Thermal characterization of optical fibers usingwavelength-sweeping interferometry

Luc Perret,* Pierre Pfeiffer, Bruno Serio, and Patrice TwardowskiLaboratoire des Systèmes Photoniques, Université de Strasbourg—Ecole Nationale Supérieure de Physique,

Boulevard Sébastien Brant, BP10413, 67412 Illkirch, France

*Corresponding author: luc.perret@ensps.u‑strasbg.fr

Received 25 January 2010; revised 7 June 2010; accepted 9 June 2010;posted 9 June 2010 (Doc. ID 123173); published 18 June 2010

In this paper, we report a new method of thermal characterization of optical fibers using wavelength-sweeping interferometry and discuss its advantages compared to other techniques. The setup consistsof two temperature-stabilized interferometers, a reference Michelson and a Mach–Zehnder, containingthe fiber under test. The wavelength sweep is produced by an infrared tunable laser diode. We obtainedthe global phase shift coefficients of a large effective area fiber and gold-coated fiber optics with a 10−7

accuracy. © 2010 Optical Society of AmericaOCIS codes: 120.0120, 060.2270, 120.3180.

1. Introduction

Absolute distance interferometry (ADI) based ontunable lasers has well-identified error sources, suchas wavelength-sweeping nonlinearities, data proces-sing, atmospheric turbulences and refractive indexvariations, ground vibrations, and reference etalonstability. We recently explored the two first sourcesof uncertainty, linked to our external-cavity laserdiode (ECLD) [1,2] and our data analysis method[3]. There are extra solutions to deal with the atmo-spheric or ground perturbations, such as the additionof a weather station or the combination of two inver-sely swept lasers. In our case, we rely on the highsweeping speed and sampling frequency to limittheir influence, and we perform averaging over sev-eral measurements.

The last point is the reference etalon stability.Most ADI setups use an open interferometer madein Zerodur, arguing that it would compensate the at-mospheric perturbations. It is true for short dis-tances, but it becomes irrelevant when targetinglong distances because the atmospheric conditionsare no longer coupled between the reference place

and the target site. Moreover, the ground propertiesmay change along the way, so that the vibrations arealso decoupled. On the other hand, we see an advan-tage in using a fibered etalon: in space applications,the weight and size are crucial points regarding tocosts. Zerodur etalons are quite heavy, and theirlength is limited for a given size by the complexityof multiple reflections. On the contrary, fibered eta-lons are light and can reach very long optical pathdifferences (OPDs) in a minimal volume.

To our knowledge, however, few studies have beenmade on fibered etalons, maybe due to the fact that,usually, fibered Mach–Zehnder interferometers areused as a temperature detector and need to be sen-sitive in that case. One can cite [4], who implementeda Mach–Zehnder using insensitive fibers: the geom-etric change of the fiber is compensated for by itsrefractive index change. We worked on another ap-proach that consists of compensating the globalphase shift due to the temperature drift of one armby the shift of the other arm in order to keep the OPDconstant [5]. To realize such a Mach–Zehnder, we im-plement our range finder in a reversed way, in orderto deduce the phase shift from the increase of the fi-ber OPD with temperature relative to a fixed targetlength.

0003-6935/10/183601-06$15.00/0© 2010 Optical Society of America

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2. Thermal Dependence of Optical Fibers

The thermal effects generally listed in optical fibersare the photoelastic effect and the thermo-optic effectin the core and the material coefficients of thermalexpansion (CTEs) of the different layers, as well astheir mechanical coupling [6–8]. Interpretation mod-els for multilayer fibers have been developed for sta-tic [9] and dynamic [10–12] cases. A more generalmodel was made by [13,14]. We consider these ther-mal effects independently of the dispersive effects,which means that we neglect the variation of the po-larization mode dispersion and of the chromatic dis-persion coefficients with temperature. The globalphase shift coefficient can then be written as [6]

S ¼ 1Φ ×

dΦdT

¼ 1n ×D

×dðn ×DÞ

dT; ð1Þ

where Φ is the phase in the fiber, n is the refractiveindex, and D is the geometric length.

