Temperature coefficient of the high-frequency guidedacoustic mode in a photonic crystal fiber

Emile Carry, Jean-Charles Beugnot, Birgit Stiller, Min W. Lee,Hervé Maillotte, and Thibaut Sylvestre*

Institut FEMTO-ST, Université de Franche-Comté, CNRS UMR 6174, 25030 Besançon, France

*Corresponding author: thibaut.sylvestre@univ‐fcomte.fr

Received 15 June 2011; accepted 14 September 2011;posted 13 October 2011 (Doc. ID 149325); published 9 December 2011

High-frequency guided acoustic Brillouinmodes have recently been observed in small-core silica photoniccrystal fibers. In this paper, we investigate the temperature dependence of the optical sideband frequencygenerated by one of these guided acoustic waves. The experimental results show a temperature coeffi-cient of 100kHz=°C at an acoustic resonance frequency of 1:15GHz and are in very good agreement withthe theoretical predictions. This coefficient demonstrates a temperature sensitivity 10 times larger thanthat previously reported in conventional single-mode fibers, which is promising in view of potentialapplications to optical fiber sensors. © 2011 Optical Society of AmericaOCIS codes: 290.5830, 060.2370, 060.4005.

1. Introduction

Photonic crystal fibers (PCFs) have recently wit-nessed a renewed interest because of their abilityto harness acousto-optic effects such as Brillouinscattering [1,2]. Compared to what is commonly ob-served in conventional single-mode fibers, the peri-odic wavelength-scale air-hole microstructure ofsilica PCFs deeply alters the elastic waves distribu-tion, leading to new characteristics for both forwardand backward Brillouin scatterings [3]. In this re-spect, several groups have recently reported thatforward or guided acoustic wave Brillouin scatter-ing (GAWBS), which has long been considered as anoise source for telecommunications and quantumoptics, substantially increases in PCF for a few high-frequency guided acoustic modes [4–8]. Further in-vestigations have revealed that these high-frequencyguided acoustic waves are trapped within the core ofair-hole microstructure, leading to a strong acousto-optic overlap and therefore enhanced scattering effi-ciency [4,5,8]. On the other hand, lower frequencyacoustic modes of the fiber cladding are substantially

attenuated by the air-hole microstructure that actsas an “acoustic barrier” for cladding acoustic modes[4]. These new characteristics of forward Brillouinscattering open a way for potential applications totemperature or strain-optical fiber-based sensors.

In this paper, we investigate the temperaturedependence of a high-frequency guided acoustic wavein a kilometer-long solid-core PCF. We first reportthe experimental observation of the fundamentalacoustic mode optically excited inside the fiber micro-structure at a resonance frequency of 1:15GHz. Theexperimental results will be then compared with thenumerical computations based on the finite elementmethod (FEM). The PCF will be placed in a climaticchamber. By varying the temperature of the chamberwe will measure a shift of this acoustic frequencyto be compared with the theoretical predictions.Results will show an order of magnitude higher sen-sitivity to temperature than previous works in con-ventional single-mode fibers [9,10].

2. Experiment and Numerical Simulations

Polarized GAWBS in an optical fiber originatesfrom optically excited radial elastic modes and leadsto phase modulation and the occurrence of a set ofnew frequencies in the optical spectrum [11]. To

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detect such an effect, we set up the fiber loop mirrordepicted in Fig. 1 [12]. As a pump laser, we use adistributed-feedback (DFB) erbium-doped fiber laser.The laser emission at 1549:74nm is amplified by anerbium-doped fiber amplifier (EDFA). The amplifiedspontaneous emission (ASE) emitted by the EDFAhas been partially removed using a 5nm bandpassfilter which improves the observation of GAWBS.The output of the EDFA is then split into two beamsusing a 50=50 fiber coupler and injected in a counter-propagative loop mirror made with the PCF undertest. In the absence of GAWBS, the fiber loop actsas a mirror and all the power is reflected back tothe input port of the coupler. However, each beamsuffers in fact GAWBS effect and the phase modula-tion induced by the GAWBS is converted to ampli-tude modulation by interferences at the output portof the coupler. The GAWBS spectrum is recorded inthe electrical domain by using a fast photodiode fol-lowed by an RF amplifier and an RF spectrum ana-lyzer. The polarization controller and the polarizerare set to optimize the GAWBS signal. The PCF un-der test is then placed into a climatic chamber with atemperature range between −20 °C and 60 °C. Wealso use a proportional—integral—derivative (PID)

controller to regulate the temperature in the climaticchamber.

