Linear to radial polarization conversion in the THz domain using a passive system

Linear to radial polarization conversionin the THz domain using a passive

system

T. Grosjean1, F. Baida1, R. Adam2, J-P. Guillet2, L. Billot 1, P. Nouvel2,J. Torres2, A. Penarier2, D. Charraut1, L. Chusseau21Institut FEMTO-ST, Université de Franche-Comté, UMR 6174 CNRS,

Département d’Optique P.M. Duffieux,16 route de Gray, 25030 Besançon cedex, France.

2Institut d’Électronique du Sud, Université Montpellier 2, UMR 5214 CNRS,Place E. Bataillon, 34095 Montpellier, France.

[email protected]

Abstract: This paper addresses a passive system capable of converting alinearly polarized THz beam into a radially polarized one. This is obtainedby extending to THz frequencies and waveguides an already proven conceptbased on mode selection in optical fibers. The approach is validatedat 0.1 THz owing to the realization of a prototype involving a circularwaveguide and two tapers that exhibits a radially polarized beam at itsoutput. By a simple homothetic size reduction, the system can be easilyadapted to higher THz frequencies.

© 2008 Optical Society of America

OCIS codes: (220.4830) Systems design; (230.5440) Polarization-selective devices;(230.7370) Waveguides; (260.5430) Polarization

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1. Introduction

For twenty years, considerable improvements have been brought to THz systems and the fieldhas seen an astonishing development of its experimental tools in the inspection of materialsand the spectroscopy of chemical species [1] and biological samples [2]. As experienced in theoptical domain, the generation and use of radially polarized beams should have a significantimpact in the evolution of research in the THz domain, especially in near-field microscopy (andderived techniques) and THz plasmonics.

At optical frequencies, these highly symmetric fields have brought an important added valuein high numerical aperture focusing and conventional microscopy [3-7], single molecule prob-ing [8], near-field optical microscopy and spectroscopy [9, 10], laser cutting [11], particle trap-ping and accelerating [12, 13], high-power laser emission “stability” [14, 15]. All these studiestake benefit from the total field symmetry provided by radial polarization. Such a property canlead, for example, to focused fields with either a strong longitudinal component [3, 4, 16] or ap-polarization state with symmetry of revolution.

So far, only a very limited number of systems allows the generation of radially polarizedTHz beams. Most of them are based on the excitation of the mode sustained by metallic wireswhose electric field distribution is radially distributed around the wire [17-19]. The use of pho-toconductive antennas with radial symmetry seems to solve the problem of coupling efficiencybetween THz radiation and the wire mode [18]. However, the radiation efficiency of the wiremode in free space is questionable. Recently, it has been shown that optical rectification givesan alternative solution for the generation of THz radially polarized pulses [20]. However, bothsystems require the design of a proper active THz source.

In this paper, we propose a new concept ofpassiveradial polarizer at THz frequencies. Sucha system is aimed at working with continuous waves and it is specially designed for radiating infree space a radially polarized doughnut mode. It has the advantage to be adaptable to any kindof existing THz sources. In a first section, the principle of the proposed THz radial polarizer isdescribed. Then, the concept is validated with a first prototype.


2. Principle of the passive THz radial polarizer

2.1. From Optics to terahertz

The wide development of the terahertz techniques is partly due to the successful transposition ofsome optical concepts to the THz domain. For example, the extension to THz frequencies of thewell-known near-field optical microscopy has opened new perspectives in the local observationof physical and biological materials with submicrometer resolution [21-27]. We suggest herethat the generation of THz radially polarized beams can also get benefits from the know-howof the optics community.

