification of the need for a complete characteriza-tion of its optical properties. In this paper, we report newresults, from an intensive investigation campaign involv-ing a network of laboratories in Europe, on the character-ization of the main properties relevant for laser applica-tions: structure and transmission (Section 2), specificheat, thermal expansion, and thermo-optic coefficients(Section 3), accurate lattice phonon spectra (Section 4),electro-optic and piezoelectric constants (Section 5), linearoptical and thermo-optic dispersions (Section 6), phase-matching predictions (Section 7), nonlinear coefficients(Section 8), parametric downconversion (Section 9), andoptical damage thresholds (Section 10). The results pre-sented here show that LIS is superior to the existing chal-copyrites in terms of high-power deep mid-IR downcon-version applications pumped directly from the near IR.The preliminary work on LISe has just started and willnot be reported here.25

2. COMPOSITION, STRUCTURE, ANDTRANSMISSIONSingle-domain crystals of LIS are grown by theBridgman–Stockbarger technique in a vertical setup withcounterpressure on seeds along (001) and (010)directions.8–10,18,26–28 The directed crystallization is per-formed from a melt of elemental Li, In, and S. In themelt zone the temperature is maintained at ;1100 K anddecreases to ;900 K in the growth zone. The chargedampoules are moved in an optimal thermal gradient of10–15 K/cm at a rate of ;10 mm/day. This technique al-lows the growth of crystal ingots with diameters up to 20mm and lengths up to 50 mm.18 Although sometimes col-orless to a great extent, the as-grown ingots are usuallymilky because of small inclusions of various phases, andit is necessary to anneal them in Li2S or S2 vapor at tem-perature close to the melting point (Tmelt ; 1000 °C).18

The crystal coloration after the thermal postgrowth treat-ment changes then from almost colorless (or slightly yel-low) for as-grown to salmon-rose tinge, depending on thegrowth and postgrowth treatment conditions and chemi-cal composition. Optical elements with aperture up to 1cm2 and length up to 15 mm could be prepared for opticalmeasurements or for nonlinear frequency conversion.


Precise chemical analysis—using differentialdissolution techniques and the inductively coupledplasma method—showed that the composition ofcolorless (or yellow tinge) and rose samples isLi0.98In1.03S2.00(Li0.96In1.06S1.98) and Li0.86In1.04S1.98 ,respectively.18 Lithium deficit (NLi :NIn , 1) is observedfor all samples, the annealed rose ones being character-ized by a higher sulfur content (NLi1In :NS , 1). Theband-structure nature of LIS has been confirmed to be ofthe direct type (direct transitions between parabolicbands).13,14 The forbidden bandgap values estimated byus (Eg 5 3.72 and 3.57 eV at 80 K and 300 K, respec-tively, which are in good agreement with previousmeasurements),13,14,22,23 the position of the long-waveedge of transparency (13 mm at an absorption of 6 cm21),and the crystal symmetry group were found identical forall crystal colorations, although small variations in latticeparameters owing to point defects were also observed.29,30

A detailed and general structural analysis of AIBIIIC2VI

compounds, where AI is an alkali metal such as Li, hasbeen given by Kish et al.31 A fragment of the structure of

Fig. 1. Fragment of the orthorhombic unit cell structure (thebox frame gives the orientation of the unit cell). The 3 emptyareas materialized with light gray spheres indicate the locationof octapores.

Fig. 2. Polarized transmission spectra of an annealed LISsample (thickness 5 mm), not corrected for the Fresnel loss.

LIS is shown in Fig. 1 (see Figs. 2.1.1–2.1.2 in Ref. 28 forthe full unit cell representation). It is formed by LiS4and InS4 tetrahedrons, and the S22 ions are arranged inhexagonal packing with tetragonal and octahedral cavi-ties (tetra- and octapores).31 Compared with the denserchalcopyrite structure of AGS or AGSe,32 the b-NaFeO2structure of Li chalcogenides allows the presence of emptycavities within the unit cell volume. The less denseb-NaFeO2 structure allows, in particular, doping withrare-earth active ions that can be hosted inside the oc-tapores. Such a preliminary doping experiment withNd31 ions was previously reported with the aim of inves-tigating rare-earth-doped LIS potential as a self-down-converting material.33 The values of the orthorhombiclattice parameters are a 5 6.874(1) Å, b 5 8.033(2) Å,and c 5 6.462(1) Å for as-grown colorless LIS, and a5 6.890(1) Å, b 5 8.053(1) Å, and c 5 6.478(1) Å forslightly yellowish samples. They are slightly lower thanthe values reported by Hoppe8 and Boyd et al.9 or Kami-joh et al.10,11 and Kish et al.34 but fit most closely to thelast one. They modify to a 5 6.896(1) Å, b5 8.058(2) Å, and c5 6.484(4) Å for rose annealedsamples. Concomitantly, the density changes from r5 3.52 g/cm3 to r5 3.44 g/cm3. We have chosen c , a, b where c is the polar twofold axis that coincides withthe selection of Boyd et al.9 This convention satisfies therecommendation of Roberts35 for unique designation ofthe orthorhombic class mm2. Note that in the following,in contrast to Roberts35 and the ANSI/IEEE Standard,36

we do not introduce an additional frame for reporting thenonlinear tensor properties but, for simplification and inaccordance with the tradition, use the crystallographicabc frame for reporting the nonlinear optical susceptibil-ity (see Section 7). Also, instead of small-case lettersxyz, as suggested by Roberts,35 we use the capital lettersXYZ for designation of the principal optical axes suchthat nX , nY, nZ . Since for LIS one has nb , na, nc , the principal frame assignment will be X ↔ b,Y ↔ a , and Z ↔ c.

Figure 2 shows the polarized transmission spectra of athick (L 5 5 mm) annealed optical element. Dependingon the growth and annealing conditions, some absorptionbands owing to the various point defects—in particularexcess sulfur ions occupying interstitial sites—may limitthe transmission window in the visible side. These vis-ible bands, responsible for the rose coloration of the an-nealed samples, restrict the range of high-transmission(T ; 70%) to 0.8–8.1 mm. The postgrowth thermaltreatment, however, improves considerably the transpar-ency within the above window. The absorption coeffi-cient a(l) within the full transparency window deducedfrom the spectra amounts to 0.1–0.15 cm21. These val-ues are overestimated, since from direct laser line trans-mission experiments using various laser sources in therange 0.78–2.53 mm and several samples, the average re-sidual absorption of a typical annealed sample was foundto be lower. At 2.53 mm, e.g., the total loss coefficient (ab-sorption and scattering) estimated amounts to 0.05 cm21.At 780 nm, the loss coefficient measured with a diodelaser source ranged between 0.05 and 0.2 cm21, depend-ing on the strength of the weak point-defects relatedbands,18 seen also in Fig. 2.


3. THERMAL AND THERMO-OPTICPROPERTIESThe thermally related properties of a new nonlinear ma-terial are crucial in assessing its potential in real nonlin-ear conversion devices pumped by high-power cw orpulsed lasers. The performance of devices based onmid-IR chalcogenides is often limited by deleterious ther-mal effects (lensing, expansion).4,7,24 The thermal figureof merit of a material can be defined by the quantity h5 (dn/dT)/K, where dn/dT is the thermo-optic indexvariation and K is the thermal conductivity. The largerthis quantity is, the more severe are the thermal limita-tions. A second thermal quantity, tD 5 w0Cp/4K, whereCp is the mass specific heat of the material and w0 is thebeam radius, gives the characteristic time of heat diffu-sion outside the pumped volume. The larger this diffu-sion time, the stronger the thermal-lensing effects.7 It ishence important to know Cp , K, and dn/dT. In addition,the thermo-optic coefficients are needed to predict phase-matching performance in x (2) interactions. Let us pointout that no data have been published on the thermalproperties of single-domain crystalline LIS.

A. Specific Heat at Constant PressureUsing Al2O3 as a reference, we estimated Cp(T5 300 K)5 92.9 6 1.1 J/mol/K for crystalline rose color

LIS (57.91 mg), which is only slightly higher than whathas been previously measured for polycrystalline LIS (90J/mol/K) in Ref. 37. The temperature dependence in the[2160 °C; 210 °C] range could be fitted by

Cp~T ! 5 114.02 2 5708 3 T21 2 187540 3 T22, (1)

where T is in Kelvin. The general theoretical expressionof Cp(T) for anharmonic solids is

Cp~T ! 5 12RFF~xD! 1 (k51

N

ckTkG , (2)

where R is the molar gas constant, xD 5 TD /T (TD is theDebye temperature), and F(xD) is the Debye function de-scribing the temperature dependence in the harmonic lat-tice vibration approximation,

F~xD! 53

xD3 E0

xD x4exdx

~ex 2 1 !2. (3)

The value of N and the absolute magnitudes of the coeffi-cients ck in the sum expansion in Eq. (2) can be consid-ered as a measure of the degree of lattice anharmonicity,while the sign of ck is essentially determined by the shapeof the interatomic potential. In Eq. (2), the leading coef-ficients c1 and c3 were found negative for all AIBIIIC2

VI

chalcogenide compounds, and the magnitude of ck wasfound ;10 times higher and independent of the anion C22

for Li compounds. This means that the anharmonic con-tribution of the lattice potential energy is much strongerin LiInC2

VI compounds (N 5 4 in Eq. 2) than in AIBIIIC2VI

chalcopyrite compounds (N 5 3). In LIS, this is relatedto the specific nature of the Li—S bond, which is abouttwice weaker than the In—S bond.38 As a consequence,the temperature dependence of Cp(LIS) is much weaker

than for AgInS2 and AGSe,39 and the resulting Cp(T) val-ues for LIS are the lowest of all chalcogenides. By a calo-rimetric absorptance (A) measurement, the absorption co-efficient a can be estimated from A 5 mCpDT/PDt 5 12 exp(2aL), where m is the mass in mol, DT is the tem-perature rise, P is the laser power, and Dt is the irradia-tion time. We irradiated at 1064 nm an annealed LISsample of dimension 5 3 5 3 5 mm3 cut at 28° from the ccrystallographic axis for light propagation in the a–cplane (m 5 0.438 g 5 2.356 3 1023 mol) and obtained anabsorption coefficient of a 5 0.037 cm21 (compare Section2).

B. Thermal ExpansionThe principal thermal-expansion and thermo-optic coeffi-cients were determined by using the absolute interfero-metric dilatometer and the experimental procedure de-scribed in Ref. 40. A two-beam modified Mach–Zehnderinterferometer arrangement is employed for dilatationmeasurements, and thermo-optic coefficients are obtainedusing the same setup by recording changes in opticalthickness of a sample acting as a thermal scanningFabry–Perot interferometer, with the natural reflectivityof the two opposite parallel facets. Three parallelepi-pedic samples of dimension 5 3 5 3 8 mm3 cut along thecrystallographic axes a, b, and c (L 5 8 mm) were usedfor these measurements. The samples were subjected tolinear temperature ramps of 0.2 °C/min in the range220 °C–1100 °C.

In a given temperature interval, dT, the linearthermal-expansion coefficients are defined as

a i 51

Li

dLi

dT, (4)

where Li is the sample length along the direction i, withi 5 a, b, c. To be consistent with our assignment of theprincipal optical axes X, Y, Z in Section 2 (and Section 6),we remind the substitutions X [ b, Y [ a, Z [ c.

For the measurement of the thermal expansion, thelight source of the absolute interferometric dilatometerwas a frequency-stabilized 2-mW He–Ne laser. A plot ofthe experimental data is reported in Fig. 3. A linear fit ofthe data gives the following temperature dependence ofthe linear thermal-expansion coefficients,

aX 5 1.61 3 1025 1 1.4 3 1028T, (5)

Fig. 3. Thermal-expansion coefficients of LIS along the axes X[ b, Y [ a, Z [ c, from 220 °C to 1100 °C.


aY 5 0.89 3 1025 1 0.7 3 1028T, (6)

aZ 5 0.66 3 1025 1 0.9 3 1028T, (7)

where T is the temperature (°C). The deviations of ex-perimental values from these fits are less than 1026 K21.At T 5 20 °C, we have aX 5 1.64 3 1025 K21, aY5 0.91 3 1025 K21, and aZ 5 0.68 3 1025 K21, respec-tively. Such values are of the same order of magnitude oreven less than those for AGS (a ic 5 1.25 3 1025 K21,a'c5 21.32 3 1025 K21),41 and AGSe (a ic 5 1.683 1025 K21, a'c 5 20.78 3 1025 K21).42

However, the main difference with those chalcopyritesis that LIS does not display their anomalous thermal-expansion behavior (opposite sign of a along the two or-thogonal directions) that is a major source of thermo-mechanical stress in high-power applications.32 Incontrast, LIS expands in the same direction as tempera-ture increases and exhibits a rather weak temperaturedependence. This favorable situation is related to thespecific nature of the weak Li—S bond already evoked inthe previous subsection.

C. Thermo-Optic CoefficientsWe shall again make use of the labels X [ b, Y [ a, andZ [ c, denoting the principal optical axes to describe thechange of the index of refraction versus temperature, for alight polarized along one of these principal axes andpropagating along another principal direction. For alight wave polarized along direction pj and propagatingalong direction ei , we define the coefficient g ji related tothermal changes in optical thickness (path) by

g ji 51

njLi

d~njLi!

dT, (8)

where nj and Li are, respectively, the refractive index andthe length of the sample, with i, j 5 X, Y, or Z and iÞ j. The normalized thermo-optic coefficients b j5 (1/nj)dnj /dT are derived from Eqs. (4) and (8) andgiven by

b j 5 g ji 2 a i . (9)

As evident from Eq. (9), the knowledge on the values ofthe thermal expansion is prerequisite for the interfero-metric determination of the thermo-optic coefficients at agiven wavelength. For the orthorhombic symmetry ofLIS it can be seen that each b j may be obtained for twodirections of light propagation. This has been performedat four laser wavelengths, and the resulting linear fits to

b j~l, T ! 5 a1~l! 1 a2~l!T, (10)

where T is measured in °C, summarized in Table 1. Theindicated uncertainties in the parameters a1 and a2 rep-resent the deviation from the mean value determinedfrom the two possible propagation directions ei for a givenorientation pj of light polarization. At l 5 1064 nm andT 5 20 °C, one has dnX /dT 5 3.725 3 1025 K21,dnY /dT 5 4.545 3 1025 K21, dnZ /dT 5 4.467 3 1025

K21. Compared with the thermo-optic coefficients ofAGS,43 these values are ; 5 times lower. Dispersion re-lations based on those wavelength-dependent data are de-rived in Subsection 6.B.

