Temperature and axial strain characteristic of cladding etchedsingle-mode ber based acousto-optic tunable lter

Chao Liu, Li Pei n, Yiqun Wang, Sijun Weng, Liangying Wu, Shaowei YuKey Laboratory of All Optical Network and Advanced Telecommunication Network of Ministry of Education, Institute of Lightwave Technology,Beijing Jiaotong University, Beijing 100044, China

a r t i c l e i n f o

Article history:Received 20 April 2014Received in revised form9 July 2014Accepted 14 July 2014Available online 12 August 2014

Keywords:Acousto-optic tunable lterTemperatureAxial strain

a b s t r a c t

The temperature and axial strain characteristic of the cladding etched single-mode ber based acousto-optic tunable lter (CE-SMF-AOTF) were described in the simulation and experiment. In the simulation,the CE-SMF-AOTF had a linear wavelength shift response to the temperature and axial strain, and thelter with small ber diameter was more sensitive to the temperature and axial strain than it with largeber diameter. In the experiment, the temperature and axial strain characteristic of the CE-SMF-AOTFwith ber diameters of 39 m and 67 m were measured. The experimental results accorded well withthe simulated ones.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Optical lters are key components for optical communicationsystems. Due to their tunable spectra, the lters can be used inoptical signal processing [1], wavelength selection [2] and opticalampliers [3]. Currently, the common optical lters include bergratings [46], acousto-optic tunable lters (AOTFs) [2], MachZehnder interferometer lters [7], FabryPerot lters [8] and so on.Among these tunable lters, the AOTFs have the advantages ofwide tunable range, good switching speed, and easy electriccontrol. Particularly, all-ber AOTFs have good compatibility withoptical ber communication systems. Therefore, there is a livelyinterest in the design of all-ber AOTFs to obtain tunable complexspectra. In 1997, an all-ber AOTF based on single-mode ber(SMF) was rst demonstrated by Kim et al. [9], and in order toenhance the coupling efciency, Li et al. designed a claddingetched SMF based AOTF (CE-SMF-AOTF) in 2002 [10]. Other typesof all-ber AOTFs are also proposed with the components such astaper ber [11] and ber grating [12,13]. For the application ofthese all-ber AOTFs, it is signicant to understand the effects ofvarious external perturbations such as temperature uctuationand axial strain on the device performance. It is because thetemperature and axial strain characteristic of the lter largelydetermine its packaging structure. There have been a few reportson the axial strain characteristics of some all-ber AOTFs [1417].In 2006, Li et al. analyzed the axial strain characteristic of the ber

taper based AOTF [15], but the variation of the ber which isinduced by the strain, is negligible. In 2009, Lee et al. reported theaxial strain characteristic of SMF based AOTF by consideration ofthe combination of acoustic and optical effects [16], but thevariation of the ber diameter has not been fully considered inthe analysis of this AOTF. To the best of our knowledge, no reportwas appeared on the temperature characteristic of the CE-SMF-AOTF.

In this paper, the temperature and axial strain characteristic ofthe CE-SMF-AOTF with different ber diameters are demonstratedin the simulation and experiment. In the simulation, the opticalresonant wavelength shift of the lter is explained by the combi-nation of the acoustic and optical effect in the ber which aresignicantly affected by the temperature and axial strain. In theexperiment, the lter with different diameters are measuredunder several temperatures and axial strains.

2. Operation of the CE-SMF-AOTF

As shown in Fig. 1, the CE-SMF-AOTF is composed of thecladding-etched single mode ber, the silica horn and the PZT.When the electrical signal is loaded on the PZT, the PZT vibrates upand down, creating a exural acoustic wave in the ber. Afterpropagating over the acousto-optic (AO) interaction region wherethe ber cladding is etched, the exural acoustic wave is absorbedby the ber coating layer. The exural acoustic wave bends theber and changes the refractive index distribution of the ber,periodically. When the ber is assumed to vibrate in the yz plane(vertical plane), the change of the refractive index n can be

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Optics & Laser Technology

http://dx.doi.org/10.1016/j.optlastec.2014.07.0120030-3992/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author.E-mail address: lipei@bjtu.edu.cn (L. Pei).