The thermo-optic effect describes the direct depen-dence of the group index N with temperature:

βT ¼ 1N

×dNdT

≈1n×dndT

: ð2Þ

The photoelastic effect is due to the appearance of abirefringence in the core refractive index because of amechanical strain [15,16]. It corresponds to an axialstretch and a radial compression, which modify thegroup index as

αp−e ¼1N

×∂N∂L

: ð3Þ

As in Eq. (2), we can directly write Eq. (3) with ninstead of N by neglecting the chromatic dispersionvariations with strain. When there is no traction ap-plied on the fiber, and when we neglect the externalpressure variations, the mechanical strain is onlyproduced by the volumic thermal dilatations of thelayers. We suppose also there is no residual strainapplied to the fiber, particularly in the case of metal-clad fibers. Such a strain can result from the differ-ence between the thermal expansion coefficients ofboth materials when the metal-clad fiber cools down.

Finally, the physical expansion of the fiber is due toa combination of layer CTEs and their mechanicalcoupling. Assuming that these terms are constantand that there is no delamination over the tempera-ture range, it can be described by the resulting globalCTE of the fiber as

αTf ¼1D×dDdT

; ð4Þ

so that Eq. (1) can be written as

S ¼ 1N

×dNdT

þ 1D×dDdT

þ 1N

×∂N∂D

×∂D∂T

; ð5Þ

or

S ¼ βT þ αTf þD × αp−e × αTf : ð6ÞThe last term is generally considered negligible

with regard to the other effects [6,10]. The typicalvalues of each layer CTE are given in Table 1[7,8]. The thermo-optic effect in the silica core of sin-gle-mode fibers (SMFs) is [10] βTSMF ¼ 8 × 10−6 °C−1.

We can thus consider that the silica CTE is negli-gible compared to the thermo-optic effect and, more-over, to the coating CTE. A major difficulty lies inevaluating the mechanical coupling between thelayers, particularly when the internal constitutionof the fibers is not fully known. The mechanical cou-pling (shear and radial pressure) depends, indeed, onthe layer radii, Young modulus, and Poisson ratios[11,12], which may be very different and not bedetailed by the suppliers. Moreover the thermo-opticeffects in a large effective area fiber (LEAF), forexample, may be different from SMFs; they can beevaluated either from the Lorentz–Lorenz formula[17–19] or from the Sellmeier coefficients [20,21].As a consequence, to implement our fibered etalon,we chose to test, experimentally, the optical lengthvariation with temperature for each fiber.

3. Thermal Characterization Setup

Differentwayshavebeenused toexplore the tempera-ture dependence of optical fibers. Most of them arebased on a fringe counting technique in Fabry–Perot[18]orMach–Zehnder [9,12,22–24] interferometersorbased on fiber Bragg gratings (FBGs) [21,25]. Someothersusean intensitymodulation [6], a time-of-flightmeasurement [6], or a low-coherence interferometer[18]. We use an original double-interferometer setup,where the reference is given by a Michelson interfe-rometerbetween two fixedarmsonastabilizedopticaltable, whereas the fiber under test is included in a fi-bered Mach–Zehnder (Fig. 1). The beam of an ECLDworking around 1530 nm without mode hopping issent intoboth interferometers.Thus, each interferom-eter iproduces a signal describedbyEq. (7)whereLi isthe corresponding OPD:

Iiðr; tÞ ¼ ðI1iðr; tÞ þ I2iðr; tÞÞ· ð1þ ViðtÞ · cosð2π=λðtÞ · Li þΦ0iÞÞ: ð7Þ

Ata first-orderapproximation,we canpoint out abeatfrequency [Eq. (8)], which is isolated by a Fouriertransform technique described by [26]