4. VIBRATIONAL PROPERTIESThe vibrational properties have been investigated bymeans of Raman spectroscopy and infrared reflectivity inpolarized light at room temperature. The group-theoryanalysis shows that, at the zone center for the b-NaFeO2structure, the 48 normal phonon modes are distributedamong the various irreducible representations of the C2v

9

factor group as follows:

Gvib 5 12A1 1 12A2 1 12B1 1 12B2 . (11)

The three acoustic phonon modes have A1 , B1 and B2symmetries; the 45 remaining (optical) modes are Ramanactive. A1 modes will be active when the experimentalconfiguration selects a diagonal aa, bb, or cc componentof the Raman tensor, while the selection of ba, ca, and cbcomponents will respectively allow the observation of theoptical phonons of A2 , B1 , and B2 symmetry. WithA2-type phonons being infrared inactive, the IR-reflectivity spectra should then contain 11 polar modes ofeach A1 , B1 , and B2 symmetry with dipole moment re-spectively parallel to c, a, and b crystallographic axes. Intheory, every optical phonon may then be observed bymeans of IR reflectivity and/or Raman scattering. None-theless, depending on various factors such as the more orless polar character of bonds, even an active mode may beunobservable.

To obtain results on every phonon type, we used twoLIS rose-tinge samples cut from the same ingot, withsizes 4 3 4 3 5 mm3 and parallel optically polished fac-ets (4 3 4 mm2) normal to a and c axes. Infrared reflec-tion spectra were recorded in the spectral range 18.3–600cm21, and this whole range of data was used to adjust theparameters of the dielectric permittivity model shown inEq. (12). The experimental spectra, recorded at quasi-normal incidence (at an angle of incidence of 6°) with anelectric field polarization parallel to a, b, and c axes, areshown in Fig. 4 (symbols). As can be seen from thesegraphs, each reflectivity spectrum is rather complex andexhibits several more or less overlapping bands, and thehigh-energy band(s) in each polarization generally showsome additional structure (slight inflexion in the bandshape) that suggests, in addition to a strong mode, thepresence of several other modes contributing to the same

Table 1. Principal Normalized Thermo-Optic Co-efficients b jÄ(1Õnj)dnj ÕdTÄa1¿a2T of LIS [Eq.

(10)] at Four Laser Wavelengths

l (mm) b j (°C21) 105a1 (°C21) 108a2 (°C22)

bX 3.41 6 0.06 3.1 6 0.30.4765 bY 4.11 6 0.07 4.6 6 0.9

bZ 4.08 6 0.02 4.7 6 0.4bX 2.28 6 0.07 1.5 6 0.4

0.6328 bY 2.76 6 0.05 2.1 6 0.4bZ 2.69 6 0.01 2.4 6 0.1bX 1.75 6 0.07 1.0 6 0.06

1.0642 bY 2.10 6 0.11 1.3 6 0.5bZ 2.03 6 0.08 1.3 6 0.1bX 1.50 6 0.07 0.7 6 0.17

3.392 bY 1.83 6 0.14 1.1 6 0.5bZ 1.73 6 0.03 1.0 6 0.02


band. Actually, from the numerical analysis of the ex-perimental results, it is found that for each direction ofpolarization, there are three polar modes in the high-frequency band (350–420 cm21) and medium-frequencyband (250–350 cm21), and the remaining five polarmodes, not all observable in Fig. 4, are in the low-frequency region (,250 cm21).

Polarized micro-Raman spectra were recorded using aRaman spectrometer equipped with a confocal microscopeand a liquid-N2 cooled CCD detector in the region 12–600cm21 in triple substractive configuration with an 1800grooves/mm grating. To increase the quality and resolu-tion of the spectra, we chose to use the 647-nm red line ofan argon–krypton laser (P 5 100 mW) which experienceslower absorption loss than a green laser44). To avoid pos-sible influence of surface defects, the confocal microscopefocused the laser beam at a depth of 60 mm under the sur-face. A scattering geometry is described by the notatione1( p1p2)e2,45 where ei identifies the propagation direc-tion of the laser light, polarized along pi , e and p being a,b, or c crystallographic axes; the subscripts i 5 1 and 2refer to incident and scattered beams, respectively. Fig-ure 5 shows some of the experimental spectra. The Ra-man spectra are dominated by a strong mode of A1 sym-metry at ;268 cm21, also apparent in the IR reflectivityspectra for E//b and E//c.

Owing to the respective mass of the atoms, high (low)-frequency modes obviously imply movements of Li—S(In—S) bonds. Phonons of medium frequency (250–350cm21), visible in both IR-reflectivity and Raman scatter-

Fig. 4. Infrared reflection curves (symbols) recorded with polar-ized light with an electric field parallel to the crystallographicaxes a—B1 modes, b—B2 modes, and c—A1 modes. The con-tinuous lines represent in each case the best-fit reflectivitycurves calculated with the model in Eqs. (12) and (13).

ing, are attributed to In—S bonds,23 while those of high-est frequency (above 350 cm21, Fig. 4) that give rise tostrong IR bands but no observable Raman line are due toweaker Li—S bonds.38 The splitting of transverse (TO)and longitudinal (LO) optical polar modes observed in theinfrared measurements for any of the explored polariza-tions is rather important in the high-frequency region(strong IR bands), which attests to a highly polar (ionic-ity) character of Li—S bonds in this crystal. The split-ting decreases with the phonon frequency to become sosmall for low frequency modes that no correspondingband appears in the reflectivity spectrum, which indicatesa mostly covalent character of the In—S bonds. How-ever, even if a phonon cannot be observed by means of IRreflectivity, its Raman activity may be high, which is thecase for modes lying below 100 cm21. Actually, intenseRaman lines appear in the low- and mid-frequency re-gions, while almost no line can be detected above roughly350 cm21. In order to fit the experimental IR-reflectivityspectra and get the best-fit reflectivity curves (lines inFig. 4, in a good agreement with experimental points), weused the so-called four-parameter model, convenient torepresent even asymmetrical and wide bands.46 Thismodel expands the factorized form of the dielectric per-mittivity function as

e~v! 5 e8 2 ie9 5 e`)j51

NV j,LO

2 2 v2 1 ig j,LOv

V j,TO2 2 v2 1 ig j,TOv

(12)

to fit a reflectivity curve described by the Fresnel formula

R~v! 5 UAe~v! 2 1

Ae~v! 1 1U2

. (13)

Fig. 5. Polarized Raman spectra (shifted for reasons of clarity)recorded at room temperature. The experimental configura-tions b(aa)b, c(bb)c, and b(cc)b correspond to A1 modes,c(ba)c to A2 modes, b(ca)b to B1 modes, and a(cb)a to B2modes.


In the b-NaFeO2 structure, the model implies for a givenpolarization N damped oscillators, the number N being atmost equal to 11 (number of theoretically observablemodes, predicted in this structure by group-theory analy-sis). The jth damped oscillator represents the jth ob-served infrared active couple of modes, characterized byfour adjustable parameters, namely, the longitudinalV j,LO and transverse V j,TO angular frequencies, and thecorresponding damping frequencies g j,LO and g j,TO . Thehigh-frequency limit values of the dielectric constant isalso adjusted to yield e`(A1) 5 3.99, e`(B1) 5 4.09, ande`(B2) 5 3.97.

Table 2 lists the wave numbers n j 5 V j/2pc and damping rates g j 5 g j/2pc (expressed in cm21) of the observedoptical phonons deduced from IR reflectivity and/or Ra-man scattering experiments, assigned to the various irre-ducible representations of the C2v

9 factor group. Thetransverse (TO) and/or longitudinal (LO) character of theobserved Raman-active phonons have been determinedwith the help of the IR reflectivity results (the notationTO ' LO means that the splitting is too weak to be un-ambiguously identified). These data allow computationof the linear dielectric properties of LIS in the far-IR

Table 2. Zone-Center Phonon Wave Numbers (nTO ÕnLO) and Damping (gTO ÕgLO), in cm21

PhononSymmetry

IR ReflectivityRaman

ScatteringWave Numbers n j Dampings g j

A1TO/LO(cm21)

-/- -/- 56.4 (TO ' LO)-/- -/- 88.1 (TO ' LO)-/- -/- 112.7/113.3

128.6/138.2 3.0/4.4 129.1/135.2266.0/267.1 8.5/8.7 268/269274.2/279.2 9.2/8.7 273/-274.2/279.2 9.2/8.7 273/-313.6/313.8 4.9/5.0 314 (TO ' LO)323.7/333.7 6.2/11.3 323.4/333341.7/356.0 14.3/13.9 341/-357.0/373.0 14.5/14.7 357/-373.1/399.0 14.3/16.5 -/399

A2(cm21)

59.468.7

117.8125.9157.4

IR inactive 253.5297.4319.4332.5

B1TO/LO(cm21)

-/- -/- 61.1 (TO ' LO)-/- -/- 93.5 (TO ' LO)

125.8/133.4 2.6/3.0 125.8/133.3164.9/166.0 8.4/9.0 165 (TO ' LO)264.9/266.3 9.3/10.3 267 (TO ' LO)303.3/303.7 9.4/9.2 -/-318.3/334.6 5.0/7.2 318.7/-343.6/347.8 11.2/10.4 -/-356.4/375.9 10.4/22.8 356.5/-376.7/395.8 21.9/23.1 -/-400.4/408.6 29.7/12.4 -/-

B2TO/LO(cm21)

-/- -/- 59.3 (TO ' LO)96.1/96.4 3.3/3.1 96 (TO ' LO)

104.7/105.7 4.8/5.2 104.7/105.5132.0/132.5 10.2/10.1 133 (TO ' LO)142.7/144.9 6.1/6.9 143.2 (TO ' LO)276.5/285.1 8.0/8.4 276.2/285324.6/329.8 5.9/7.3 325.2 (TO ' LO)333.4/336.0 7.2/7.5 334 (TO ' LO)348.0/358.4 10.3/8.9 348/-362.2/397.7 8.6/11.0 362/-398.6/410.4 11.1/11.9 -/-


range, using Eq. (12). Typically, TO and LO frequenciesdeduced from IR-reflectivity experiments are determinedto better than 1 cm21. The precision of a Raman-activephonon frequency is also generally better than 1 cm21, ex-cept for broad and low-intensity lines for which it de-creases to 2 cm21. The transverse or longitudinal char-acter of the Raman-active modes for A1 , B1, and B2symmetries has been determined with the help of the IRreflectivity results where this TO or LO character is ap-parent. Nonobserved IR-active modes indicate a smallTO ' LO splitting and generally did not allow an accu-rate determination of TO and LO frequencies from Ra-man spectra, but only of a mean value labeled by TO' LO. A few Raman lines have been attributed to an in-terference by an intense line active in another geometry.These Raman results complement those from previousstudies performed with unpolarized23,26,28 and polarizedlight.47

The accurate determination of the frequencies in Table2 allows estimation of the interatomic bonding force con-stants in LIS, using the theoretical considerations devel-oped by Neumann about the correlation between the vi-brational modes of compounds with sphalerite,chalcopyrite, and b-NaFeO2 structures.48 According tothis model, the vibrational spectrum of a crystal withb-NaFeO2 structure contains two sphaleritelike modes,the TO-frequencies of which are nearly independent ofthe polarization direction. Further, one of these sphaler-itelike modes always corresponds to the highest nTO fre-quency found in the IR reflectivity spectra. If the inter-action between the atoms is restricted to next-nearestneighbors, which is justified by the high bond ionicities inLi-containing ternary compounds, the wave numbers ofthe transverse optical modes of these sphaleritelikemodes in LiBIIIC2

VI are given by49

nTO,k2 5

1

p2c2~ak 2 dak!S 1

mk1

1

mCD , (14)

with the superscript k in the first parenthesis denotingLi—C or B—C cation–anion bonds (in the present case,C 5 S and B 5 In). Here c is the speed of light, ak isthe mechanical bond-stretching force constant, mk is themass of the cation, and mC is the mass of the chalcogenanion. The quantity dak accounts for the fact that, in thecase of IR active modes, the local atomic displacementsgive rise to a nonvanishing net dipole moment per unitcell and thus, to additional dipole–dipole interactions. Itis given by dak 5 A3(ek)2/(16e0sk

3), where sk is the aver-age bond length (sLi-S 5 0.2438 nm, sIn-S 5 0.2452 nm),and ek 5 0.28efk(Zk 1 ZC) is an effective charge depend-ing on the bond ionicity fk and the valences of the cationand anion participating to the bond. In Ref. 38, from anunpolarized IR reflectivity spectrum of polycrystallineLIS restricted to the region 200–400 cm21, the highest-frequency TO/LO mode identified corresponds to 356/406cm21 and the second TO/LO sphaleritelike mode to 323/334 cm21. Actually from the inspection of Table 2, thehighest-frequency sphaleritelike modes with nearly iden-tical frequencies in B1 and B2 symmetries are respec-tively the 400.4/408.6 cm21 and 398.6/410.4 cm21 (thismode is not observed in A1). The second sphaleritelike

mode is recognized from Table 2 as the 323.7/333.7 cm21

(A1), 318.3/334.6 cm21 (B1), and 324.6/329.8 cm21 (B2),close to the value identified in Ref. 38. The Li—S bondforce constant deduced from Eq. (14) by Sobotta et al.,38

aLi 5 24.7 N/m, is then underestimated by (400.4/356)2

5 24%, while the In—S bond force constant, deducedfrom the second sphaleritelike mode remains unchangedto aIn 5 53.4 N/m. But even with this slight correction,the Li—S bond remains still about twice weaker than theIn—S bond. In contrast the strength of the Ag—CVI

bond in chalcopyrite compounds is more comparable tothat of the BIII-CVI bonds,38 underlining the specific na-ture of the lithium–chalcogen bond in crystals with tetra-hedral coordination of the atoms. As a consequence, theincreased lattice phonon energy of LIS, as compared withAGS or AGSe, favors heat dissipation; hence a higherthermal conductivity is expected. Indeed, an unpub-lished measurement of LIS thermal conductivity yieldedKa 5 6.0 W/(m•K), Kb 5 6.2 W/(m•K), and Kc5 7.6 W/(m•K),50 i.e., 5 times larger than for AGS and of the samemagnitude as for LiNbO3 .