The SEM image of the PCF under test is shown inFig. 3(a). It consists of a standard triangular latticewith a core diameter dc ¼ 2:7 μm, holes diameterd ¼ 2:55 μm, and a pitch Λ ¼ 2:9 μm (d=Λ ¼ 0:88). Ithas a length of 1:3km, a loss factor α ¼ 5:4dB=km,and an effective single-mode area of 6:2 μm2 at1550nm. We first perform some measurements atroom temperature outside the climatic chamber.Figure 2(a) shows the experimental scattered Bril-louin spectrum. As can be seen, several GAWBSfrequencies are generated from 100MHz to morethan 1:8GHz. We can clearly see one mainly excitedacoustic mode at a resonance frequency of 1:154GHz.Hereafter we will focus our attention on this mainintense peak and we will neglect all the others thatcorrespond to cladding modes or higher-order acous-tic modes.

To identify the origin of this high-frequency guidedacoustic mode at 1:154GHz, we have performedFEM-based numerical simulations of both the opticaland the acoustic modes using the COMSOL software.For that purpose the PCF cross-section is importedfrom the SEM image shown in the Fig. 3(a) and thenmeshed. We have then used the RF module to solvethe optical mode and a custom partial differentialequation (PDE) model for full-vectorial 2D acousticmodeling. For acoustic parameters we have consid-ered the silica density r ¼ 2203kg · m−3, Young’smodulus EY ¼ 73:1GPa, Poisson ratio νP ¼ 0:17.For optical parameters, the numerical simulationsrun with the silica parameter and index n ¼ 1:444,yielding an effective refractive index neff ¼ 1:392.

Fig. 1. Experimental setup for measuring the temperature coef-ficient of guided acoustic wave Brillouin scattering in a photoniccrystal fiber.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Pow

er (

a. u

.)

Frequency (GHz)

0.2

0.4

0.6

0.8

11.151 GHz

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

(a)

(b)

0

Experiment

Theory

0.2

0.4

0.6

0.8

1

0

Fig. 2. (a) Experimental results: RF spectrum recorded at room temperature showing the guided acoustic wave Brillouin scatteringspectrum with a dominant peak at 1:154GHz. (b) Theoretical result: FEM-based numerical simulation of the elasto-optic coefficientκ2 versus the acoustic frequency.

6544 APPLIED OPTICS / Vol. 50, No. 35 / 10 December 2011

The single optical mode at 1550nm, confined in thecenter of the microstructure, is illustrated in colorplot in Fig. 3(b). Both the optical and acoustic modalshapes are then combined to estimate the elasto-optic diffraction coefficient κ that reads as [1]

κ ¼ZσEiEjpijklSkldxdy: ð1Þ

In the above expression, σ is the fiber transversesection, Ei and Ej the pump and scattered opticalmodes, respectively, pijkl the strain-optical tensor,and Skl the acoustic strain tensor. κ2 represents theacousto-optic field overlap and therefore models theGAWBS spectrum. The result for our PCF is depictedin Fig. 2(b) that shows a set of new generated fre-quencies including a main peak at 1:151GHz, in verygood agreement with the experimental results shownin Fig. 2(a). The very small discrepancy between the-oretical and experimental acoustic frequencies canbe attributed to the scale error on the SEM image.To get better insight into this acoustic mode trappedby the air-hole microstructure, we first derive thestrain energy density (SED) that reads as [13]:

WS ¼ 12

�∂u∂x

Txx þ∂ν∂y

Tyy þ�∂u∂y

þ ∂ν∂x

�Txy

�; ð2Þ

where ðu; v;wÞ and (Tkl) are the mode displacementsand stresses exported from the FEM mode solver, re-spectively. We further calculate the kinetic energy,i.e., the movement localization that writes as [13]

E ¼ 12ρw2ðu2 þ v2 þw2Þ: ð3Þ

The SED and kinetic energy of the main acousticmode at 1:151GHz are plotted in Figs. 3(c) and 3(d),

respectively. It can clearly be seen that the acousticmode is spatially localized within the fiber core andresults from radial compression and dilatation of theair-hole microstructure. In fact, the acoustic mode isidentified as the fundamental phonon of the radialR01 mode in the numerical simulation.