Optics & Laser Technology 65 (2015) 131136

expressed as [11]

nx; y; z n01k2aS0y cos kaz 1where n0 is the effective local index, is the elasto-opticcontribution to the index change, ka 2=a is the vector of theacoustic wave, S0 is the amplitude of the exural acoustic wave,and a is the acoustic wavelength.

The change of the refractive index in the ber causes thecoupling from the HE11 mode in the core to the HE21 mode in thecladding at the resonant wavelength where the phase matchingcondition is satised: the acoustic wavelength ashould be thesame as the optical beat-length LB between the core mode HE11and the cladding mode HE21 [14],

a LB 2

11212

where 11 and 21 are the propagation constants of the core modeHE11 and the cladding mode HE21, respectively.

Then the HE21 mode is absorbed by the ber coating layer,giving rise to a wavelength notch in the transmission spectra. Thecoupled mode equations between the HE11 mode and the HE21mode can be given by [11]

dE11dz

iKseiszE21 0;dE21dz

iKse iszE11 0 3

where E11 and E21 are mode eld intensity of the HE11 mode andthe HE21 mode respectively, Ks is the AO coupling coefcient, ands 11212=a is a detuning parameter that is zero at theoptical resonant wavelength, respectively.

3. The temperature characteristic of the CE-SMF-AOTF

When the temperature of the CE-SMF-AOTF varies, the acousticwavelength a and the optical beat-length LB change, leading tothe shift of the optical resonant wavelength. In a cylindrical opticalber, the ber diameter is much smaller than the acousticwavelength of lowest order exural acoustic wave. Therefore, the

frequency f a of the exural acoustic wave can be expressed as [16]

f a 2

2a

EaIaS

1

2aTa

42EaIa

!" #1=24

where Ea, Ia, , S and Ta are Young's modulus, the area moment ofinertia, the ber density, the cross-sectional area of the ber, andthe initial tension in the longitudinal direction of the ber,respectively. When the temperature changes T , because the areamoment of inertia and the initial tension can be given by

Ia 4

d2

4; Ta EaS

ll EaST ; 5

respectively, the acoustic wavelength a of the lowest orderexural acoustic wave can be expressed as

a Cext2

pf a

T

T2 f a

Cext1Td

2svuut 6where Cext is the speed of the acoustic wave in ber, f a is theacoustic frequency, is the thermal expansion coefcient of theber, and d is the ber diameter. For silica, the values of Cext and are about 5760 m/s and 5:5 107=oC, respectively.

Based on Eq. (6), the relationship between the acoustic wave-length a and the ber diameter d can be obtained, as shown inFig. 2. In the simulation, the acoustic frequency f a is 0.9 MHz. Thegraph shows that the acoustic wavelength decreases with thedecrease of the ber diameter, and when the temperatureincreases, the acoustic wavelength also increases.

When the temperature changes T , the parameters of the bervaries. According to the thermal expansion effect and thermo-optic effect, the radius and refractive index of ber core and bercladding are changed as [18]:

for the ber core,

rco rco0 1T; nco nco0 1coT; 7for the ber cladding,

rcl rcl0 1T; ncl ncl0 1clT; 8where rco0 and r

cl0 are the initial radius of the ber core and ber

cladding, nco0 and ncl0 are the initial refractive index of the ber core

and ber cladding, co and cl are the thermo-optic coefcient ofthe ber core and ber cladding, respectively.

Fig. 3 shows the relationship between the effective refractiveindex of the ber mode (HE11 and HE12) and the ber diameter d.The calculation is based on Eqs. (7) and (8), and the characteristicequation for the core mode and the cladding mode which areobtained from the step-index ber geometry [19]. In theFig. 1. The schematic for measurement of the CE-SMF-AOTF.

Fig. 2. Acoustic wavelength as a function of the ber diameter for three differenttemperatures.

Fig. 3. The relationship between the effective refractive index of the ber modeand the ber diameter for three different temperatures.