A last important feature from the vibrational spectra isthat the phonon spectrum for LIS is located at wave num-bers below 410 cm21. The IR wavelength cutoff (8.1 mm)in Fig. 2 quite exactly corresponds to three times thishighest-energy phonon. The long-wavelength shape ofthe transmission curves—and limit of the transparencyrange—seems then to be simply due to multiphonon pro-cesses. It is worth mentioning that, although the vibra-tional investigations have used rose-tinge samples, thephonon spectrum should not depend on coloration sinceall LIS samples display the same IR cutoff edge, with orwithout annealing.

5. PIEZOELECTRIC AND ELECTRO-OPTICCOEFFICIENTSA. Apparent Electro-Optic CoefficientsThe measurement of electro-optic coefficients involves thedetermination of changes in optical thickness when ap-plying an electric field to the material. LIS belongs tothe symmetry class mm2 for which the electro-optic ten-sor exhibits five nonzero components, namely, r13 , r23 ,r33 , r42 , and r51 .36 In this subsection, we describe theelectro-optic effect in the principal optic frame, whereXYZ are the axes of the index ellipsoid, which coincidewith the crystallographic bac axes. We address only theri3’s coefficients that can be obtained by applying a fieldE3 along the Z axis, which does not lead to a rotation ofthe ellipsoid. Optical interferometric methods may beadvantageously used in this case for their determination.An applied electric field E, with respective components(E1 , E2 , E3) along the principal axes (X, Y, Z), willmodify the index ellipsoid according to

~nX22 1 r13E3!X2 1 ~nY

22 1 r23E3!Y2 1 ~nZ22 1 r33E3!Z2

1 2r42E2YZ 1 2r51E1XZ 5 1. (15)

New indices ni(E3) (i [ 1, 2, 3 [ X, Y, Z) are given by

ni~E3! 5 ni 21

2ni

3ri3E3 , (16)


where d (ni) 5 2(1/2)ni3ri3E3 represents the variation of

the refractive index ni .Owing to the piezoelectric effect, the field E3 will also

generate a variation d (Lj) of the crystal thickness Ljalong a given direction ej such that

d ~Lj! 5 Ljd3jE3 , (17)

where d3j ( j 5 1, 2, 3) are components of the piezoelec-tric tensor.36 For a light wave propagating along direc-tion ej and polarized along direction pi of the crystal, thevariation d (niLj) of the optical path niLj induced by anapplied electric field E3 will be

d ~niLj! 5 niLjS d3j 21

2ni

2ri3DE3 . (18)

We define the effective electro-optic coefficients as

ri3eff 5 2

2

ni2 S d3j 2

1

2ni

2ri3D (19)

with j 5 1, 2, which represent in fact the (apparent)electro-optic coefficients obtained in most experimentswhere the piezoelectric contribution is ignored. Themeasurements of the ri3

eff’s were performed by using thetechnique of phase-modulated thermal-scanninginterferometry.51 In this method, as for the measure-ments of thermo-optic coefficients, the sample acts as aFabry–Perot thermal-scanning interferometer in whichphase modulation is achieved by applying an ac field E3along the Z axis. Various configurations of light polariza-tion (EX , EY , EZ) and wave vector k (kX , kY) were usedto determine the apparent electro-optic coefficients of LIS.

The two LIS samples of aperture 5 3 5 mm2 used forthe thermo-optic data measurements with lengths L5 8 mm along the X and Y propagation axes were sup-plied with gold-evaporated electrodes on their Z facets.The low-frequency (480 Hz) applied voltage was 200 Vpeak to peak, and linear temperature ramps of 0.2 °C/minwere used from 20 °C to 55 °C. Measurements of appar-ent electro-optic coefficients were performed at 1.064 mmby using a 100-mW TEM00 single-frequency Nd:YAG la-ser. In the scanned temperature interval, a constantvalue has been observed for each of them; they are sum-marized in Table 3. These data feature a quite weakelectro-optic effect in LIS, and the large discrepancy ob-served between r33(X)

eff and r33(Y)eff suggests a strong contri-

bution of the piezoelectric effect to the apparent electro-optic one.

Table 3. Apparent Electro-Optic Coefficients ofLIS; 3(X) and 3(Y) Represent the Values of r33

eff Ob-tained for a Light Propagation along X and along

Y, Respectively

i ri3eff (pm/V)

1 2.18 6 0.042 2.82 6 0.333(X) 0.93 6 0.033(Y) 0.11 6 0.02

B. Piezoelectric and Pure Electro-Optic CoefficientsThe nonvanishing piezoelectric coefficients d31 , d32 , andd33 were measured by using the modified Mach–Zehnderarrangement of the absolute interferometric dilatometerin a manner similar to the one employed for dilatationmeasurements. Phase modulation of the interferencepattern is performed by applying to the samples the samevoltage and same thermal-scanning procedure as de-scribed previously. The algebraic sign of the coefficientswas attributed according to the ANSI/IEEE Standard176-1987 on piezoelectric crystals,36 and we have found inpm/V units and in the XYZ frame, d31 5 25.6 6 0.1,d32 5 22.7 6 0.2, and d33 5 17.5 6 0.2.

From Eq. (19) we determine the pure electro-optic coef-ficients r13 5 1.0 pm/V, r23 5 0.4 pm/V, and r335 21.3 pm/V, which reveals a rather small true electro-optic effect compared with the piezoelectric one. Therelative uncertainty in these values is close to 15%.These measurements confirm that, as AGS or AGSe, LISis a poor candidate for electro-optic or piezoelectric baseddevices. A comparison of our results with earlier data ofNegran et al.52 cannot be meaningful since the r13 , r23 ,and r33 that were measured there did not account for thepiezoelectric contribution and were not determined inde-pendently, but as a linear combination.

C. Comparison of the Electro-Optic and PyroelectricCoefficientsFrom the anharmonic oscillator model developed byGarrett,53 Soref54 yields a semi-empirical relationship be-tween the pyroelectric coefficient at constant stress ( ps

5 (DPs /DT)s) and the second-order electronic suscepti-bility x (2) describing the linear (true) electro-optic effect:

ps 5 x~2 !~v 6 0; v, 0!2Cv

e0me2~ve

2 2 v2!2

mv i2NAe2 S 3A 1 B

C 1 3D D .

(20)

The pyroelectric coefficient ps gives the variation of thespontaneous polarization DPs induced by a temperaturevariation DT. The parameters me and e are the massand charge of the electron, ve and v i are respectively theelectronic and ionic resonance frequencies, Cv is the mo-lar specific heat at constant volume (which differs fromthe specific heat at constant pressure Cp measured inSubsection 3.A by a negligible quantity), and NA , theAvogadro number. The constant terms A, B, C, and D arethe coefficients related to the third-order expansion of thecrystal potential energy in the electronic and ionic coordi-nate system qe and qi .54 The ratio (3A 1 B)/(C1 3D) indicates the extent to which the predominantionic contribution to the anharmonic potential at v ' v idiffers from the predominant electronic one at v @ v i .This ratio is expected to be constant whatever the mate-rial, suggesting a linear relationship between the electro-optic and pyroelectric coefficients. This hypothesis wasverified for a few known materials, mostly of the oxidetype.54

By using Cv 5 Cp and x333(2) 5 n3

4r33 from the previoussubsection, the pyroelectric coefficient measuredpreviously55 as a function of temperature and its value ex-trapolated at 300 K, ps 5 6 3 10210 C•cm22 K21, we ob-


serve that Soref ’s hypothesis is confirmed for the ternarysemiconductor LIS, as it was already shown for the binaryone, CdS.54 We note also that a rather good estimate ofthe pyroelectric effect may be deduced from electro-opticmeasurements and vice versa, but this requires at first anaccurate determination of the piezoelectric contribution.

6. LINEAR OPTICAL AND THERMO-OPTICDISPERSIONSWe now address, in light of the vibrational spectra re-sults, the most important data for a nonlinear material:linear optical and thermo-optic dispersion relations thatallow accurate prediction of the phase-matching direc-tions and temperature tunability.

A. Sellmeier Equations at Room TemperatureThe only available dispersion data of LIS, measured usingthe minimum deviation technique, were compiled by Boydet al. in 19739 and fitted to one-pole (UV) Sellmeierequations56 reproduced also in Refs. 21, 57, and 58. Al-though the accuracy of their index determination was notreported, from subsequent nonlinear phase-matched con-version experiments, it appeared that the Sellmeier equa-tions based on their data are accurate to predict the bire-fringence (through angle acceptance bandwithmeasurements19) but fail to predict accurately the abso-lute phase-matching directions. Discrepancies of severaldegrees from the expected phase-matching angles werereported.20 Such deviations cannot be attributed to theX-ray sample orientation uncertainties (60.5°). Further-more, we have checked that the phase-matching angles,and hence the linear refractive indices, are independentof crystal coloration or exact stoichiometry.

A phase-matching direction is labeled by (u, w), where uis the angle of the wavevector respective to the polar Z(c)axis and w is the azimuthal angle between its projectionin the X2Y (b2a) plane and the X(b) axis. To refit theSellmeier equations given in Ref. 56, we have used the ex-perimental type II (eoe, oeo) SHG angles measured in thefundamental wavelength range lP @2.5–6# mm,20,44

supplemented with new recent data derived from type II(eoe) difference-frequency generation (DFG) in the X–Yplane (see Subsection 9.B), where in the wavelength-tuning mode, mid-IR downconversion in the range l1P @6.6–7# mm was achieved at normal incidence. Table4 compiles the experimental phase-matching data used toderive the following room-temperature (T0 5 20 °C) two-pole Sellmeier equations, valid over the full transparencywindow, using a nonlinear least-square fit of the data,

nX2 5 6.686059 1

0.1385833

l2 2 0.059103341

2047.46509

l2 2 897.7476,

(21)

nY2 5 7.095493 1

0.1422326

l2 2 0.066146401

2511.08936

l2 2 988.2024,

(22)

nZ2 5 7.256327 1

0.15072

l2 2 0.068236521

2626.10840

l2 2 983.0503.

(23)

In Eqs. (21)–(23), the wavelengths are expressed in mi-crons. The three IR wavelength poles lIR(X) 5 29.96mm, lIR(Y) 5 31.44 mm, and lIR(Z) 5 31.35 mm (i.e.,n(X) 5 333.7 cm21, n(Y) 5 318.1 cm21, and n(Z)5 318.9 cm21) correspond to the medium-frequency pho-non band centers of symmetry B2 , B1 , and A1 , respec-tively, attributed to the In–S vibrations (see Table 2). Wenote that another two-pole Sellmeier set of equations thatrecently appeared59 is based on the old index data of Boydet al.,9 while the mid-IR poles were not associated withphonon frequencies. Figure 6 displays the principal in-dices of refraction deduced from Eqs. (21)–(23). No indexcrossing (no(l) 5 ne(l)) is found in the blue part of thedispersion data, in contrast with the uniaxial AGS.43

The two optic axes, lying in the X–Z plane, determine thepropagation directions where the index of refraction is in-dependent of the polarization. The angle between thetwo optic axes is 2VZ , where VZ is the angle of each axiswith the polar Z axis. VZ is wavelength dependent andcan be calculated from3

sin VZ 5nZ~nY

2 2 nX2 !1/2

nY~nZ2 2 nX

2 !1/2. (24)

Figure 7 plots VZ as a function of the wavelength, usingEqs. (21)–(23) (solid curve) and using the Sellmeier equa-tions of Ref. 56 (dashed curve). Let us note the differentbehavior for l , 1 mm (absence of a retracing behavior).Note that although the principal indices on which the olddispersion relations are based were measured from theminimum deviation technique in 1973,9 the absorption co-efficient of the prism samples used then was quite differ-ent (much larger than in Fig. 2 up to ; 2.5 mm), whichobviously is the reason for the difference observed in Fig.7. Since VZ . 45°, LIS is a negative biaxial crystal. Atlonger wavelengths it can be regarded as quasiuniaxial,which is a consequence of the two indices nY and nZ beingvery close. Therefore no phase matching can be expectedfor propagation directions in the vicinity of the X princi-pal axis.