3. Temperature Coefficient

In this section we investigate the temperature de-pendence of the acoustic mode at 1:154GHz. For thatpurpose, the PCF is now placed into the climaticchamber and the GAWBS spectrum is recorded everyminute by tuning the box temperature from −20 °C to60 °C by 1 °C step and we have averaged 100 acquisi-tions. The temperature dependence of the GAWBSspectrum and the main acoustic frequency νA is re-presented in Figs. 4(a) and 4(b) as a color plot anda solid line, respectively. As expected, we measurea strong frequency shift of the optical sideband fre-quency scattered by the guided acoustic mode thatlinearly increases with the temperature. By applyinga linear fit of the experimental data, we have ob-tained a temperature coefficient of 106kHz=°C atthe acoustic resonance frequency.

To compare with theory, we assume that the fibercore behaves as a silica rod, which is valid for thecase of our PCF with a triangular lattice with largeholes and high air-fill fraction, as shown in Fig. 3(a).With this assumption, the acoustic resonance fre-quency f L can be therefore linked to the core diam-eter dc by the following expression [11]:

f L ¼ vsymπdc

; ð4Þ

where ym are the eigenfrequencies of acoustic modesm that depends on α ¼ vS=vL, with vS and vL asthe shear and longitudinal velocity, respectively.The temperature coefficient of the GAWBS frequencycalled θ can thus be derived as

θ ¼ 1f L

df LdT

¼ 1vL

dvLdT

; ð5Þ

where 1=vLdvL=dT is calculated by using stimulatedBrillouin backscattering parameters, with νL theBrillouin frequency shift [9]. For silica glass the tem-perature coefficient is equal to 9:2 × 10−5=°C. Usingthis parameter, we have obtained a temperaturecoefficient of the 1:154GHz acoustic mode as similarto 106:2kHz=°C, which is in very good agreementwith the experimental measurement. This tempera-ture coefficient is 10 times larger than that pre-viously reported in other fibers. For instance, inconventional single-mode fibers, a temperature coef-ficient of the torso-radial TR25 mode at 105MHz hasbeen measured as 11kHz=°C [9]. Matsui et al. [10]also obtained a similar result with the TR27 modein hole-assisted fiber (HAF). This high sensitivityto temperature is merely due to the fact that theacoustic resonance frequency generated in the PCF

Fig. 3. (Color online) (a) Scanning electron microscope (SEM)image of the cross-section of the photonic crystal fiber under test.(b) Numerical simulation of the single-mode output at 1550nm.(c) Numerical calculations of the strain energy density distributionand (d) the kinetic energy density at 1:151GHz.

10 December 2011 / Vol. 50, No. 35 / APPLIED OPTICS 6545

is about 10 times larger than those obtained inSMF. This remains however one digit lower thanthe temperature coefficient of backward stimulatedBrillouin scattering (SBS) in PCF due to its higherresonance frequency around 11GHz [14]. From theapplication viewpoint, however, GAWBS techniquehas several advantages for sensors compared tobackward SBS particularly because of the simplicityof its experimental arrangement since it does notrequire a pump-probe technique nor external ampli-tude or frequency modulation.

4. Conclusion

In this work, we have reported the observationof a highly-localized acoustic mode with a resonancefrequency of 1:154GHz in a solid-core PCF. We haveshown through numerical simulations that thisguided acoustic mode results from radial dilatationof the air-hole microstructure and is confined to thefiber microstructure. Furthermore, we have mea-sured the temperature dependence of the opticalsideband frequency scattered by this guided acoustic

wave and demonstrated an enhanced sensitivity ofabout 100kHz=°C in quite good agreement with thetheory. Therefore, PCFs and their specific acousticproperties may allow potential applications to opticalfiber sensors with a high sensitivity.