The various techniques proposed for more than 15 years for generating radially polarizedlight can be divided into active and passive systems. Active systems are generally conventionallasers whose cavity has been modified for radiating a radially polarized mode. These modifi-cations consist of inserting optical components such as axicons [28-30], phase-step elements[31], birefringent crystals [32, 33] or diffractive elements [34, 35] into the cavity in order to se-lect the desired mode. Despite good results in terms of polarization purities and/or efficiencies,these solutions do not appear to be well-adapted to the current THz sources. Passive systemsare designed for converting linearly or circularly polarized laser beams into doughnut beamsthat are radially polarized. They are set outside the laser cavity and do not produce by them-selves THz waves. Among the passive systems developed so far, one can find Mach-Zehnderinterferometers which combine the orthogonal TEM01 and TEM10 modes [36-38], computergenerated holograms [39], liquid crystal polarization converters [40-42], spiral phase system[43] and the mode selection inside few-mode optical fibers [44-46]. All these concepts seem tobe easier to extend to the THz domain as they are not limited to a specific radiation source. Thechallenge is here to extend to THz frequencies the components specifically developed for theoptical range.

2.2. Modes sustained by circular metallic waveguides

It turns out that the optical fibers used in Refs. [44-46] can find in metallic circular waveguides astraightforward counterpart for the generation of radial polarization in the THz domain. Figure1 displays the classification of the allowed propagating modes of a perfectly conducting metalliccylindrical waveguide with respect to its cutoff diameter.

TE11

0.59 0.77 0.97 1.22 1.34

TM01 TE21

TE01

TM11

Fundamental

mode TE31 Modes

Cutoff

diameter

(* )lWaveguidediameter

Fig. 1. Classification of the first modes carried by a hollow circular waveguide of perfectmetal (λ is the wavelength).

Following in wavelength, scale after the linearly polarized fundamental TE11 mode, are theradially polarized TM01 and the hybrid polarized TE′21 and TE′′21 modes. Figure 2 shows theintensity distribution and electric field orientation of these first modes into a 7λ wide circularmetallic waveguide (λ is the wavelength). The primes on the TE21 mode indicate that oneis rotated by 45° with respect to the other. The twofold degeneracy of the TE21 mode is aconsequence of cylindrical symmetry.


TE11

TM0 1

TE'2 1

TE''2 1

Fig. 2. Intensity distribution and electric field orientation (pointed out by arrows) of theTE11, TM01 and TE21 modes sustained by a 7λ wide metallic circular waveguide.

2.3. Coupling efficiency between the waveguide modes and an incoming Gaussian beam

The generation of radially polarized beams with metallic cylindrical waveguides requires first,the selective excitation of the TM01 mode and second, the efficient emission of this mode infree space. Since the concept of radial polarizer has to be independent of the configurationsof THz continuous-wave sources and wavelength, it is assumed in the following that the in-coming beam is a linearly polarized Gaussian beam whose beam-waistW is about 10λ . Suchfield confinements can be obviously achieved for example with parabolic mirrors. We also as-sume that the waveguides are made with infinitely conducting perfect metal. Perfect metal is agood approximation of the real metals of interest over the THz spectral range. For example, inthe case of aluminum, Drude model leads to complex permittivity comprised between valuesaround−3.62104 + 7.32106i at 0.1 THz and−1.62104 + 5.85104i at 10 THz. In this portionof the spectrum, the skin depth does not exceedλ/1230. Therefore, the penetration of the THzradiation into the metal is weak enough so that the transmission loss of the guided modes canbe neglected over the distance of propagation of a few tens wavelengths considered here. Let usnote that this approximation is also valid for other metals as iron, gold and silver which exhibitskin depths smaller than the ones of aluminum in the THz domain [47-49].

Generally, the energy transfer from the incident beam and the various waveguide modes isinvestigated by means of the coupling coefficientsCm defined as

Cm =Pm

Pi, (1)

wherePm andPi are the powers carried by the modes and the input beam, respectively. Whenthe incoming beams and the waveguides are much larger than the wavelength, the longitudinalcomponents of the various fields are negligible. In that case, the powersPm andPi can be seenas the Poynting vector flow through the waveguide cross section

Pi =12

ℜ∫∫

r dr dθ(Ei ×H∗i ) ·ez, (2)

Pm =12

ℜ∫∫

r dr dθ(amEm×b∗mH∗m) ·ez. (3)