C. Liu et al. / Optics & Laser Technology 65 (2015) 131136132

simulation, the parameter values are listed as: rco0 4:1 m,nco0 1:4682, ncl0 1:4631

co 8:06 106, cl 7:80 106. Asshown in Fig. 3, in the same temperature, with the decrease of theber diameter d, the effective refractive index of the core modeHE11 is constant while the effective refractive index of the claddingmode HE12 decreases. Meanwhile, with the increase of thetemperature, the effective refractive index of the core mode HE11and the cladding mode HE12 increase.

Fig. 4 illustrates the calculated transmission spectra of the CE-SMF-AOTF under various temperatures which can be obtainedfrom the coupled mode equations Eq. (3). In the calculation, theacoustic frequency f a is 0.9 MHz, and because the AO couplingcoefcient in the smaller ber diameter should be higher [10], theAO coupling coefcient Ks with the d of 39 m is 0:84K0 while theAO coupling coefcient Ks of the lter with the d of 67 m is0:66K0, where K0 is the characteristic coupling coefcient of thelter when the core mode HE11 is completely coupled to thecladding mode HE12. As shown in Fig. 4, when the temperatureincreases, the optical resonant wavelength of the CE-SMF-AOTFmoves to the longer wavelength region. Comparing Fig. 4(a) withFig. 4(b), when T increases from 0 1C to 40 1C, the opticalresonant wavelength of the lter with the d of 39 m moves from1660.22 nm to 1665.68 nm while the optical resonant wavelengthof the lter with the d of 67 m moves from 1740.93 nm to1745.50 nm. It means that the optical resonant wavelength shiftsfurther in the smaller ber diameter which is also shown in Fig. 5.Fig. 5 plots the relationship between the optical resonant

wavelength shift and the variation of temperature T . Thegraph shows that is proportional to T , and the slope of thelter with d of 39 m is larger than the lter with d of 67 mwhich means that the lter with small ber diameter is moresensitive to the temperature than the lter with the large berdiameter. Note that the 3 dB bandwidth of the CE-SMF-AOTFwith d of 39 m is larger than the one with d of 67 m. It is due tothe decrease of the ber diameter d [20].

The experimental measured spectra of the CE-SMF-AOTF forseveral temperatures at xed acoustic frequency of 0.9 MHz, isshown in Fig. 6. In Fig. 6, the lter with d of 39 m has a highertransmissivity than the one with d of 67 m. When the tempera-ture adds from 15 1C to 55 1C, the optical resonant wavelength ofthe lter moves 5.68 nm and 4.81 nm towards long wavelength,corresponding to d of 39 m and 67 m respectively. This varia-tion trend is similar to Fig. 4. Fig. 7 plots the relationship betweenthe measured resonant wavelength shift of CE-SMF-AOTF and thetemperature. As shown in Fig. 7, the lter has a linear wavelengthshift response to the different temperatures. The slope betweenthe optical resonant wavelength and the temperature in the lterwith d of 39 m, is larger than the one in the lter with d of67 m. Due to the linear response of the resonant wavelength tothe temperature, this lter also can be used as a temperaturesensor. Note that the notch depths of the AOTF are sensitive to thevariation of the temperature, which is similar to temperaturecharacteristic of the mechanically induced long-period ber grat-ing [2123]. It is because the output strain of the PZT decreaseswith the increase of the temperature [24,25], weakening theamplitude of the exural acoustic wave S0. As a result, the AOcoupling coefcient Ks would reduce, resulting in the decrease inthe notch depths of the CE-SMF-AOTF.

4. The axial strain characteristic of the CE-SMF-AOTF

Similar to the temperature characteristic of the CE-SMF-AOTF,when the axial strain is applied on the AO interaction region of theAOTF, the optical resonant wavelength also changes, due to thevariation of the acoustic wavelength a and the optical beat-length LB. In the analysis, the axial strain is the tensile strain. BasedonEq. (4), the acoustic wavelength of the lowest order exuralacoustic wave under the axial strain can be expressed as

a Cext2

pf a

2 f a

Cext1d

2svuut 9

Fig. 4. The transmission spectra of the CE-SMF-AOTF for various temperatures. (a) the ber diameter d is 39 m, (b) the ber diameter d is 67 m.

Fig. 5. The optical resonant wavelength shift of the CE-SMF-AOTF as a function ofthe temperature.