This work has been funded by the ProgrammeEuropéen de cooperation territorial INTERREG IVAand the Conseil Régional de Franche-Comté. Theauthors acknowledge Draka Comteq in France forthe loan of the photonic crystal fiber.

References1. V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre,

B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononicband-gap guidance of acoustic modes in photonic crystalfibers,” Phys. Rev. B 71, 045107 (2005).

2. P. Dainese, P. St. J. Russell, G. S. Wiederhecker, N. Joly,H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like lightscattering from acoustic phonons in photonic crystal fiber,”Opt. Express 14, 4141–4150 (2006).

3. P. Dainese, P. St. J. Russell, N. Joly, J. C. Knight,G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif,“Stimulated Brillouin scattering from multi-GHz-guided

Fig. 4. (Color online) (a) Color plot: forward Brillouin spectra recorded in a range of 1:1–1:2GHz for a temperature variation from −20 °Cto 60 °C. (b) Plot of themain peak versus the temperature. The crosses and the solid line are the experimental data extracted from (a) and alinear fit, respectively. The slope of the solid line is 106kHz=°C.

6546 APPLIED OPTICS / Vol. 50, No. 35 / 10 December 2011

acoustic phonons in nanostructured photonic crystal fibres,”Nat. Phys. 2, 388–392 (2006).

4. J.-C. Beugnot, T. Sylvestre, H. Maillotte, G. Mélin, andV. Laude, “Guided acoustic wave Brillouin scattering in photo-nic crystal fibers,” Opt. Lett. 32, 17–19 (2007).

5. D. Elser, U. L. Andersen, A. Korn, O. Glöckl, S. Lorenz,C. Marquardt, and G. Leuchs, “Reduction of guided acousticwave Brillouin scattering in photonic crystal fibers,” Phys.Rev. Lett. 97, 133901 (2006).

6. N. Shibata, A. Nakazono, N. Taguchi, and S. Tanaka, “ForwardBrillouin scattering in holey fibers,” IEEE Photon. Technol.Lett. 18, 412–414 (2006).

7. J. E. McElhenny, R. K. Pattnaik, J. Toulouse, K. Saitoh, andM. Koshiba, “Unique characteristic features of stimulatedBrillouin scattering in small-core photonic crystal fibers,”J. Opt. Soc. Am. B 25, 582–593 (2008).

8. B. Stiller, M. Delqué, J.-C. Beugnot, M. W. Lee, G. Mélin,H. Maillotte, V. Laude, and T. Sylvestre, “Frequency-selectiveexcitation of guided acoustic modes in a photonic crystal fiber,”Opt. Express 19, 7689–7694 (2011).

9. Y. Tanaka and K. Ogusu, “Temperature coefficient ofsideband frequencies produced by depolarized guided acous-tic-wave Brillouin scattering,” IEEE Photon. Technol. Lett.10, 1769–1771 (1998).

10. T. Matsui, K. Nakajima, T. Sakamoto, K. Shiraki, andI. Sankawa, “Structural dependence of guided acoustic-wave Brillouin scattering spectra in hole-assisted fiber andits temperature dependence,” Appl. Opt. 46, 6912–6917(2007).

11. R. Shelby, M. Levenson, and P. Bayer, “Guided acoustic-waveBrillouin scattering,” Phys. Rev. B 31, 5244–5252 (1985).

12. N. Nishizawa, S. Kume, M. Mori, T. Goto, and A. Miyauchi,“Symmetric and asymmetric fiber loop mirrors for observingguided-acoustic-wave Brillouin scattering in polarization-maintaining fibers,” Opt. Lett. 19, 1424–1426 (1994).

13. R. N. Thurston, “Elastic waves in rods and clad rods,”J. Acoust. Soc. Am. 64, 1–37 (1978).

14. L. F. Zou, X. Y. Bao, V. S. Afshar, and L. Chen, “Dependence ofthe Brillouin frequency shift on strain and temperature in aphotonic crystal fiber,” Opt. Lett. 29, 1485–1487 (2004).

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