Unit vectorez defines the direction of the waveguide axis. Constantsam andbm are the com-ponents of respectively the input electric and magnetic field distributions onto them–mode.Their expressions are based on the overlap integrals between the incoming and the mode field


distributions

am =∫∫

r dr dθ(Ei ×H∗m) ·ez∫∫

r dr dθ(Em×H∗m) ·ez

, (4)

bm =∫∫

r dr dθ(E∗m×H i) ·ez∫∫r dr dθ(E∗m×Hm) ·ez

. (5)

The expression of the field distribution(Em,Hm) can be easily calculated by adapting theprocedure given in Ref. [50] to the hollow cylindrical waveguide made in perfect metal.

In the following, the axis of symmetry of the input Gaussian beam is supposed to be alignedand centered with respect to the cylindrical waveguide. Assuming that(Ei ,H i) defines the inputbeam waist, we have

Ei(x,y,0, t) =1

4π2 exp(−iωt)∫∫

ei(u,v)G(u,v)exp[i(ux+vy)] dudv, (6)

H i(x,y,0, t) =1

4π2 exp(−iωt)∫∫

hi(u,v)G(u,v)exp[i(ux+vy)] dudv. (7)

where G(u,v) =πW2exp[−(u2+v2)W2

4

], andhi = (k× ei)/(ωµ0) with k = (u,v,w) being the

wave vector,ω the wave angular frequency andµ0 the permeability of the vacuum. Expres-sionsei(u,v)G(u,v) andhi(u,v)G(u,v) define the plane wave spectrum of the input electricand magnetic fields, respectively.

Figure 3(a) reports the coupling between the incident linearly polarized Gaussian incomingbeam and the cylindrical waveguide modes as a function of the waveguide diameter. In thisbasic configuration, only the fundamental mode TE11 that is linearly polarized is excited witha maximum efficiency of 0.87 for a waveguide diameter of 13λ .

2.4. Selection of the radial mode of a cylindrical metallic waveguide

Our approach for selectively exciting the upper mode TM01 radially polarized is divided in twosteps. The first one, borrowed from Ref. [46], consists of inverting the polarization directionof the input beam (configuration 1) or the fundamental waveguide mode (configuration 2) overhalf their cross sections. Then, the two halves are in phase opposition. Note that in configura-tion 1, this polarization inversion is carried out before the injection of the input beam insidethe waveguide, whereas in configuration 2, it is realized inside the waveguide on the linearlypolarized fundamental mode. Figures 3(b) and 3(c) show the coupling efficiencies between theGaussian beam and the waveguide modes in configurations 1 and 2, respectively. In both cases,the energy of the fundamental mode that was solely excited without field reversal as shown inFigure 3(a), is now transferred into modes TM01 and TE21 (see Figs. 3(b) and 3(c)). The max-imum coupling efficiency between the incident gaussian beam and the waveguide mode TM01

reaches 44% in configuration 2 (at a waveguide diameter of 13λ ) whereas it is limited to 28%in configuration 1 (at a waveguide diameter of 10.3λ ). The second step of the TM01 modeselection consists of filtering out the TE21 mode. This task can be fulfilled by channeling theTM01 and the TE21 modes excited in configurations 1 or 2 into a smaller hollow cylinder whosediameter is comprised between the cutoff diameters of the two modes (cf Fig. 1). In that case,only TM01 (with the lower cutoff diameter) is transmitted through the small waveguide, TE21

being completely reflected. This operation can be carried out by tapering the large waveguideso that its output aperture matches the entrance aperture of the small one (see inset of Fig. 4).