C. Liu et al. / Optics & Laser Technology 65 (2015) 131136 133

where is Poisson's ration. For silica, the value of is 0.16. Fig. 8shows the acoustic wavelength a as a function of the berdiameter d under the axial strain of 0 , 450 , and 900 . Inthe calculation, the value of acoustic frequency f a is also 0.9 MHz.As shown in Fig. 8, the acoustic wavelength decreases with thedecrease of the ber diameter in the same axial strain, and theacoustic wavelength also increases when the axial strain increases.

When the axial strain is applied on the CE-SMF-AOTF, thecore and cladding of the ber become an anisotropic positiveuniaxial crystal whose optical axis is parallel to the ber's axis, andthe refractive indices of the transverse and longitudinal electricelds in the ber would be different. According to the elasto-opticeffect, the transverse and longitudinal indices of the ber core andber cladding can be written as [26]:for the ber core,

ncot nco0 12nco30 p12p11p12;ncoz nco0

12nco30 p112p12

10for the ber cladding,

nclt ncl0 12ncl30 p12p11p12;nclz ncl0

12ncl30 p112p12

11where p11 and p12 are the strain-optic coefcients. For silica, thevalues of p11 and p12 are 0.113 and 0.252, respectively. In addition,according to the Poisson effect, the radius of the ber core andcladding would be changed as [26]

rco rco0 1; rcl rcl0 1 12

Based on Eqs. (10)(12) and the characteristic equation for thecore mode and the cladding mode which are obtained from thestep-index uniaxial ber geometry [26], the relationship between

Fig. 6. The experimental measured spectra of the CE-SMF-AOTF for several temperatures. (a) the ber diameter d is 39 m, (b) the ber diameter d is 67 m.

Fig. 7. The relationship between the measured resonant wavelength shift and thetemperature. The line is the linear tting, and the triangle and the cross are theexperimental data.

Fig. 8. Acoustic wavelength as a function of the ber diameter for three differentaxial strains.

Fig. 9. The relationship between the effective refractive index of the ber modeand the ber diameter for three different axial strains.

C. Liu et al. / Optics & Laser Technology 65 (2015) 131136134

the effective refractive index of the ber mode (HE11 and HE12) andthe ber diameter for three different axial strains can be shown inFig. 9. In the calculation, the values of nco0 , n

cl0 , and r

co0 are the same

as those applied in Fig. 3. In Fig. 9, with the decrease of the berdiameter d, the effective refractive index of the core mode HE11 isinvariable while the effective refractive index of the cladding modeHE12 decreases in the same axial strain. When the axial strainincreases, unlike the temperature-induced optical effect, theeffective refractive index of the core mode HE11 and the claddingmode HE12 decrease.

Fig. 10 demonstrates the calculated transmission spectra of theCE-SMF-AOTF under different axial strains which can be obtainedfrom the coupled mode equations Eq. (3). In the calculation, thevalues of the acoustic frequency f a and the AO coupling coefcientKs are the same as those applied in Fig. 4. As shown in Fig. 10,similar to the temperature characteristic, the optical resonantwavelength of the lter move to the longer wavelength region,and the wavelength shift of the lter with small ber diameter ismore than the lter with large ber diameter. Fig. 11 shows theoptical resonant wavelength shift as a function of the axialstrain. It shows that is also proportional to the axial strain, andthe slope in the lter with d of 39 m is larger than the one in thelter with d of 67 m. It means that the lter with small berdiameter has a higher sensitivity to the axial strain than the lterwith the large ber diameter.

Fig. 12 plots the measured spectra of the CE-SMF-AOTF forseveral axial strains at xed acoustic frequency of 0.9 MHz.

As shown in Fig. 12, with increase of the axial strain, the opticalresonant wavelength of the lter moves to the longer wavelengthregion. When the axial strain increases from 0 to 900 , theoptical resonant wavelength of the lter with d of 39 m shifts28.28 nm, which is larger than 10.58 nm of the lter with d of67 m. This variation trend is also similar to Fig. 10. Noted thatunlike the temperature characteristic, the notch depths of the lterare insensitive to the axial strain. It is because the acoustic energyis not affected by the axial strain, and therefore the AO couplingefciency in the ber can remains constant [16]. The measuredoptical resonant wavelength shift is shown in Fig. 13 as a functionof the axial strain. The optical resonant wavelength of the lter isproportional to the axial strain, as expected from Fig. 11, and theslope between the optical resonant wavelength and the axialstrain in the lter with d of 39 m, is larger than the one in thelter with d of 67 m. Due to the highly linear response of theresonant wavelength to the axial strain and good reproducibility,the axial strain can be used in the tuning the optical resonantwavelength, instead of changing the acoustic frequency.