The agreement between the experimental phase-matching data used to derive Eqs. (21)–(23) and the cal-culated ones is illustrated in Fig. 8 (solid curves) andTable 4. The accuracy of phase-matching angle predic-tion is 61.5°. The eight last SHG points in Fig. 8 werediscarded from the nonlinear fit for obvious lack of reli-ability. Only a two-pole form leads to the smallest re-sidual discrepancies between calculated and experimen-tal data, while the former one-pole Sellmeier equations56

are unable to predict SHG near the cutoff wavelength of;6 mm. Let us note that there is a discrepancy of ;16°between the experimental phase-matching angles forSHG in the Y–Z plane and the ones calculated with theold Sellmeier equation, which means that the Y–Z bire-fringence given by Eqs. (21)–(23) is more accurate. Theprevious one-pole Sellmeier equations also predict DFGwavelengths ;140 nm longer than experimentally ob-served. Under the usual designation l1 > l2 . l3 , the


Table 4. Phase-Matching Conditions for Type II SHG and DFG in LiInS2

Wavelength (nm)a Phase-Matching Angles (u, w)b

l1 l2 l3 Measured Calculated

SHG(XY: eoe) 2366 2366 1183 (90, 82.1) (90, 83.908)(XY:eoe) 2469 2469 1234.5 (90, 73.1) (90, 72.755)

2527 2527 1263.5 (90, 69.8) (90, 69.235)2583 2583 1291.5 (90, 67.4) (90, 66.507)2900 2900 1450 (90, 57.9) (90, 56.884)3400 3400 1700 (90, 50.7) (90, 50.543)3700 3700 1850 (90, 48.3) (90, 49.392)3900 3900 1950 (90, 49.0) (90, 49.381)4450 4450 2225 (90, 51.6) (90, 51.772)4950 4950 2475 (90, 56.3) (90, 56.543)5350 5350 2675 (90, 62.8) (90, 62.227)5550 5550 2775 (90, 66.0) (90, 65.916)5750 5750 2875 (90, 69.1) (90, 70.508)5900 5900 2950 (90, 71.4) (90, 75.006)

SHG(YZ: eoo) 2542.7 2542.7 1371.35 (35.4, 90) (36.452, 90)

2552.7 2552.7 1276.35 (34.0, 90) (34.684, 90)2570.4 2570.4 1285.2 (31.0, 90) (31.508, 90)2587 2587 1293.5 (28.7, 90) (28.435, 90)2602.3 2602.3 1301.15 (25.9, 90) (25.481, 90)2606.7 2606.7 1303.35 (25.1, 90) (24.592, 90)2631.4 2631.4 1315.7 (19.6, 90) (19.211, 90)

DFG(XY: eoe) 6585.14 872.240 770.220 (90, 42) (90, 42.170)

6623.95 865.801 765.716 (90, 42) (90, 42.145)6719.87 850.443 754.905 (90, 42) (90, 42.076)6762.44 843.761 750.162 (90, 42) (90, 42.046)6832.63 833.187 742.629 (90, 42) (90, 41.992)6899.92 822.391 734.810 (90, 42) (90, 41.967)6989.56 810.827 726.544 (90, 42) (90, 41.863)

a 1/l1 1 1/l2 5 1/l3 with l1 > l2 . l3 .b In degree.

Fig. 6. Principal refractive indices of LiInS2 as computed fromEqs. (21)–(23). The inset plots show the UV and mid-IR por-tions on an expanded scale and also a comparison with a calcu-lation based on the Sellmeier expansions from Ref. 56 (dashedcurves).

DFG angular acceptance (FWHM) measured at fixedwavelengths was Dw 5 0.19° for a crystal length of 10mm, i.e., much smaller than the uncertainty on crystalorientation (60.5°). Hence the uncertainty (61 nm atmaximum) of wavelength measurement in Table 4 cannotexplain the ;40-nm shift observed with the previous Sell-

Fig. 7. Angle VZ between the optic axes and the Z axis in LIScalculated with the Sellmeier expansion of Ref. 56 (dashedcurve), and the new Sellmeier expansion (Eqs. (21)–(23)) (solidcurve).

d31 d32 d33 0 0 0


meier equations, confirming the increased accuracy indispersion provided by Eqs. (21)–(23).

B. Thermo-Optic Dispersion RelationsThe thermo-optic coefficients b j [Eq. (10)] are functions ofboth temperature T (in °C) and wavelength l (in mm). Inanalogy with the index dispersion equations at room tem-perature (see previous subsection), the parametersak(l) (k 5 1,2) in Table 1 are fitted according to the fol-lowing two-pole functional form:

ak~l! 5 C0,k 1C1,k

l2 2 l01,k2

1C2,k

l2 2 l02,k2

. (25)

Table 5 compiles the fitting parameters C0,k , C1,k , C2,k ,l01,k , and l02,k . According to the definition b j5 (1/nj)dnj /dT, the index of refraction at a given tem-perature T will be given by

Fig. 8. Phase-matching angles for type II (eoe or oee) SHG inthe X–Y principal plane (main frame) and type II (oeo or eoo)SHG in the Y–Z plane (inset frame) of LIS. The fundamentalsource for l , 2.65 mm (l . 2.75 mm, respectively) is the idlerwave of a Nd:YAG-pumped nanosecond LiNbO3 parametric oscil-lator (the frequency-doubled radiation from a free-electron laser).The symbols refer to experiments, while the solid curves are cal-culated from Eqs. (21)–(23). The dashed curves are computedfrom the Sellmeier equations of Ref. 56.

n~l, T !

n~l, T0!5 expFa1~l!~T 2 T0! 1 a2~l!

~T 2 T0!2

2 G. 1 1 a1~l!~T 2 T0! 1 a2~l!

~T 2 T0!2

2,

(26)

where T0 5 20 °C and n(l, T0) is given by Eqs. (21)–(23).

These thermo-optic dispersion relations will have to berefined by experimental temperature phase-matchingdata in the future. Relations (25) with the constant val-ues in Table 5 would provide a suitable basis for such arefit procedure. They predict a FWHM temperature ac-ceptance of DTL 5 248 °C•cm (L: crystal length) atroom temperature for the type-II (eoe) SHG at the funda-mental l 5 2.5 mm in the X-Y plane. Hence LIS is ex-pected to be very stable against self-induced thermalphase-mismatch effects. As a counterpart, its tempera-ture tunability is expected to be somewhat limited. Forthe DFG of near-IR sources (l3 5 754.905 nm, l25 850.443 nm, see Table 4), the FWHM temperature ac-ceptance is predicted to be only DTL 5 46 °C•cm.

7. PHASE-MATCHING INVESTIGATIONSA. Effective Nonlinearity and Hobden ClassificationThe phase-matching loci and the effective nonlinearity forLIS is analyzed in the XYZ principal optic axis frame, butthe tensor elements of the nonlinear susceptibility are de-fined traditionally, in accordance with ANSI/IEEE Stan-dard 176-1987,36 in the abc crystallographic frame wherec is the polar twofold axis as in Ref. 9. The chosen con-vention nX , nY , nZ , in order to have the two opticaxes in the X–Z principal plane, affects therefore the ex-pressions for the effective second-order nonlinearity deff .

The general form of the contracted d (2) tensor for theorthorhombic class mm2 reads as

d~2 ! 5 F 0 0 0 0 d15 0

0 0 0 d24 0 0G . (27)

Table 5. Fitting Parameters Describing the Thermal and Wavelength Dispersion of the PrincipalThermo-Optic Coefficients of LISa

ak j C0,k C1,k C2,k l01,k l02,k

(°C21) (°C21•mm2) (°C21

•mm2) (mm) (mm)

X 2.899680 3 1025 0.2033761 3 1025 297.0535 3 1025 0.3475601 14.86755a1 Y 2.478267 3 1025 0.2612463 3 1025 122.3207 3 1025 0.3391212 13.91854

Z 3.315830 3 1025 0.2555208 3 1025 364.9813 3 1025 0.3451539 15.44113

(°C22) (°C22•mm2) (°C22

•mm2) (mm) (mm)

X 1.987083 3 1028 0.1860292 3 1028 250.0777 3 1028 0.3886392 14.25991a2 Y 0.1523235 3 1028 0.2601335 3 1028 2191.8712 3 1028 0.3969192 14.79803

Z 20.6564806 3 1028 0.4291068 3 1028 2343.1015 3 1028 0.3435849 14.94811

a b(l, T) 5 1/ndn/dT 5 a1(l) 1 a2(l)T [Eqs. (10)], where the ak(k 5 1,2) coefficients are fitted according to the expansions in Eq. (25). The j labeldenotes the direction of polarization of light ( j 5 X,Y,Z).


For an arbitrary propagation direction assuming collin-ear interaction and neglecting the spatial walk-off effect,analytical expressions for deff can be derived in our con-ventions from the general formulas presented by Dmit-riev et al.,60

deffssf 5 2d15 sin u cos d ~cos u sin w sin d 2 cos w cos d!

3 ~cos u sin w cos d 1 cos w sin d!

1 2d24 sin u cos d ~cos u cos w cos d 2 sin w sin d!

3 ~cos u cos w sin d 1 sin w cos d!

1 d31 sin u sin d ~cos u sin w cos d 1 cos w sin d!2

1 d32 sin u sin d ~cos u cos w cos d 2 sin w sin d!2

1 d33 sin3 u cos2 d sin d, (28)

defffsf 5 deff

sff

5 2d15@sin u cos d ~cos u sin w sin d 2 cos w cos d!2

1 sin u sin d ~cos u sin w sin d 2 cos w cos d!

3 ~cos u sin w cos d 1 cos w sin d!#

2 d24@sin u cos d ~cos u sin w sin d 1 sin w cos d!2

1 sin u sin d ~cos u cos w cos d 2 sin w sin d!

3 ~cos u cos w sin d 1 sin w cos d!#

2 d31 sin u sin d ~cos u sin w sin d 2 cos w cos d!

3 ~cos u sin w cos d 1 cos w sin d!

2 d32 sin u sin d ~cos u cos w cos d 2 sin w sin d!

3 ~cos u cos w sin d 1 sin w cos d!

2 d33 sin3 u sin2 d cos d (29)

for type I and type II phase matching, respectively, wherethe superscripts ‘‘s’’ and ‘‘f’’ stand for the ‘‘slow’’ and ‘‘fast’’eigenmodes of polarization and their sequence follows theusual convention l1l2l3 with l1 > l2 . l3 . The angled, whose introduction simplifies the expressions andwhich is determined from

tan 2d 5cos u sin 2w

cot2 VZ sin2 u 1 sin2 w 2 cos2 u cos2 w(30)

(0 , 2d , p), defines the polarization directions of theslow and fast waves that are orthogonal to each other. Itis the angle between the polarization direction of the slowwave and the plane of propagation containing the princi-pal Z axis. An approach for the generalization of the deffexpressions in the case of collinear interactions takinginto account the spatial walk-off can be found in Ref. 61.

In the principal planes, the expressions (28) and (29)for deff are reduced to

deffeoe 5 deff

oee 5 2~d24 sin2 w 1 d15 cos2 w! ~X –Y plane!,(31)

deffoeo 5 deff

eoo 5 2d24 sin u ~Y –Z plane!, (32)

deffooe 5 1d31 sin u ~X –Z plane, u , VZ!, (33)

deffoeo 5 deff

eoo 5 2d15 sin u ~X –Z plane, u . VZ!,(34)

with superscripts ‘‘o’’ and ‘‘e’’ denoting the ordinary andextraordinary beams. LIS behaves as an optically nega-tive uniaxial crystal in the X–Y and X–Z (for u , VZ)planes and as an optically positive uniaxial crystal in theY–Z and X–Z (for u . VZ) planes. Assuming the Klein-man symmetry condition to hold, then d15 5 d31 and d245 d32 .

The phase-matching loci for collinear SHG can be cat-egorized using the classification of Hobden.62 Our calcu-lations based on the relatively simple transcendentalequations derived by Yao et al.63 predict that no phase-matched SHG is possible below 1617 nm. LIS entersHobden class 13 at 1617 nm, class 11 at 1783 nm, class 10at 2353 nm, and class 9 at 2675 nm; then it goes back toclass 10 at 5493 nm, to class 11 at 6111 nm, to class 13 at8224 nm, and finally no SHG phase matching is possibleagain above 8710 nm. These transitional fundamentalwavelengths correspond to propagation directions alongthe Y or along the Z principal axes (noncritical phasematching) either for the ssf or the fsf (sff ) polarizationconfigurations.

Figure 9 illustrates the different classes for SHG in LISat several representative fundamental wavelengths. Thesurface of the unit sphere is projected onto the X–Z planeof the crystal. The direction of the wave vectors of theinteracting waves for phase matching as given by their in-terception with the surface of the unit sphere is plotted.

Fig. 9. Stereographic projections of the SHG in the first octantof LIS calculated for wavelengths representative of the Hobdenclasses. Type I (ssf ) interaction (solid curves) and type II( fsf, sff ) interactions (dashed curves). The wavelength anno-tations refer to the fundamental ones.


The stereographic projection of the first octant is pre-sented only, but the loci in the other octants can beobtained by mirror reflections across the principal planes.We do not present plots of the angle d, which can be easilycalculated from Eq. (30). Its dispersive properties (deter-mined by the angle VZ) lead to slightly different values atthe three interacting wavelengths, but normally the effecton the conversion efficiency can be neglected. Qualita-tive arguments relating the spatial walk-off (magnitudeand direction) to the topology depicted in Fig. 9 can befound in Ref. 35. The calculation of the spatial walk-offfor an arbitrary propagation direction is beyond the scopeof this paper but several works provide suitable ap-proaches to this aim.64–67 Analytical approaches for theestimation of acceptance parameters based on the small-signal approximation in the general case of biaxial crys-tals can be found in Refs. 65 and 68. We note here onlythat, since the angle VZ for LIS is not far from 90°, thedispersive properties and in particular the spectral accep-tance are not expected to be substantially modified bypropagation outside the principal planes. Figure 9 indi-cates that double solutions for the angles exist (e.g., forHobden’s class 9), which is equivalent to the existence ofpoints outside the principal planes where ]w/]u 5 0holds. This means that noncritical phase matching inone direction can also occur outside the principal planes(e.g., at w 5 26.7°, u 5 74.35° for ssf-type SHG at 4 mm).