Figure 4 displays the channeling efficiency of mode TM01 as a function of the taper angleθ .This channeling efficiency is defined as the ratio between the energies carried by the TM01 modeinside the small and the large waveguides. BOR-FDTD (Body-Of-Revolution Finite Difference


0.65

0.7

0.75

0.8

0.85

0.9

TE11

Incident gaussian

beam

C

waveguide diameter

Other modes : C=0

8 l 20 l10 l 12 l 14 l 16 l 18 l

(a)

0.1

0.15

0.2

0.25

0.3

0.35

TM01

TE21

Incident gaussian

beam

C

waveguide diameter

Other modes : C=0

8 l 20 l10 l 12 l 14 l 16 l 18 l

(b)

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

TM01

TE21

Fundamental

mode

C

waveguide diameter

Other modes : C=0

8 l 20 l10 l 12 l 14 l 16 l 18 l

(c)

Fig. 3. (a) Coupling efficiencyC between a linearly polarized Gaussian beam and the var-ious modes sustained by a cylindrical hollow waveguide of perfect metal, as a functionof the waveguide diameter. (b) Configuration 1, half the incoming Gaussian beam cross-section has been phase retarded byπ (see inset). (c) Configuration 2, half the fundamentalmode cross section initially excited has been phase retarded byπ (as shown in the inset).

Time Domain) algorithm [51, 52] with spatial uniform mesh has been used to simulate thepropagation of the mode inside the tapered waveguide. The transmission has been calculatedas the normalized transmitted Poynting vector flux by the incident one. The flux in each case isdetermined by integrating the Poynting vector over the cylinder sections. In the case reportedhere, the diameters of the large and the small hollow cylinders are 7λ and 0.9λ , respectively.As shown in Fig. 1, the small circular waveguide fulfills the condition required for transmittingTM01 and filters out TE21. The transmission efficiency of the TM01 mode through the systemkeeps lower than 5% for taper angles smaller than 62 degrees but grows rapidly for larger anglesand almost reaches≈ 90% for θ = 83◦ which is considered as a quasi adiabatic regime of thetaper.

2.5. Efficiency of the linear to radial polarization conversion

From the study detailed above, the efficiency of the linear to radial polarization conversioncan be evaluated by multiplying the efficiencies calculated previously for the two steps of theTM01 mode selection. Figure 5 shows the total efficiency as a function of the large waveguidediameter, for a width of the small waveguide of0.9 λ and a taper angle of80◦. For this angle,


0 10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Taper angle (degree)qP

ow

er t

ransm

issi

on

TM +TE01 21 _

q

TM01

Fig. 4. Channeling efficiency of the TM01 mode as a function of the taper angleθ . Thediameters of the large and small waveguides are 7λ and 0.9λ , respectively.

the channeling efficiency, calculated for a diameter of7 λ , is about 77%. This value has beenkept constant for calculating the efficiency of the radial polarizer.

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Effic

ienc

y

waveguide diameter8 l 20 l10 l 12 l 14 l 16 l 18 l

Fig. 5. Efficiency of the TM01 mode selection as a function of the diameter of the first(large) waveguide; dashed line: configuration 1; solid line: configuration 2, configurationsare detailed in §2.4.

The second configuration of polarization reversal leads to a maximum efficiency of linear toradial polarization conversion larger than 34% for a large waveguide diameter of13λ whereasthe maximum efficiency of the first one is limited to 22% at large waveguide diameter of10.3 λ .Therefore, the configuration of radial polarizer which involves a polarization reversal inside thefirst (large) waveguide seems to be better adapted for radially polarizing THz waves.

2.6. Far-field emission

Because the TM01 mode frequency is close to the cutoff inside the small waveguide, the freespace radiation efficiency of the polarizing device is not maximum. This problem can be solvedby placing a circular horn antenna at the end of the small waveguide for adapting the electro-magnetic impedance of the output TM01 guided mode to vacuum.


2.7. Prototype design and fabrication

Figure 6 depicts the preliminary system aimed at validating the above presented concept ofradial polarizer at a frequency of 0.1 THz. It consists of a tapered waveguide coupled to a dis-continuous phase element (DPE). The latter is a dielectric plate whose output interface exhibitsa step. The step heighth = λ/2(n−1) induces aπ-phase retardation for the thicker part of theplate with respect to the thinner one when a radiation goes through the system at normal inci-dence. When the step is orthogonal to the direction of the incident linear polarization, the DPEinduces the desired phase conversion for the generation of radial polarization (Fig. 7). Such adielectric system is widely used in optics for the generation of radially polarized beams [53, 31,38, 46].