5. Conclusions

The temperature and axial strain characteristic of the CE-SMF-AOTF are demonstrated and analyzed in the simulation andexperiment. The temperature and axial strain which are appliedin the lter, changing both acoustic and optical properties of theber, result in the optical resonant wavelength shift of the lter.Based on the coupled mode equations of the lter, the transmis-sion spectra of the lter with the ber diameter d of 39 m and67 m under different temperatures and axial strains are simu-lated. According to the simulation results, the optical resonantwavelength of the lter moves to the longer wavelength regionwhen the temperature or axial strain increase, and the opticalresonant wavelength shift is proportional to the variation of thetemperature or axial strain. The slope between the optical reso-nant wavelength and the temperature or axial strain increaseswith decrease of the ber diameter, which means the lter withsmall ber diameter is more sensitive to the temperature or axialstrain than the lter with large ber diameter. In the experiment,the transmission spectra of the lter with the ber diameter d of39 m and 67 m under different temperatures and axial strainsare measured. When the temperature adds from 15 1C to 55 1C, theoptical resonant wavelength adds 5.68 nm in the lter with d of39 m, which is larger than 4.81 nm in the one with d of 67 m;and when the axial strain increases from 0 to 900 , theoptical resonant wavelength of the lter with d of 39 m shifts

Fig. 10. The transmission spectra of the CE-SMF-AOTF for various axial strains. (a) the ber diameter d is 39 m, (b) the ber diameter d is 67 m.

Fig. 11. The optical resonant wavelength shift of the CE-SMF-AOTF as a function ofthe axial strain.

C. Liu et al. / Optics & Laser Technology 65 (2015) 131136 135

28.28 nm, which is larger than 10.58 nm of the lter with d of67 m. The variation trend of experimental results accord wellwith the simulated ones. These research results can be applied inthe designing the packing structure of the CE-SMF-AOTF, and usedas the temperature or strain sensor.

Acknowledgment

This work was supported by the Fundamental Research Fundsfor the Central Universities (No. 2014YJS028).

References

[1] Xin X, Zhang L, Liu B, Yu J. Dynamic -OFDMA with selective multicastoverlaid. Opt Express 2011;19:784755.

[2] Zhang WD, Huang LG, Gao F, Bo F, Xuan L, Zhang GQ, et al. Tunable add/dropchannel coupler based on an acousto-optic tunable lter and a tapered ber.Opt Lett 2012;37:12413.

[3] Flatow K, Hou H, Sorin W. Overview of dynamic gain-attening technologies.J Lightwave Technol 2002;19:1609.

[4] Dong XY, Yang XF, Shum P, Chan CC. Tunable WDM lter with 0.8-nm channelspacing using a pair of long-period ber gratings. IEEE Photon Technol Lett2005;17:7957.

[5] Dong XY, Shum P, Yang XF, Lim MF, Chan CC. Bandwidth-tunable lter andspacing-tunable comb lter with chirped-ber Bragg gratings. Opt Commun2006;259:6458.

[6] Xu O, Lu SH, Liu Y, Li B, Dong XW, Pei L, et al. Analysis of spectralcharacteristics for reective tilted ber gratings of uniform periods. OptCommun 2008;281:39905.

[7] Salceda-Delgado G, Martinez-Rios A, Monzn-Hernndez D. Tailoring MachZehnder comb-lters based on concatenated tapers. J Lightwave Technol2013;31:7617.

[8] Dong XY, Shum P, Chan CC, Yang XF. FSR-tunable fabry-Perot lter withsuperimposed chirped ber Bragg gratings. IEEE Photon Technol Lett2006;18:1846.