B. SHG in Principal PlanesThe SHG phase-matching directions in the principalplanes are shown in the lower part of Fig. 10. The twofirst panels (X–Y) and (Y–Z) in the bottom part corre-spond respectively to the experimental phase-matchingplots in the main and inset panels of Fig. 8. The transi-tional wavelengths enumerated above can be easily iden-tified there. The SHG ranges where deff Þ 0 are 1783–8224 nm for type I (ooe) phase matching in the X–Zplane, 2353–6111 nm for type II (eoe) phase matching in

Fig. 10. SHG phase matching in the principal planes of LIS.Thick curves in the lower part show fundamental wavelengthsfor which deff Þ 0, and thin curves indicate cases where deff van-ishes. The inverse group velocity mismatch GVM (D31 5 v3

21

2 v121 and D32 5 v3

21 2 v221, where v1 , v2 , v3 denote the group

velocities ]v i /]ki at l1 , l2 , and l3) is shown in the upper partfor the cases where deff Þ 0. The solid (dashed) curves corre-spond to the branch with longer (shorter) wavelengths.

the X–Y plane, and 2353–2675 nm and 5493–6111 nm fortype II (oeo) phase matching in the Y–Z plane. We ob-serve an interesting feature in this crystal: the SHG lim-its with deff Þ 0 are larger for propagation outside theprincipal planes where type I phase matching down to1617 nm and up to 8710 nm is possible. Under the con-vention nX , nY , nZ , the largest birefringence and con-sequently the shortest SHG wavelength is obviouslyachieved for type I interaction and propagation along theY axis. However, in LIS when the Y axis is approachedin the principal planes X–Y or Y–Z deff for type I interac-tion vanishes, and this is true also for the limiting case ofpropagation along the Y axis. This is the reason whypropagation outside the principal planes can be used, e.g.,to shorten the SHG lower wavelength limit (Fig. 9). Asimilar situation is known to exist and has been experi-mentally verified in KTP.69

It is seen from Fig. 10 that in the Y–Z plane, the type IIinteraction is quasi-angle noncritical (but wavelengthcritical; see inset of Fig. 8), which ensures a large accep-tance angle and a small walk-off angle. In contrast, type Iinteraction in the X–Z plane and type II interaction in theX–Y plane have regions of quasi-wavelength-noncriticalphase matching (]F/]l ; 0) centered at 3889 nm and3803 nm, respectively (Fig. 10, see also Fig. 8). LettingF 5 w or u, the walk-off angles in the upper panels ofFig. 11 are calculated using the simplified formulatan ri 5 @ni

e(F)#21]nie/]F valid for uniaxial crystals, where

the subscript i 5 1, 2, 3 is associated with wavelengthl i (l3

21 5 l221 1 l1

21) and nie(F) is the extraordinary in-

dex of refraction of the walking-off wave as given by theuniaxial analogy in the principal planes. We preservedits sign, which is in accordance with the correspondingphase-matching angles, i.e., a positive value of the walk-off means that the Poynting vector is at an angle largerthan the phase-matching angle and vice versa. Note thatthe walk-off is very similar for the two branches of the so-lution for phase matching in all three principal planes.In the X–Y plane, these branches and the two differentwalk-off parameters (we have here two extraordinary

Fig. 11. SHG internal angular acceptance (bottom) and walk-offangles (top) in the principal planes of LIS. Thick solid curvescorrespond to the branches with longer wavelengths from Fig.10, and thick dashed curves correspond to the branches withshorter wavelengths. Only the cases with deff Þ 0 are included.


waves) are almost undistinguishable. The maximumwalk-off amounts to r3 5 11.15° in the X–Z plane forSHG at 3889 nm.

The acceptance angle is evaluated from the phase-velocity mismatch Dk(dF) owing to an angular deviationdF5 F 2 FPM of the wavevectors around the nominalphase-matched direction FPM . A Taylor expansion of Dkleads to

Dk~dF! 5 gCPMdF 1 gNCPM~dF!2 1 ... , (35)

where gCPM 5 @](Dk)/]F#F5FPMvanishes for noncritical

phase matching (NCPM, i.e., for F 5 0, 90°) and gNCPM5 1/2@]2(Dk)/]F2#F5FPM

. The acceptance angle, de-fined as the bandwidth at FWHM of the sinc2(DkL/2)phase-mismatch function, is given by DF5 2.784/ugCPMuL for a critical phase matching (CPM),while for NCPM it is DF 5 u2.784/gNCPMLu1/2. The lowerpanels of Fig. 11 display the acceptance angles (for alength L 5 1 cm) in the three principal planes. The ac-ceptance curves, computed with gCPM only in the expan-sion (35), are interrupted near noncriticality at maximumvalues corresponding to the ones calculated for L5 1 cm using gNCPM only. Although that type of presen-tation in Fig. 11 is not very accurate in these limits, westill prefer it, since it permits the results to be presentedas scalable with respect to the crystal length L (simulta-neous consideration of both derivatives would not allowthis). The experimental comparison of type II SHG ac-ceptance angles in the Y–Z and X–Y planes is shown withsymbols in Fig. 12, for l 5 2590 nm. The solid curvesdepict the plane-wave sinc2(DkL/2) phase-mismatch tun-ing functions computed with the first-order term in Eq.(35), with gCPM(uPM) 5 (p/l)@n2

e r2#uPM5 7.2 3 1023

mm21 (type II (oeo) SHG in the Y–Z plane) andgCPM( wPM) 5 (p/l)@2n3

e r3 2 n1e r1#wPM

5 3.17 3 1022

mm21 (type II (eoe) SHG in the X–Y plane). The perfectmatch of the theoretical curves with the experimental

Fig. 12. Experimental angular tuning curves for type II SHG ofl 5 2590 nm in the X–Y plane (at FPM [ wPM 5 66.2°, blankcircles) and in the Y–Z plane (at FPM [ uPM 5 27.9°, blackcircles). The larger acceptance angle in the Y–Z plane is due tothe much smaller DnY–Z 5 20.007 birefringence as comparedwith DnX–Y 5 20.035 (Fig. 6). The walk-off angles are r1 . r35 12.2 mrad (X–Y) and r2 5 2.8 mrad (Y–Z). The crystallengths are L 5 6 mm (sample LIS(1) used in X–Y) and L5 7 mm (sample LIS(2) used in Y–Z plane); see Subsection 8.A.The fundamental beam (diameter 2v0 ' 2.6 mm) is the idleroutput of a ns Nd:YAG-pumped LiNbO3 OPO.

symbols high-lights both the accuracy of the dispersiondata and the single-domain feature of the samples used.

The chosen presentation of the inverse group-velocitymismatch in the upper part of Fig. 10 is equivalent to thespectral acceptance Dn but contains the sign as additionalinformation. In the simplest cases of type-I SHG or de-generate DFG, we have, e.g., DnL 5 0.886/uD31u and thegain bandwidth in optical parametric amplification as-suming a narrow-band pump wave at l3 is inversely pro-portional to uD21u 5 u1/v2 2 1/v1u. The two parametersD31 and D32 vanish at 3889 nm in the X–Z plane, whichmeans large spectral acceptance for the SHG of shortpulses where the second derivative of the wave-vectormismatch comes into play. The situation is different fortype II interaction in the X–Y plane: here D32 5 2D31 at3803 nm, at 2915 nm D32 vanishes, and at 4946 nm D31vanishes, but in none of these cases does an extremum ofthe spectral acceptance occur, because in type II SHG ofshort pulses all three waves should be considered asbroadband. Thus long crystals can be used to increasethe conversion efficiency for type I SHG in the X–Z planenear 3889 nm even at femtosecond pulse durations. Fortype II SHG of femtosecond pulses near 3803 nm in theX–Y plane, the second harmonic will not be lengthened ei-ther because the temporal walk-off between the two po-larizations of the fundamental wave will limit the inter-action length, but consequently the conversion efficiencywill be low.

C. Sum and Difference-Frequency MixingType I phase-matching in the X–Z plane for non-degenerate three-wave interactions (sum- and difference-frequency mixing as well as optical parametric genera-tion, amplification, and oscillation) is presented in Fig. 13where two branches of the solution can be seen. Thewhole transparency range of LIS can be covered for 0°, u , 40° in the X–Z plane, but deff increases with thephase-matching angle u. Note that deff 5 0 for NCPM(u 5 0°) and that the situation u . VZ (Eq. 34) is neverreached. At larger angles u, we observe a retracing be-havior in the left branch; e.g., in the case of OPO, oneand the same pump wavelength l3 corresponds to two

Fig. 13. Type I (ooe) phase matching for sum- and difference-frequency generation in the X–Z plane of LIS and several valuesof the polar angle: 0°-NCPM (thick solid curves 1), 20° (curves2), 30° (curves 3), 35° (curves 4), 40° (curves 5) and 45° (curve 6).The wavelengths are such that l3

21 5 l221 1 l1

21, with l1 . l2. l3 . The curves are terminated at the left and top side by thetransparency range of the crystal.


pairs (l1 , l2) of signal–idler wavelengths (curve 5). Inthis region the spectral acceptance is very large. Thusfor u 5 40° (left branch of curve 5), l3 5 900 nm, and l25 1150 nm, all three group velocities are very close: atthe point where D31 5 0, we have D32 5 23 fs/mm. Thismeans that this phase-matching configuration is espe-cially suitable for frequency conversion of femtosecondpulses. In optical parametric amplifiers (OPAs) this ad-vantage can be utilized, however, only in combinationwith a control of the spectral bandwidth through the seedsignal. In the regions near the degeneracy points (SHGpoints), we have on the other hand D21 5 0, but the waveat l3 can have in general a different group velocity. Sucha regime is attractive for broadband parametric amplifi-cation in the field of a narrow-band pump pulse as in thecase of chirped pulse optical parametric amplification.70

For femtosecond-laser based frequency metrologyapplications,71 this phase matching, when implementedin a synchronously pumped OPO, would provide a widefrequency comb grid spanning the 10–12-mm region use-ful for high-precision spectroscopy of spherical referencestandard molecules. Increasing the phase-matchingangle (curve 6 for u 5 45° in Fig. 13), the two branchesmerge into a closed contour, and we approach the pointwhere SHG phase matching only for a single wavelengthis possible (see Fig. 10), and all three group velocities areagain very close, but the tunability in that case is verylimited.

The curves for type II phase matching in the X–Y plane(Fig. 14) have a completely different shape. The twobranches of the solution are represented by curves of op-posite curvature that can cross at two points where phasematching for degenerate DFG or SHG occurs. With de-creasing phase-matching angle, these branches separateand a single crossing point is reached (see the curves 3 forw 5 50°), which corresponds to the single SHG solutionin Fig. 10. For yet smaller angles, no crossing occurs,and the degeneracy point is not reached. For all phase-matching curves presented, we observe again a retracingbehavior at longer l3 : for each l3 , two couples (l1 , l2)are phase matched. At the point where these two pairsmerge into one (at the maximum l3 permitting phase

Fig. 14. Type II (eoe and oee) phase matching for sum- anddifference-frequency generation in the X–Y plane of LIS and sev-eral values of the azimuthal angle w: 35° (curves 1), 40° (curves2), 50° (curves 3), 60° (curves 4), and 90° NCPM (thick curves 5).The curves are terminated at the left and top side by the trans-parency range of the crystal.

matching), the waves at l1 and l2 have equal group ve-locities, and similarly to the case discussed for Fig. 13,broadband parametric amplification with a narrow-bandpump wave can be realized. The deviation from thepump group velocity remains, however, essential. Thus,e.g., at w 5 90° and l3 5 3310 nm, D21 . 0 and D31. D32 . 21.65 ps/cm. Improved pump group matchingat this point occurs when decreasing the phase-matchingangle w in accordance with Fig. 10.

Comparing Fig. 14 to Fig. 13, we note that at relativelyshort l3 (e.g., 1064 nm), full tunability with a fixed crys-tal cut is achievable only in the X–Z principal plane. Thegroup velocity mismatch depends on the specific wave-lengths chosen. At l3 5 1064 nm (a case interesting forparametric downconversion), D21(X 2 Z) , D21(X 2 Y)up to l1 5 10 mm. This means that in this practicalwavelength range, type II phase matching in the X–Yplane is more advantageous for the development ofnarrow-band parametric generators or oscillators.

Our analysis of the phase-matching properties of LIS isjust a first-order approximation because it is based on thesmall-signal limit where saturation is neglected. We con-sidered also only collinear interactions. Noncollinear in-teractions recently attracted great interest because in ad-dition to the possibility to improve the tunability, tospatially separate the beams, and to compensate for thespatial walk-off, this can considerably reduce the group-velocity mismatch.72 The latter is very promising forshort-pulse interactions. Explicit expressions for non-collinear phase matching in the principal planes of a bi-axial crystal can be found in Ref. 73 and calculations ofnoncollinear group-velocity matching for arbitrary wavevector directions in Ref. 68.

8. SECOND-ORDER NONLINEARCOEFFICIENTSThere has been only one characterization study of thenonlinear properties of LIS made by Boyd et al. in theearly 1970s.9 The samples used then were of limited sizeand poor quality, and besides, their results were derivedonly from non-phase-matched SHG at 10.6 mm (wedgetechnique). Further, their measurements were per-formed relative to the nonlinearity of GaAs, which wasseveral times corrected during the past years. So it isimportant to confirm or to correct these previous resultsusing phase-matched second-order interactions on ma-ture samples of adequate size.

The elements dij of the nonlinear tensor (27) have beendetermined from the measurement of the SHG efficiencyof various laser sources, using either type I or type II in-teractions in the principal planes of LIS and also out ofthem. Two kinds of measurements have been performed:in one kind (Subsection 8.A), the source is the idler output(in the range 2.4–2.6 mm) of a 12-ns pulse-width, 10-Hzrepetition-rate, type I LiNbO3 OPO.19 Long sampleswere used, and hence the residual absorption and thebeam walk-off effect, as well as the focusing effects, haveto be taken into account to derive the nonlinear coeffi-cients. The second independent series of SHG experi-ments (Subsection 8.B) used femtosecond pulses and verythin oriented samples. This allows neglect of the effect ofabsorption and beam walk-off and focusing effects, the


data analysis in the low-depletion limit being derivedfrom the standard plane-wave SHG theory.