40mm

f=100Ghz

q

l/(2(n-1))

n

DPETeflon

Waveguide system, Al

Fig. 6. Schema of the first radial polarizer prototype. It is composed of a DPE and a focusingwaveguide system.

DPE

TE11

_

T +TE21

M01

_

Fig. 7. Effect of the DPE onto the incident free space Gaussian beam. The waveguide modesexcited with and without DPE are also indicated.

The DPE is fabricated by micromachining a 3.5 mm high step onto one of the two faces ofa polytetrafluoroethylene (PTFE) plate whose index of refractionn is close to 1.43 at 0.1 THz.The DPE is set outside the waveguide system in order to finely center the phase step withrespect to the waveguide entrance aperture thanks to a precision translation stage. As discussedin §2.4, the fine positioning of the DPE outside the waveguide system is made at the expenseof some loss of efficiency.

The focusing waveguide system has been fabricated by micromachining an aluminum rod.At its heart, a 6 mm long hollow cylindrical waveguide of 2.7 mm (0.9λ ) diameter supports the


simultaneous propagation of both the TE11 and TM01 modes. Input is tapered with a circularhorn up to an external aperture of diameter≈ 40 mm for channelling an incoming 30 mm(10 λ ) wide Gaussian beam to the small waveguide. Adiabatic conversion of the free-spacepropagating mode is ensured by a taper angleθ higher than80◦ of resulting attenuation≤1.1 dB as a result of calculations of Fig. 4. The output of the waveguide is also tapered but to alimited diameter of4 mm. This circular horn antenna ensures a sufficient power density at theoutput aperture with an enhanced free space radiation of the system. Relatively high intensitiesat the system output are required for the detection of the radially polarized beam with lowefficient micro-probes.

2.8. Simulation of the prototype

A preliminary numerical study of the ability of this prototype to polarize radially THz radiationsis conducted by using a home-made BOR-FDTD code. This latter is based on the discretiza-tion of the Maxwell equations when they are expressed in cylindrical coordinates. By this way,the axis-symmetry of the structure is fully analytically treated to reduce the dimension of thestudied problem by explicitly expressing the azimuthal dependence in Maxwell equations. Thisleads to consider a 2D meshing in the (r,z) space instead of a 3D one for the three cylindri-cal coordinates (r,z,φ ). Because aluminum shows very high permittivities in the THz domain[47], transmission losses inside the metallic structure are negligible and the prototype has beenmodelled with perfect metal for convenience.

In Fig. 8, the transmission through the waveguide system is evaluated for two incomingfree space eigenmodes with (Fig. 8(a)) radial and (Fig. 8(c)) hybrid polarizations. These twomodes are supposed to be coupled to the TM01 and TE21 modes inside the metallic structure,respectively. In both cases, the injection plane is located at 20 mm in front of the entrance facetof the device. The field distributions of the input beams in the injection plane are the ones ofthe TM01 (Fig. 8(a)) and TE21 (Fig. 8(c)) guided mode of a cylindrical waveguide at the desiredfrequency. These initial conditions are calculated using a N-order FDTD code [54] especiallyelaborated for the determination of the eigenfrequencies of an axis-symmetrical structure [55].

Figures (8(d) and (f)) show that the radially polarized incident beam (coupled to mode TM01)is transmitted through the system (Fig. 8(d)) whereas the incoming beam with hybrid polariza-tion (which couples to mode TE21) is stopped at the entrance of the hollow cylinder waveguide(Fig. 8(f)). For a better view of this phenomenon, the fifth root of the electric intensities arerepresented in Fig. 8(d,e,f). Note that the length of the cylinder is larger than the evanescenttail of TE21 inside the waveguide. This explains the negligible output far-field re-emission ofthis mode (Fig. 8(i)). The transmission of the degenerated mode that is usually produced by theDPE (Figs. 8(b,e,h)) can be simulated simply by adding the field distributions calculated in thetwo last cases. We see that the two lobe incident field distribution (Fig. 8(b)) is converted intoa doughnut output beam that is related to the selective transmission of the TM01 mode radiallypolarized through the metallic structure (Fig. 8(h)). An efficiency of 11% has been calculatedfor this preliminary configuration of waveguide system. Note that this value do not take intoaccount the reflections of the input beam onto the interfaces of the DPE.