[9] Kim HS, Yun SH, Kwang IK, Kim BY. All-ber acousto-optic tunable notch lterwith electronically controllable spectral prole. Opt Lett 1997;22:14768.

[10] Li Q, Liu XM, Peng JD, Zhou BK, Lyons ER, Lee HP. Highly efcient acoustooptictunable lter based on cladding etched single-mode ber. IEEE PhotonTechnol Lett 2002;14:3379.

[11] Birks TA, Russell PSJ, Culverhouse DO. The acousto-optic effect in single-modeber tapers and couplers. J Lightwave Technol 1996;14:251929.

[12] Li ZX, Pei L, Liu C, Ning TG, Yu SW. Research on FBG-based longitudinal-acousto-optic modulator with Fourier mode coupling method. Appl Opt2012;51:73148.

[13] Liu C, Pei L, Li ZX, Ning TG, Yu SW, Kang ZX. Spectra analysis of nonuniformFBG-based acousto-optic modulator by using Fourier mode coupling theory.Appl Opt 2013;52:331823.

[14] Diez A, Kakarantzas G, Birks TA, Russell PSJ. High strain-induced wavelengthtunability in tapered bre acousto-optic lters. Electron Lett 2000;36:11878.

[15] Li H, Zhang Y, Wen CY, Soh YC. Design of tunable composite spectrums usingall-ber acoustooptical lters subject to strain control. J Lightwave Technol2006;24:1855.

[16] Lee KJ, Hwang I-K, Park HC, Kim BY. Axial strain dependence of all-beracousto-optic tunable lters. Opt Express 2009;17:234857.

[17] Kang Z, Liu C, Sun J, Ma L, You H, Jian S. Investigation on the cladding etchedsingle-mode ber acousto-optic tunable lter and its axial strain character-istics. Acta Opt Sin 2013;33:1206003.

[18] Zhang Z-J, Shi W-K, Gao K, Fang Z-J. Thermo-optic coefcient and temperaturesensitivity of long-period ber gratings. Opt Tech 2004;30:525 (-525).

[19] Erdogan T. Cladding-mode resonances in short- and long-period ber gratinglters. J Opt Soc Am A 1997;14:176073.

[20] Jin T, Li Q, Zhao JH, Cheng K, Liu XM. Ultra-broad-band AOTF based oncladding etched single-mode ber. IEEE Photon Technol Lett 2002;14:11335.

[21] Sohn KR, Peng G-D. Mechanically formed loss-tunable long-period bergratings realized on the periodic arrayed metal wires. Opt Commun2007;278:7780.

[22] Garca-de-la-Rosa LA, Torres-Gmez I, Martnez-Ros A, Monzn-HernndezD. Temperature impact on mechanically induced long-period ber gratings.Opt Laser Eng 2011;49:7147.

[23] Wang H-Y, Chuo S-M, Huang C-Y, Wang LA. Embedded corrugated long-periodber gratings for sensing applications. Appl Opt 2012;51:14538.

[24] Atushi O, Sadayuki T, Satoru T. Temperature characteristics for multilayerpiezoelectric ceramic actuator. Jpn J Appl Phys 1985;24:209.

[25] Wang D, Fotinich Y, Carman GP. Inuence of temperature on the electro-mechanical and fatigue behavior of piezoelectric ceramics. J Appl Phys1998;83:534250.

[26] Zhang Z, Shi W. Eigenvalue and eld equations of three-layered uniaxial bersand their applications to the characteristics of long-period ber gratings withapplied axial strain. J Opt Soc Am A 2005;22:251626.

Fig. 12. The experimental measured spectra of the CE-SMF-AOTF for several axial strains. (a) the ber diameter d is 39 m, (b) the ber diameter d is 67 m.

Fig. 13. The relationship between the measured resonant wavelength shift and theaxial strain. The line is the linear tting, and the triangle and the cross are theexperimental data.

C. Liu et al. / Optics & Laser Technology 65 (2015) 131136136

Temperature and axial strain characteristic of cladding etched single-mode fiber based acousto-optic tunable filterIntroductionOperation of the CE-SMF-AOTFThe temperature characteristic of the CE-SMF-AOTFThe axial strain characteristic of the CE-SMF-AOTFConclusionsAcknowledgmentReferences