Table 1. Coefficients of Thermal Expansion of CommonCoating Materials for Fiber Optics

Materials CTE ½°C−1� × 10−6

Silica 0.55Copper 17Gold 14Aluminum 23Acrylate 100 (order of magnitude)

3602 APPLIED OPTICS / Vol. 49, No. 18 / 20 June 2010

f bi ¼α0 × Li

λ02: ð8Þ

The sweeping speed α0 and the starting wave-length λ0 are common to both interferometers, so thatthe ratio R between the Mach–Zehnder and the

Michelson beat frequencies is equal to the ratiobetween their OPDs.

The main advantage of this method is the possibi-lity to trigger the acquisition at any stable tempera-ture, whereas fringe counting and phase shiftingtechniques need the knowledge of the start and endtemperatures as well as the exact fraction of fringesor phase [23]. Compared to the time-of-flight method,this method is more precise than with picosecondlasers and less sensitive to wavelength dispersionerrors than with femtosecond lasers. Recently, atime-of-flight technique based on low-cost radiofre-quency modulation reached a good resolution [27];however, it suffers, like other modulation techniques,the existence of a limited unambiguous measure-ment range, which needs to be adapted to the initiallength and the predicted length variation of the fi-bers. Fiber Bragg gratings are ideal for local mea-surements and can typically achieve a 0:01 nm=°Cdrift, so that a high-resolution wavelength measure-ment is needed to reach a good sensitivity intemperature [21,25].

Temperature control remains the limiting factor inresolution. Ovens are not very accurate (typicallywithin 1 °C), and the equilibrium is slow. A direct

Fig. 1. (Color online) Thermal characterization of fiber setup: PD,photodiode; ECLD, external-cavity laser diode; RR, retroreflector;BS, beam splitter; HC, heated circulator; and FC, fiber coupler.

Fig. 2. (Color online) (a) LEAF of 2:00 m and (b) LEAF of 5:02 m;the line is the regression of themean ratios (circles) over eight tem-peratures, and the stars are the computed ratios of each one of thethree acquisitions of 217 samples at each temperature.

Fig. 3. (Color online) Gold-coated fiber of (a) 2:96 m and (b)4:81 m; the line is the regression of the mean ratios (circles) overeight temperatures, and the stars are the computed ratios of eachone of the three acquisitions of 217 samples at each temperature.

20 June 2010 / Vol. 49, No. 18 / APPLIED OPTICS 3603

bath is easier to heat or cool down, but turbulencesproduce pressure (strain) variations [22] and tem-perature inhomogeneities [21]. A solution may be theuse of a capillary to protect the fiber [9,28] or the useof solid thermal grease [24]. However, the capillarymust be changed each time to test a different fiberlength. Fiber Bragg gratings are not suitable for com-paring the behavior of different lengths.

Our test fiber is wound around an 80 mm metallicmandrel, so that the effect of curvature on dilatationis negligible [9], and placed in an oil bath without acapillary. By this way, we can easily change the fiberlength to test and ensure similar conditions for eachfiber. The counterpart is the possible influence of thecoating swelling in the final results, which is heresupposed to be negligible. This oil bath is heatedin a water bath by circulating water using a LaudaMT heating circulator, in order to get a homogeneoustemperature without the drawback of turbulence(Fig. 1). Indeed, the oil is more viscous, and we waitfor the thermal equilibrium between each measure-ment by controlling three equally spaced thermistorsaround the mandrel. The Michelson interferometeris in a temperature-controlled environment. Weachieve a temperature homogeneity better than0:03 °C in oil, whereas thermal grease heated byresistors allows only a 0:5 °C homogeneity [24].