3. Experimental setup

The experimental setup of generation and characterization of the radially polarized beam issketched in Fig. 9. A continuous-wave linearly polarized radiation is generated at 0.1 THz. Thesource is an electronic synthesizer followed by a sextupler from Spacek Labs Inc. Availableoperating bandwidth of this commercial system is 75-110 GHz with a nearly constant0 dBmoutput. A WR10 horn antenna is connected to the source for improving the free space radiationefficiency. After their collection and collimation with a parabolic mirror, waves propagate under


15.2 mm15.2 mm

TM0120 mm

+

20 mm

(a)S

agitta

l sections (

inte

nsity)

Outp

ut in

tensity

31.25 mm 31.25 mm31.25 mm

Input in

tensity

15.2 mm

TE2120 mm

X10-5

(b) (c)

(d) (f)

(g) (h) (i)

(e)

Fig. 8. FDTD simulation of the focusing waveguide system. The real case is simulatedin the middle column whereas the right and left columns show the projection of the fielddistribution in a basis of eigenmodes. We see that the degenerated space mode (b) that isproduced with the DPE is the result of the combination of (a) a radially polarized modeand (c) a four-spot mode with hybrid polarization. (d,e,f) show the fifth root of the electricintensities in a longitudinal cross-section of the device for the three input modes. (g,h,i)exhibit the electric intensities in a lateral plane located at 15 mm from the output side ofthe device.


a form close to a Gaussian beam whose waist is about 30 mm (10λ ), as shown in Fig. 10(a).

Fig. 9. Scheme of the experimental setup.

The polarization converter is placed into the THz beam so that the DPE is set close to thebeam waist and the waveguide system is positioned in contact to the DPE. The waveguide iscarefully centered and aligned with respect to the incoming beam propagation axis. The DPEcan be translated transversally with a 1D translation stage that ensures an accurate centering ofthe DPE phase step with respect to the waveguide input aperture. Detection involves a Schottkydiode coupled to a PTFE pyramidal probe of principle similar to the one described in Ref.[56]. The probe was built from a WR10 waveguide (inner sizes1.27 mm× 2.54 mm) filledwith a PTFE parallelepiped ended by a pyramid of 3 mm height protruding from the waveguideend. The two opposite largest facets of the tip were metal coated using Ni pulverization. Thesensitive end facet area exhibits dimensions of20×40µm. The detection provided by this tip isthus specially engineered to be polarization sensitive since this collection system picks up onlyone transverse component of the electric field. The distance between the polarizer end facetand the probe is kept lower than 0.2 mm (λ/15) during image acquisitions by raster-scanning.The probe system is mounted onto a 2D motorized translation stage, with optimal resolution of100 nm, for scanning the end aperture of our device.

4. Results and discussion

Figure 10 shows the properties of the field before and after its transmission by the waveg-uide system when the DPE is removed. Images in Fig. 10(b) reports the intensity of the fieldcomponents parallel and perpendicular to the incident polarization direction as observed at thewaveguide system end. Those images have been taken by two successive acquisitions, with ascan step of≈ 200µm and by rotating the probing device by90◦ between the two scans. Asa major consequence, the upper part of the Fig. 10(b) displays a bright spot whereas the lowerpart shows an intensity distribution which just exceeds the detection background. These imagesdemonstrate that the output field distribution is linearly polarized along the polarization direc-tion of the incoming beam. Such a polarization property is due to the excitation of the TE11

mode inside the waveguide structure.The acquisitions realized with the DPE in front of the focusing system are reported in Fig. 11.