A. Measurements Based on Gaussian Beam SHGTheoryIn order to remain in the low pump depletion limit, thepeak on-axis fundamental intensity used was below 10MW/cm2, and the maximum idler energy of theLiNbO3-OPO was 10 mJ at l 5 2590 nm. The spectrallinewidth of the idler was below 15 GHz, and the trans-verse beam profile resembled a Gaussian. Three thicksamples of different coloration (rose and yellowish) wereused in conjunction with weak focusing, producing aGaussian beam waist of either w0 ; 1 mm or w0; 1.3 mm. Sample LIS(1) was rose annealed, cut at w5 66.5°, u5 90°, for type II (eoe) SHG in the X–Yplane, with dimensions 4 3 4 3 6 mm3 (L 5 6 mm).Sample LIS(2) was yellowish (as-grown), cut at w5 90°, u 5 28°, for type II (oeo) SHG in the Y–Z plane,with dimensions 4 3 4 3 7 mm3 (L 5 7 mm). LIS(1)and LIS(2) were the same samples already used in Sub-section 6.A; see Fig. 8 and also Fig. 12. Sample LIS(3)had an almost identical cut as LIS(1) ( w 5 66°, u5 90°) but was of yellowish tinge and with dimensions4 3 4 3 5 mm3 (L 5 5 mm). We have checked that, asthe linear dispersion data, the nonlinear coefficients donot significantly depend on coloration when the additionalabsorption effect of the yellow samples was taken into ac-count. For typical pump energy Ev 5 1 mJ and w05 1.3 mm, LIS(2) yielded E2v 5 2.5 mJ, while LIS(1)yielded E2v 5 11 mJ and LIS(3), E2v 5 7 mJ. The differ-ence between the efficiencies of LIS(1) and LIS(3) wasmainly due to the much stronger second-harmonic ab-sorption of the latter (a2v 5 0.27 cm21).44 For LIS(1),the residual fundamental and harmonic absorptionamounted to av,2v 5 0.05 2 0.06 cm21, while for LIS(2),av,2v . 0.6 cm21.44

The measurements were performed relative to a dual-band antireflection-coated KTP sample with L5 5.93 mm, cut at w 5 0°, u 5 56.4°, for SHG of l5 2.53 mm in the X–Z plane. The measured nonlinearcoefficient of KTP was d24 5 2.3 6 0.2 pm/V74 and servedas a reference, without having to correct for dispersionsince the measurement wavelength was almost identicalto that used for LIS. We only corrected for the residualabsorption loss (av 5 0.068 cm21 at 2.59 mm) of this KTPsample, owing to OH2 band.74 According to the Gauss-ian beam SHG theory in the nanosecond pulse regime, theeffective nonlinearity in the absence of depletion scalesas75

deff2 5 GSH

tv2

t2v

ce0n2l3

16p2Lh, (36)

where GSH 5 E2v /Ev2 is the pulse energy conversion effi-

ciency (in unit of J21), n is the average index of refractionat fundamental and harmonic wavelengths, and h is thewalk-off-focusing function that accounts for diffraction,absorption and beam walk-off effects. The exact expres-sion of h for type II interaction can be found in Ref. 76.The second-harmonic pulse duration was taken as t2v

. tv /A2. In the nanosecond regime and for the given

crystal lengths, group-velocity mismatch can be safely ne-glected in SHG. The advantage of measuring the LIS co-efficient relative to a reference material stems from thefact that it is necessary neither to evaluate the absoluteenergies nor to take into account the loss owing to the nu-merous filter sets used to isolate the fundamental andsecond-harmonic fields, since from Eq. (36), the ratio ofthe two deff’s scales as

deff2 ~LIS!

deff2 ~KTP!

5GSH(LIS)

GSH(KTP)

n2~LIS!

n2~KTP!

L~KTP!

L~LIS!

h~KTP!

h~LIS!.

(37)

The efficiencies GSH were derived from the linear fit of theplot of E2v versus Ev

2 , for fundamental energies rangingfrom 0 to 5 mJ.44 The results of the data analysis, aver-aged over the two waist values, are the following:

deff@LIS~2 !# 5 1.36~615% !deff~KTP!, (38)

deff@LIS~1 !# 5 3.05~615% !deff~KTP!,(39)

deff@LIS~3 !# 5 3.15~615% !deff~KTP!.(40)

The rather large uncertainties are mainly due to the un-certainty in the absorption coefficients through the evalu-ation of the h focusing functions. Given that deff(KTP)5 d24 sin u (u 5 58.7° at l 5 2590 nm), from Eqs. (38)and (32), one derives d24(LIS) 5 5.73 6 20% pm/V. Thetwo last relations, Eqs. (39) and (40), were averaged toyield, using Eq. (31) and the determined value of d24 ,d15(LIS) 5 7.946 20% pm/V. The ratio of the two non-linear coefficients is hence found to be d24 /d15 5 0.72.

B. Measurements Based on Femtosecond SHGThe SHG experiments with femtosecond pulses were per-formed also in the low depletion limit for the fundamentalin order to avoid complications from saturation effectsand spatial effects across the beam cross section. The co-efficient d31 was estimated by type I SHG in the X–Zplane from Eq. (33), once it was known it was used for thedetermination of d24 from type II SHG in the X–Y planeusing Eq. (31) and assuming Kleinman symmetry to hold(i.e., d15 5 d31). Finally the diagonal element d33 wasmeasured by type I SHG outside the principal planes us-ing Eq. (28) and the already determined off-diagonal com-ponents of the d (2) tensor, again assuming Kleinman sym-metry. Note that a similar strategy was used previouslyto determine d33 of KTP by phase-matched SHG,77 and asoutlined there, the error in the determination of this di-agonal element is normally larger since it accumulatesthe uncertainties of the other coefficients. Alternativelythe plane Y– Z could be used for determination of d24 asdone in the previous subsection; however, the spectraltunability is very narrow in this principal plane (see Fig.10), which is not adequate for measurements with broad-band femtosecond pulses.

All three LIS samples used here were annealed androse in color, had an aperture of 4 3 5 mm2, and were 0.2mm thick. They were cut at w 5 0°, u 5 34° [LIS(4)],w 5 59°, u 5 90° [LIS(5)], and w 5 30°, u 5 44°


[LIS(6)], respectively. The small thickness allows neglectof absorption or scattering losses, the focusing effects, andalso spatial beam walk-off effects. This measurementwas also relative, and we used as a reference sample anAGS crystal with the same dimensions cut at w5 45° andu 5 45° for type I SHG. In order to minimize the errororiginating from the still different group-velocity mis-match, the pulsewidth at the fundamental was chosenrelatively large (160 fs in all cases) since LIS sampleswith thickness less that 0.2 mm could not be preparedwith sufficient quality. This pulsewidth corresponds tospectral bandwidths of 80–90 nm. For d36 of AGS, weused the value of 13.9 pm/V,78 which was measured at asimilar wavelength (l 5 2.53 mm) and actually relativeto d24 of KTP using the same value for the latter as in theprevious subsection. In the plane-wave approximationand having in mind the equal fundamental energy andcrystal thickness, deff of LIS was determined simply from

deff2 ~LIS!

deff2 ~AGS!

5E2v~LIS!

E2v~AGS!

@1 2 R~AGS!#3

@1 2 R~LIS!#3

n3~LIS!

n3~AGS!,

(41)

where n3 is the product of the three refractive indices in-volved, and R takes into account the Fresnel reflections atthe entrance surface (twice for the fundamental) and theexit surface (second harmonic).

The femtosecond source at 1-kHz repetition rate was aKTP-based OPA that was seeded by the frequency-doubled idler of a BBO-based OPA, both OPAs beingpumped by the same 800-nm, 40-fs pump source (Ti:sap-phire regenerative amplifier). The 3-mm KTP used inthe OPA ensured sufficiently long wavelengths that can-not be achieved by b-barium borate (BBO). Seeding bythe frequency-doubled idler of the BBO-OPA was pre-ferred against seeding by the signal wavelength for tworeasons: The signal wavelengths available from theBBO-OPA were not short enough to produce idler wave-lengths above 2.5 mm with the KTP-OPA, and frequencydoubling in a 2-mm-thick BBO crystal of the idler used forseeding resulted in temporal broadening and spectralnarrowing, which was a prerequisite to improve the accu-racy. SHG was performed at 2330 nm with LIS(4), 2850nm with LIS(5), and 2300 nm for LIS(6). In all casesmore than 5 mJ at the fundamental were available so thatit was possible to reliably measure the SHG with a large-area pyroelectric detector even at low conversion effi-ciency. We established that up to a conversion efficiencyof 20% (energy) into the second harmonic, the result didnot change. In the case of LIS(6) the polarization angle dwas adjusted by a He-Ne laser monitoring the polariza-tion rotation by the leakage through an analyzer until aneigenmode was reached. No additional improvement ofthe SHG efficiency could be observed later by furtheralignment of this angle, which was in good agreementwith the calculated value from Eq. (30). Note that thedispersion of the optic axis angle VZ (see Eq. (24) and Fig.7) is relatively small and the deviation between visible(633 nm) and 2300 nm is less than 2°, so that the errororiginating from that effect is estimated to be less than5%. The following results are values of the d (2) tensor

components scaled to l 5 2300 nm by using Miller’s rule,i.e., assuming the same wavelength dispersion for thesecond-order nonlinearity as for the linear susceptibility,

d31~LIS! 5 7.25~65% ! pm/V, (42)

d24~LIS! 5 5.66~610% ! pm/V, (43)

d33~LIS! 5 216~625% ! pm/V. (44)

The uncertainties are related to the group-velocity mis-match and to the relatively large angular acceptance us-ing thin samples. The above results are in very goodagreement with the values obtained in the previous sub-section by a completely different strategy, and we alsoconfirmed the different sign of the diagonal element d33as established by Boyd et al.9 Note that if the resultsfrom Ref. 9 which were obtained by non-phase-matchedSHG, are renormalized using a more recent value ofd14(GaAs) 5 83 pm/V,35 we arrive at d31 5 6.14 pm/V,d32 5 5.31 pm/V, and d33 5 9.8 pm/V. Having in mindthe different wavelength (10.6 mm) used in Ref. 9, we ob-tain a good agreement within 620% with the presentwork for all three nonlinear coefficients.

C. Effective Nonlinearity of LISOnce the nonlinear coefficients are determined, the effec-tive nonlinearity deff can be easily calculated in the prin-cipal planes using Eqs. (31)–(33). The main conclusiondrawn in Ref. 9, namely, that the maximum deff isachieved in the X–Y plane where it is wavelength (angle)independent because of the similar magnitude of d24 andd15 , remains valid with our updated values for the dij’s.However, as already mentioned in Subsection 7.B, inter-esting effects can be expected for propagation outside theprincipal planes. Figure 15 shows the calculateddeff( w, u) for SHG using Eqs. (28) and (29) with the non-linearities obtained in the previous subsection and as-suming for simplicity a constant angle VZ 5 66° betweenthe optic axes and the Z principal axis (see Fig. 7), whichfor the wavelengths selected leads to only negligible er-rors. The fundamental wavelengths indicated in the fig-ure correspond exactly to the phase-matching stereo-

Fig. 15. Effective nonlinearity for type I (ssf, solid curves) andtype II ( fsf, dashed curves) SHG outside the principal planes ofLIS as a function of the azimuthal angle w. The labels indicatethe fundamental wavelengths corresponding to the ( w, u) phase-matching loci of Fig. 9.


graphic projections presented in Fig. 9, where the valuesfor the polar angle u for the limiting cases w 5 0, 90° canbe seen. As can be seen from the figure for type I SHG inthe Hobden classes 9, 10, and 11 (see Subsection 7.A andRef. 62), the improvement in deff when propagating out-side the principal planes is not significant. On the con-trary, for Hobden class 13, it is definitely advantageous touse propagation outside the principal planes for maxi-mum deff in type I SHG. In type II SHG the curves inFig. 15 have a different character and maximum deff isachieved always in the X–Y plane, which is advantageousas compared with type II SHG in the Y–Z plane.

For various applications, it is important to consider thedownconversion into the mid-IR of high-power sources,e.g., lasers emitting at 1064 nm (Fig. 16). For the se-lected wavelengths, the absolute negative extremum ofthe type II curves that occurs in the X–Y plane (right end,with deff

eoe(90°, w) . 26.5 pm/V) is larger than the extre-mum of the type I curves in the X–Z plane (i.e., on the leftside, with 14 , deff

ooe(u, 0°) , 5 pm/V). Hence type II in-teraction in the X–Y plane has larger deff than type I in-teraction in the X–Z plane. However, propagation out-side the principal planes allows reaching of a slightlylarger maximum 27 , deff

ssf(u, w) , 27.5 pm/V for type Iinteraction which can be advantageous since other pa-rameters such as the spectral bandwidth can be better intype I interaction. We believe the potential for future ap-plications of LIS in the mid-IR is related also to the utili-zation of propagation schemes outside the principalplanes.