4. Results

We tested different lengths of LEAF and gold-coatedSMFs, between 20 and 60 °C, which interested us in

implementing a reference fibered interferometer.Our LEAF is produced by Corning, and it is a nonzerodispersion-shifted fiber, featuring a larger mode-fielddiameter while remaining single-mode. The 125 μmglass fiber is coated with a multilayer acrylate CPC6coating having an outside diameter of 245 μm. Thegold-coated SMF is a silica/silica ASI-9.0/125-G fromFiberguide and has an outside diameter of 155 μm.For a given length, we can see that the thermaldependence can be approximated by a linear fit overthe temperature interval with a relative uncertaintyat 1σ of some 10−6 (Figs. 2 and 3).

The thermal phase shift coefficient S is given bythe beat frequencies ratio R [Eq. (2)], assuming thatall the other lengths are constant (the Michelson andthe other Mach–Zehnder fibered arm):

S ¼ 1LF

·dLF

dT¼ 1

R·dRdT

; ð9Þ

where LF is the fiber optical length. The temperaturedependence of the beat ratio dR=dT is approximatedby the slope of the regression line; S is then computedusing the mean ratio value over the temperaturerange (see Table 2).

The values at different lengths are consistent witheach other. However, we observe an important dis-persion at each temperature, increasing with tem-perature. So we added thermal isolation along thecouplers fibers to avoid their dilatation when

Table 2. Experimental Results for LEAF and Gold-Coated Fibers

FiberRelative

Uncertainty × 10−6Standard Deviation at

Each Temperature × 10−6 S½°C−1� × 10−6

LEAF 5:02 m 5.6 20 to 45 6.82LEAF 2:99 m 6.9 2 to 45 6.89LEAF 2:00 m 8.4 8 to 50 7.17Gold 4:81 m 6.3 5 to 65 8.49Gold 2:96 m 8 12 to 25 9.06

Fig. 5. (Color online) Gold-coated fiber of 2:751 m with the im-proved setup; the line is the regression of the mean ratios (circles)over eight temperatures, and the stars are the computed ratios ofeach one of the six acquisitions of 217 samples at each temperature.

Fig. 4. (Color online) LEAF of 2:00 m with the improved setup;the line is the regression of themean ratios (circles) over eight tem-peratures, and the stars are the computed ratios of each one of thesix acquisitions of 217 samples at each temperature.

3604 APPLIED OPTICS / Vol. 49, No. 18 / 20 June 2010

the air above the bath gets hotter, and we cut thecirculator during the measurements to suppressany induced turbulence. Figures 4 and 5 and Table 3show a decrease of the dispersion by a factor of 5, andthe linear fit is made with a relative uncertainty re-duced by a factor of 2. This means that our resolutionwas indeed limited by the external temperature gra-dient and turbulences. Additional measurements al-low us to estimate that the contribution of vibrationson the standard deviation is constant over the tem-perature range and is about 5 × 106. Our improvedsetup realizes a measurement of S at better than 3 ×10−7 °C−1 (see Table 3).

5. Conclusion

We report a new setup to measure the global thermalphase shift of optical fibers based on a wavelength-sweeping ECLD. We demonstrated the influence ofthe external temperature gradient and of the turbu-lence over dispersion and resolution and tested dif-ferent types and lengths of fibers with consistentresults. We give the phase shift values of LEAF andgold-coated SMF as 6:82 × 10−6 and 8:81 × 10−6 °C−1,respectively, with a resolution of 3 × 10−7 °C−1. Thissetup could be useful to dimension fibered etalonor to study the relationship between the mechanicaland optical properties of fiber optics.

This work is supported by the Alsace RegionalCouncil and the Oseo Agency.

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Table 3. Experimental Results for LEAF and Gold-Coated Fibers with Improved Setup

FibersRelative

Uncertainty × 10−6Standard Deviation at

Each Temperature × 10−6 S½°C−1� × 10−6

LEAF 2:00 m (six measurements per temperature) 3.5 3 to 7 6.81LEAF 2:00 m (three measurements per temperature) 3.9 1 to 11 6.78Gold 2.751 (six measurements per temperature) 3.7 3 to 13 8.81

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