Images obtained when the axis of the polarizing probe stage is set parallel and perpendicular tothe incoming polarization direction are displayed in Figs. 11(a) and 11(b), respectively. Theseorientations are indicated by white arrows on each image. A numerical reconstruction of theoutgoing beam from Figs. 11(a) and 11(b) is provided in Fig. 11(c) whereas cross-sections ofFig. 11(a) along the horizontal direction (solid curve), and Fig. 11(b) along the vertical direction


(a)

(b)

Fig. 10. (a) Measured intensity before the DPE (dots) compared with a theoretical gaus-sian beam (solid line). (b) Images of the transmitted intensity obtained without DPE whenthe polarizing probe axis is parallel (upper part) and perpendicular (lower part) to the inci-dent polarization direction. Intensities are normalized to the same maximum value for bothimages.

(dashed curve) are plotted in Fig. 11(d).Two-grain structures jump out in Figs. 11(a) and 11(b). As expected, their directions follow

the prescribed axis of the polarizing micro-detection system. The numerical combination ofthese two orthogonal patterns leads to an annular shape intensity distribution. The null intensityat the beam center (see Fig. 11(d)) evidences that the fundamental TE11 mode, whose maximumis expected at the center, has been totally rejected by the structure. Moreover, the visibilityof the two-spots pattern remains unchanged when the probe axis is rotated (Figs. 11(a) and11(b)). This is another evidence that all higher modes, except TM01, are reflected by the system.These observations validate our concept of THz radial polarizer. Note that the efficiency of thisprototype cannot be measured with precision by means of the detection tools that we used.This is partly due to the fact that there is no direct coupling between a radially polarized beamand the fundamental mode of a rectangular waveguide. From the discussion of §2.4, it can beenhanced by inserting the DPE inside the focusing structure. This can be achieved, for example,by adapting a cylindrical waveguide to the entrance of the focusing taper. This will be made ina close future for fabricating the first THz experiments involving radial polarization.


(a) (b) (c)

(d)

Fig. 11. Acquisition results of the field distribution transmitted by the prototype over a scanof 7× 7 mm2. (a) and (b) are images acquired for two orthogonal axis of the polarizingdetection probe (axis indicated by arrows). (c) Numerical combination of (a) and (b). (d)Horizontal cross-section of (a) (solid curve) and vertical one of (b) (dashed curve).


5. Conclusion

A new THz radial polarizer suitable to convert the usual linearly polarized signal from a mil-limeter or sub-millimeter source is described and demonstrated at≈ 100GHz. Its principle ofoperation involves an adequate mode filtering in a metallic cylindrical waveguide that supportsonly TE11 and TM01 propagating modes. The correct system operation arises with the selectionof the radially polarized TM01 mode that is ensured by means of a discontinuous phase elementplaced at the entrance of the system. A nearly optimum design of such a passive radial polarizerhas been given owing to numerical FDTD calculations of the coupling efficiency of a Gaussianpropagating linearly polarized beam to the TM01 mode of a large circular waveguide. Aperturesize of this input cylindrical waveguide as well as the design of the taper that follows have beenoptimized. The experimental realization has been conducted at 0.1 THz. The built polarizer hasshown an operation in excellent agreement with the theoretical design. Doughnut modes havebeen observed at polarizer output with a very high rejection of the fundamental TE11 mode.Provided that micromechanical machining difficulties can be overcome, the proposed design isstraightforwardly scalable to much higher frequencies in the whole THz domain. In the future,this polarizer coupled to an axicon is aimed at generating very small focal spots with enhancedlongitudinal electric field for THz near field imaging purposes.

Acknowledgments

Authors are indebted to the Agence Nationale de la Recherche for supporting this research un-der contract #ANR06-BLAN-0073. They are grateful to D. Courjon for helpful discussions.One of us (RA) also thanks jointly the CNRS and the Région Languedoc-Roussillon for doc-toral fellowship.


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Linear to radial polarization conversion in the THz domain using a passive system