9. PARAMETRIC DOWNCONVERSIONA. Femtosecond Optical Parametric AmplificationAs outlined in Section 1, LIS possesses the largest band-gap among all known mid-IR nonlinear crystals, which re-sults in an extremely low TPA near 800 nm. This uniquefeature can be utilized for the generation of femtosecondpulses in the mid-IR by downconversion of the most

Fig. 16. Effective nonlinearity for type I (ssf, solid curves) andtype II ( fsf, dashed curves) downconversion of l3 5 1064 nm ra-diation (optical parametric generation, amplification, or oscilla-tion) to three selected idler wavelengths l1 5 4, 7, 10 mm forpropagation outside the principal planes of LIS as a function ofthe azimuthal angle w.

widely used Ti:sapphire femtosecond laser systems oper-ating near 800 nm. In Ref. 21, initial results were pre-sented in the 4.8–9-mm region, but the gain and the out-put energy (2 nJ) were extremely low with a 1.5-mm-thickLIS sample used as a seeded OPA. Here we report animprovement by a factor of ;50 for the output idler en-ergy and an extension of the tunability range.

We applied for this experiment a cube of 5 3 53 5 mm3 of rose annealed LIS cut at w 5 41° and u5 90° for type II interaction in the X–Y plane. Thesingle-stage traveling-wave-type OPA was pumped bylonger pulses in order to increase the interaction length.We used 300-fs pump pulses at 820 nm from a Ti:sapphireregenerative amplifier operating at 1 kHz. The pulselengthening was achieved by adjustment of the pulsecompressor, and the pump pulses were not bandwidthlimited (approximately three times the Fourier limit).About 30 mJ were used to generate a continuum in a2-mm-thick sapphire plate, and five different interferencefilters between 875 and 975 nm were used to select por-tions (of ;10 nm) of the continuum for seeding the OPA atthe signal wavelength (Fig. 17). The seed pulse durationwas measured by sum-frequency cross correlation with asmall fraction of the pump pulses in a 0.5-mm-thick typeI BBO crystal and deconvolution yielded a pulse FWHMof the order of 400 fs (;3 times above the Fourier limit).The OPA was pumped by 150 mJ, and the pump beam pa-rameters corresponded to a peak on-axis pump intensityof 60 GW/cm2.

The mid-IR spectra depicted in Fig. 17 were recordedwith a 0.5-m monochromator (150 grooves/mm grating)and a liquid-N2-cooled HgCdTe detector. Tunability from5 up to almost 12 mm (i.e., the mid-IR cutoff wavelength ofFig. 2) could be demonstrated. From 8 to 12 mm, an al-most constant energy level exceeding 80 nJ could beachieved, despite the stronger absorption. This can beattributed to the lower group-velocity mismatch at longeridler wavelengths21 and also to the increasing seed levelwhere these effects compensate for the reduced transmis-sion. The pulse duration of the idler pulses was esti-

Fig. 17. Idler spectra (the labels indicate FWHM) that demon-strate the achieved tunability with the LIS-based OPA. Theblack circles show the experimentally achieved output idler en-ergy, the blank circles show the achieved (internal) signal gain,and the diamonds show the applied seed (signal) energy.


mated from sum-frequency cross correlation with a820-nm reference pulse in a 0.3-mm-thick type I AGScrystal in which the group mismatch between the two in-put pulses ranged from 715 fs/mm at l1 5 9.5 mm to 800fs/mm at l1 5 6.5 mm. Figure 18 shows the correspond-ing cross-correlation traces. The deconvolved pulse dura-tion at 7.65 and 9.51 mm (585 fs in both cases) corre-sponds to bandwidth-limited Gaussian-shaped idlerpulses (time–bandwidth product equal to 0.44).

Thus, owing to its low intensity-dependent absorptionloss (more than 100 times less than in AGS), LIS is theonly nonlinear crystal that permits the direct frequencyconversion of high peak power short pulses from the800-nm region to the mid-IR above ;5 mm in a singlestep. For such deep mid-IR conversion, LIS allows avoid-ance of the use of cascaded dual-stage OPA/DFG down-conversion setups (the first stage being usually based onoxide materials and the second stage based on AGS,HgGa2S4 , or GaSe). The results in this section were ob-tained with amplified pump pulses at low (1 kHz) repeti-tion rates. Similar single-stage downconversion of high-repetition-rate (100 MHz) Ti:sapphire femtosecondoscillators should be possible in synchronously pumpedLIS-based OPOs. A further potential application of LISin femtosecond technology that relies on the extremelylow TPA near 800 nm21 is related to the generation ofsingle (or sub-) cycle femtosecond pulses (both at low andhigh repetition rates) in the mid-IR by DFG of spectralcomponents belonging to the same broadband spectrum ofan ultrashort 800-nm pulse.79 If 15-fs-long bandwidth-limited pulses centered at 800 nm are used for this pur-pose, the generated mid-IR wavelength is ;10 mm, atwhich wavelength a 30 fs long pulse would possess onlyone optical cycle. The basic limitation in the conversionefficiency when using GaSe as previously demonstratedfor this purpose79 was its strong TPA at 800 nm.

B. Continuous-Wave Mid-IR DFGWe report in this subsection the first DFG experiments(5.5 , l1 , 11.3 mm) ever performed with LIS, whosepartial results were already used to derive the accurateSellmeier equations of Subsection 6.A. Continuous-wave

Fig. 18. Cross-correlation traces at two idler wavelengths ob-tained by sum-frequency mixing with a 820-nm, 300-fs referencepulse. The deconvolved Gaussian pulse durations (FWHM) arein both cases 575 fs.

(cw) DFG is most suited for high-resolution spectroscopyin the mid-IR range: When both DFG laser sources havelinewidths , 1 MHz, the mid-IR radiation at l1 allowsperformance of sub-Doppler spectroscopy of heavy atmo-spheric molecules with only ;1 mW of power. Until now,cw DFG of two near-IR lasers for the generation of deepmid-IR light used either AGS80–82 or GaSe.83 We demon-strate that LIS is an alternative promising candidate,since we report cw parametric generation up to 11.3 mmwith an uncoated yellowish LIS sample of dimensions 53 5 3 10 mm3 (L 5 10 mm), cut in the X–Y plane fortype II (eoe) DFG at u 5 90°, w 5 42°.

Two tunable cw single-frequency Ti:sapphire laserswere used as difference-frequency mixing sources. Thelaser beams, orthogonally polarized, were collinearly fo-cused onto the crystal with a 35-cm focal-length lens,yielding a nearly optimal w0 5 55 mm waist for bothpump wavelengths l3 , l2 . The pump wavelengthswere blocked after the sample by a 1-mm-thick uncoatedgermanium (Ge) filter, and the mid-IR radiation was de-tected by a calibrated liquid-N2-cooled HgCdTe photocon-ductive detector with a 1 3 1 mm2 active area. The de-tected voltage was amplified by a low-noise preamplifierand fed to a lock-in amplifier.

In Table 4, we have already seen that at fixed w5 42°, wavelength tuning alone can cover only the 6.6–7-mm range, limited by the tunability range of the Ti:sap-phire lasers (from curves 2 and 3 of Fig. 14, a tunabilityrange extending into the blue would be required to extendthe DFG to ;10 mm). Taking profit of angle tuning,mid-IR radiation was generated with broad wavelengthtunability in the 5.5–11.3 mm spectral region with com-bined pump laser wavelength (l3) and crystal angle ( w)tuning81: In Fig. 19, one Ti:sapphire laser was fixed atl2 ; 836 nm, and the other (l3) was tuned from 724 to778 nm. The solid curves are calculated phase-matchingcurves from Eqs. (21)–(23), highlighting the accuracy ofthe Sellmeier equations that were fitted using the fixed-angle DFG data of Table 4.

Figure 20 displays the mid-IR spectral tuning band-width around 1510 cm21 (l1 ; 6.6 mm), when l2 is set at865.3 nm and l3 is tuned around 765 nm, correspondingto a quasi-normal incidence phase matching. A Dn1; 10 cm21 ( n 5 1/l [ n/c) FWHM spectral bandwidth is

Fig. 19. Wavelength and angle tuning characteristics of type II(eoe) DFG of two cw Ti:sapphire lasers in LIS. The solid curvesare calculated from the Sellmeier equations of Subsection 6.A.


obtained, within which sharp atmospheric water-vaporabsorption lines can be observed. The FWHM plane-wave spectral acceptance for this pump tuning mode ex-presses as3

Dn1 5 1.722p

L F ]Dk

]n1G

n1PM

21

, (45)

where ]Dk/]n1 can be expanded, taking the constraintn3 2 n2 5 n1 into account, as

]Dk

]n15

2p

c Fn3~ w! 2 l3

]n3~ w!

]l32 n1~ w! 1 l1

]n1~ w!

]l1G

[ 2pD31 . (46)

In Eq. (46), the angle-dependent indices are the extraor-dinary indices in the X–Y plane. From Eqs. (45) and(46), the calculated spectral acceptance is Dn15 214 GHz (Dn1 . 7.2 cm21), corresponding to a pumptuning over Dl3 5 0.42 nm. The bandwidth broadeningobserved in Fig. 20 is attributed to the focused beameffect.84

Let us note that despite the strong mid-IR absorptionat 11.3 mm (Fig. 2), we could still detect ;3-nW mid-IRpower for input powers P3 5 200 mW and P25 265 mW. This power is generated by the last exit lay-ers of material. For the same incident powers, the de-tected power at l1 5 7 mm was P1 5 33.5 nW. The netconversion efficiency at this wavelength, corrected for allFresnel optical loss, amounted to G 5 P1 /P3P2. 1.6 mW/W2. Using the general focused-beam theoryfor DFG84 that evaluates the focusing function h for typeII DFG for the given focusing parameters, walk-off value(ur1,3u 5 0.97°) and absorption loss (a3 ; 0.15 cm21, a2; 0.1 cm21, a1 ; 0.05 cm21), we derive an effective non-linear coefficient deff(7 mm) . 5.3 pm/V. This value isslightly lower than the calculated value using Eq. (31)and the determined values of d24 and d15 (Eqs. (43) and(42)), deff . 6.55 pm/V. The difference may arise fromthe residual atmospheric water absorption lines in thisregion.

Fig. 20. Mid-IR DFG spectral tuning curve in pump tuningmode around l3 . 765 nm. The other wavelength was fixed atl2 5 865.3 nm. In this frequency scan, we could observe atmo-spheric water-vapor absorption lines in laboratory ambient airover a 42.5-cm open path between the LIS crystal and theHgCdTe detector.

10. LASER-INDUCED DAMAGE IN LiInS2

Illumination with various laser sources resulted in thefollowing photoinduced phenomena observed in LIS,whose magnitude depends on wavelength and pulse dura-tion: (i) microcracking (at l 5 5 mm using femtosecondpulses from a free-electron laser20); (ii) dendrite structureformation (at l 5 1.079 mm using nanosecond pulses);and (iii) photo-induced absorption (PIA) as gray tracks (atl 5 0.8 mm using femtosecond pulses). Optical damageof (i) and (ii) kinds is irreversible, while PIA damage is toa certain extent reversible. It disappears at lower levelsspontaneously after several hours of storage at room tem-perature or several minutes of illumation with l. 500 nm. The PIA was detected first in femtosecondOPA experiments with a 1.5-mm-thick LIS samplepumped by a 1-kHz Ti:sapphire regenerative amplifier de-livering pulses at 800 nm with a duration of 200 fs andenergy of 200 mJ.21 No surface damage was observed inthese experiments up to a peak on-axis intensity of 140GW/cm2. In principle, as with other materials, opticaldamage in the femtosecond regime is expected to occur in-directly as a result of filamentation and self-focusingthrough higher-order nonlinear effects. These studiespermitted estimation of only an upper limit on the non-linear absorption losses at 800 nm, which were indepen-dent of polarization and presumably caused by inclusions.They could not be fitted by a TPA process, and the esti-mated upper limit of TPA is bTPA ; 0.04 cm/GW at 800nm.21 This is ;100 times lower than the bTPA5 3.5–5.6 cm/GW (depending on the polarization) fittedfor a 0.3-mm-thick AGS crystal under identical condi-tions, which is a manifestation of the advantages of LISrelated to its larger bandgap. An updated value for theupper TPA limit that we derived for a different sample,namely, the LIS crystal used in Subsection 9.A, is onlyslightly higher: bTPA 5 0.05 cm/GW. Note that recentTPA measurements on KNbO3 (which belongs to the sameclass mm2) at 846 nm using a 5-mm-thick sample phasematched for cw blue-light generation yielded a TPA mag-nitude (bTPA 5 3.2 cm/GW) of the same order as that forAGS.85 In the experiment of Ref. 21, the gray tracks for-mation (leading to PIA) was attributed to non-phase-matched SHG and residual blue light absorption, i.e., thisdamage mechanism was only indirectly related to thehigh intensity of the femtosecond pulses that resulted inhigher probability for unwanted SHG. Subsequently dif-ferential absorption (before and after illumination) wasmeasured that had a magnitude reaching several cm21

and extended from 400 nm up to the near-IR (1–2 mm).86

Well pronounced maxima of this absorption were ob-served at 430 nm and 650 nm. This photochromic in-duced absorption is similar to the so-called blue-inducedinfrared absorption observed in SHG experiments withKNbO3 , for which an increased near-IR absorption coeffi-cient (0.011 to 0.056 cm21, depending on the sample andcorresponding to 2.5 to 9 times the usual linear absorp-tion) at the fundamental wavelength of 860 nm was de-tected with 100 mW of blue SH power (30 kW/cm2) gener-ated with a Ti:sapphire laser.87 The blue-inducedinfrared absorption damage was also reported to be re-versible, after a few hours of relaxation at room tempera-


ture, and could be minimized by heating the crystal orpumping at longer wavelengths.88

In order to understand the origin of the PIA in LIS, weproceeded with a direct illumination of LIS samples at300 , l , 450 nm using a 1-kW Xe lamp filtered througha monochromator for ;10 minutes: The same colorationeffect was indeed obtained, with a maximum effect at 360nm excitation and vanishing at wavelengths shorter than300 nm. Thus the PIA observed in the OPA experimentsis really caused by linear absorption of non-phase-matched blue SHG by point defects present in the lattice.In line with the photoinduced signal in absorption spectra(see Fig. 3 in Ref. 86), a complicated system of lines ap-pears in the electron spin resonance spectrum. Analysisof the angular dependence allowed us to reveal the super-position of two spectra related to different paramagneticdefects. One of them has a spin S 5 1/2 and an aniso-tropic g factor with the following principal values of the gtensor: g1 5 2.160, g2 5 2.023, and g3 5 2.023. Thisspectrum is associated with a center of axial symmetrywith g1 , is directed along the In–S bond, and is related tosulfur S2 ion in a regular site. The second spectrumcomprising a broad line at H ; 3300 Gauss ( g5 2.0024) is associated with Li0.

The interpretation of these results is the following. Atshort-wavelength excitation (l , 450 nm), the followingrecharge process occurs in LIS:

S22 1 Li1 → S2 1 Li0. (47)

Such excitation produces free charge carriers that arecaptured in some deep traps and can be released at l. 500 nm illumination. We established that the graytrack formation is maximized for excitation near 360 nmbut dropped by one order of magnitude at 420 nm, whichmeans that in OPO/OPA experiments it can be reduced byusing slightly longer pump wavelength l3 . Note thatthe same process also takes place at x-ray irradiation,which is used for crystal orientation when fabricating op-tical elements: Some darkening occurs sometimes in thebulk sample during this operation. The PIA magnitudewas found to be dependent on the LIS composition89:The effect is minimal in the case of nearly stoichiometric

Fig. 21. Measured pulse energy with crystal inserted (squares)and without it (diamonds). The drop in transmitted energy (lastsquare) indicates damage formation. Inset: Damage thresh-old, expressed as fluence, versus beam radius at the crystal sur-face.

composition. The PIA was also found to be much morepronounced in LIS than in LISe.

Systematic optical damage-threshold measurementswere performed with Nd:YAG lasers at 1064 nm—i.e.,well within the clear transmission range and far from theTPA region. Initial measurements with a 6-W cw focusedNd:YAG laser beam failed to produce measurable dam-age, and subsequent measurements were performed witha pulsed laser. The pulse energy was varied between 6mJ and 25 mJ at a repetition rate of 10 Hz and a pulsewidth of ;10 ns. The collimated Gaussian beam with abeam radius of win 5 1.47 mm was focused with a 200-mm focal-length lens to produce a beam waist with a ra-dius of w0 5 46 mm. The crystal used was a rose samplewith dimensions 4 3 5 3 5 mm3 (u 5 90°, w 5 24°).The corresponding fluences ranged from 0.19 J/cm2 to 752J/cm2, and by using different pulse energies, the same flu-ence could be sustained over a range of spot radii. TheGaussian character of the beam was verified, and thebeam radius was measured by the knife-edge technique.The onset of radiation damage was determined from theobserved sudden drop in the transmitted signal as shownin Fig. 21. At each experimental point, the crystal wasinspected visually in a low-power microscope, and thedrop in transmission was found to correlate with the on-set of visible damage at the surface. By performing ex-periments with different pulse energies, it was found thatthe damage threshold, expressed in J/cm2, tends to de-crease with increasing spot size, as seen in the inset fig-ure of Fig. 21. Although the amount of data is too limitedto warrant a detailed analysis, it suggests a leveling off at;1 J/cm2 at large spot sizes (i.e., a peak intensity thresh-old of 100 MW/cm2), and this value agrees well with thevalue 1.1 J/cm2 reported by Knippels et al. at a wave-length of 5 mm.20 The observed dependence in the insetfigure is understandable in view of the fact that as thespot size increases, it becomes increasingly difficult forheat generated at the center to diffuse to the unexposedregions of the crystal. In Fig. 21, the initial increase oftransmitted energy reflects the fact that the center of thebeam is too close to the edge to allow the entire beam tobe intercepted by the crystal when the beam radius islargest. In some cases, damage was found to extend intothe interior of the crystal.

These damage properties should be discussed in com-parison with available damage data on AGS or AGSe.For AGS under cw pumping, the onset of thermal lensinghas been previously evaluated at ;11 kW/cm2 from a cwAGS doubly resonant OPO containing ;3 W of circulatingpower at 1.26 and 2.52 mm focused to a waist of w05 90 mm.6,7 The cw damage-threshold value is actuallyunknown but is estimated to occur in the range ;20–40kW/cm2,90 despite a report that 3.5 W of cw Nd:YAG ra-diation focused to a waist of 20 mm (280 kW/cm2) did notdamage an AGS sample.91 For AGSe, the measureddamage threshold at 9 mm (cw CO2 laser) was ascertainedto be 5–22 kW/cm2,92 corroborating that chalcopyrites dis-play extremely low cw damage threshold. The fact that,for 6 W at 1064 nm, focused down to w0 5 40 mm, no vis-ible damage was observed in the LIS sample sets the cwdamage threshold to a lower limit of .120 kW/cm2. The5 times larger thermal conductivity of LIS as compared


Table 6. Summary of the Main Physical Properties of LiInS2

CRYSTALLOGRAPHIC DATAStructure Wurtzite-type (b-NaFeO2 structure)Symmetry, point group Orthorhombic, mm2 (negative biaxial)Space group Pna21

Lattice parameters (Å) a 5 6.874; b 5 8.033; c 5 6.462 (Ref. 18)Principal axes assignment (X, Y, Z) ↔ (b, a, c)Density (g/cm3) 3.46Microhardness (Pa) 145 3 107 (Refs. 26, 27)OPTICAL PROPERTIESOptical transmission (mm) 0.34–11.5Bandgap energy (T 5 300 K) (eV) 3.55 (Eic); 3.61 (Eib); 3.58(Eia) (Ref. 18)Indices of refraction at T 5 20°:

l 5 0.532 mm nX 5 2.2413; nY 5 2.2824; nZ 5 2.2991l 5 1.064 mm nX 5 2.1288; nY 5 2.1645; nZ 5 2.1734l 5 10.6 mm nX 5 2.0200; nY 5 2.0566; nZ 5 2.0595

Optical axis angles (0.35 mm , l , 11.5 mm) 55° , VZ , 80°Birefringence walk-off at 1064 nm (mrad) rX-Y 5 14.7; rX-Z 5 20SHG fundamental wavelength range (nm) 1617–8710Thermo-optic coefficients (1025/°C)at 1064 nm, T 5 20 °C

dnX /dT 5 3.72; dnY /dT 5 4.55; dnZ /dT 5 4.47

Absorption coefficient at 1.064 mm (cm21) a < 0.04Laser damage threshold:

surface, at 10 ns, f 5 10 Hz, l 5 1.064 mm 1 J/cm2

bulk, at 500 fs, f 5 25 MHz, l 5 1.064 mm .6 GW/cm2 (Ref. 20)surface, at 200 fs, f 5 1 kHz, l 5 0.8 mm .140 GW/cm2 (Ref. 21)

Two-photon absorption at 0.8 mm (cm/GW) bTPA < 0.05Nonlinear optical coefficients (pm/V)

by cw SHG at 2.5 mm d15 5 7.9(61.6); d24 5 5.7(61.2)by femtosecond SHG at 2.3 mm d31 5 7.2(60.4); d24 5 5.7(60.6); d33 5 216(64)

THERMAL PROPERTIESMelting point (°C) Tmelt ; 1000Thermal expansion at T 5 20 °C (1025/°C) aX 5 11.64; aY 5 10.91; aZ 5 10.68Specific heat at T 5 300 K (J/mol/K) Cp 5 92.9Thermal conductivity at T 5 300 K (W/m/°C) KX 5 6.2; KY 5 6.0; KZ 5 7.6 (Ref. 50)ELECTRICAL PROPERTIESPyroelectric coefficient at T 5 300 K (mC/m2 K) 6 (Ref. 55)Pure electro-optic coefficients (pm/V) r13 5 1.0; r23 5 0.4; r33 5 21.3Piezoelectric coefficients (pm/V) d31 5 25.6; d32 5 22.7; d33 5 17.5Electric conductivity (V21 cm21) sZ 5 4.3 3 10210 (Ref. 98); s 5 1 3 10212 (Refs. 22, 27)

with AGS certainly favors the use of LIS in intracavity cwapplications. Under a similar nanosecond pulsed regime,however, the ;1 J/cm2 damage threshold measured withLIS is comparable to the threshold found for AGS orAGSe.93,94 Independent measurements at longer wave-lengths (9.55 mm) with 30-ns-long pulses yielded, underidentical experimental conditions, damage thresholds of6.5 J/cm2 for LIS57 and 5.5 J/cm2 and 4.2 J/cm2 for AGSand AGSe, respectively.95

From these preliminary damage-threshold investiga-tions, it is premature to assess whether the damagemechanisms are due to native point defects or are intrin-sic to the compound. Considering the current state of theart of residual absorption on this compound, one may ex-pect that with an improvement in residual transparencyand a better control of the growth parameters toward theproduction of stoichiometric material, the above damage-threshold values can be improved.

11. CONCLUSIONSWe have characterized the main physical properties of thenewly emerging lithium thioindate chalcogenide semicon-ductor that are relevant for nonlinear applications fromthe visible up to the deep mid-IR. Table 6 summarizesthese properties, as well as those determined in previousworks. LiInS2 or LIS can now be considered as a maturecompound, and its future widespread use in nonlinear de-vices should refine all the data collected from this inves-tigation campaign. Among its most relevant advantagesover the existing mid-IR crystals, one may quote its excel-lent thermal stability and high damage threshold suitablefor high-power laser applications and its extremely ex-tended phase-matching capabilities (over its whole trans-parency range) using either type I or type II interactionsin or out of principal planes. Such an extended phase-matching capability is still compatible with low birefrin-gence walk-off angles. LIS is the only existing material


for direct downconversion from the near-IR to the deepmid-IR up to 12 mm, owing to its highest bandgap energy.Its effective nonlinearity of ;7 pm/V (slightly lower thanthat of the chalcopyrite crystals) is substantially higherthan that of the oxides of the KTP family and is almostconstant for type II interaction in the azimuthal principalplane. We have shown that LIS should be very promis-ing for the frequency downconversion of femtosecond la-ser sources. At equivalent loss level, LIS would be lesssubject to thermal lensing than AGS,6,7 permitting its usein cw OPOs for deep mid-IR generation.

The next challenge and effort will be directed to the de-tailed studies on its eventual ferroelectric properties. Incontrast with the chalcopyrites, LIS and LISe are pyro-electric as the orthorhombic symmetry oxides (KTP iso-types) belonging to the same mm2 point group. Thespontaneous polarization occurs because, in each bipyra-mid formed by two adjacent tetrapores (Fig. 1), only one isoccupied by a Li1 cation. The other one is empty, whichcorresponds to a negative effective charge. An intriguingissue, which still has not received a definite answer, iswhether such Li chalcogenides can be related to ferroelec-tric materials, i.e., if it is possible to invert their sponta-neous polarization along the polar c axis. In their shortnote,52 Negran et al. concluded that LIS and LISe do notdisplay a para-to-ferroelectric phase transition from theabsence of a sudden anomalous rise in the record of thepyroelectric current versus temperature. This is not sur-prising because of the screening effect of the high ionicconductivity of Li. They measured a pyroelectric coeffi-cient ps(300 K) 5 2.6 3 10210C/(cm2

• K). A more re-cent and reliable measurement of the pyroelectric coeffi-cient performed with our rose samples yielded a 2.3 timeshigher value (Table 6), which is 5 times smaller than thevalue for KTP.96 In contrast with Negran et al.’s report,a strong increase of the pyrocurrent slightly above roomtemperature, preceded by a sharp current spike, was no-ticed, but this increase was attributed to space charge re-laxation of the thermally activated Li1 cations.55

The issue about whether Li chalcogenides are (or arenot) related to ferroelectrics is of upmost importance, con-sidering their deep mid-IR transparency, which would al-low fabrication of quasi-phase-matched periodically poledstructures for wavelengths longer than ;4–5 mm, whichis the current limitation of oxide-based ferroelectrics suchas LiNbO3 or KTiOPO3 . The measurement of the Curietemperature (a temperature at which the material tendsto loose its spontaneous polarization), the study of its di-electric conductivity versus an applied ac electric field inorder to reveal a dielectric hysteresis loop (and the valueof the coercive field) have to be performed to answer to thequestion.

Finally, we started to investigate other Li-containingcompounds such as LiInSe2 (LISe), LiGaS2 (LGS),LiGaSe2 (LGSe), and LiGaTe2 (LGTe).25,97

ACKNOWLEDGMENTSThis Concerted Action could not have been possible with-out the grant awarded by the European Commission(DG12-MZCN directorate), in the frame of its Interna-

tional Cooperation program of the 4th Framework Pro-gram (INCO-Copernicus contract IC15-CT98-0814). Theauthors are highly grateful to J. F. Bardeau (Laboratoirede Physique de l’Etat Condense, Le Mans, France) and toP. Simon and his collaborators (Centre de Recherche surles Materiaux a Haute Temperature, Orleans, France) fortheir expert collaboration in the Raman and IR studies.We also acknowledge V. Drebushchak (Novosibirsk StateUniversity, Russia) for the measurement of the specificheat, V. Nadolinny (Institute of Inorganic Chemistry, Si-berian Branch, Russian Academy of Sciences, Novosi-birsk, Russia) for the Electron Spin Resonance resultsand J. M. Weulersse, M. Gilbert, and G. Mennerat (Com-missariat a l’Energie Atomique, Saclay, France) for theuse of their nanosecond LiNbO3-based OPO.

*Electronic address: [email protected].†Present address: Department of Molecular Science

and Technology, Ajou University, 5 Wonchun-dong,Paldal-gu, 442-749 Suwon, Korea.

‡Also at the Laser Research Center, Quantum Electron-ics Department, Vilnius University, LT-2040 Vilnius,Lithuania.

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Optical, vibrational, thermal, electrical, damage, and phase-matching properties of lithium thioindate