Acousto-optic Effect in microstructured Polymer Fiber Bragg Gratings: Simulation and Experimental Overview

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1 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMER (DOULE-CLICK HERE TO EDIT) < 1 Acousto-optc Effect n mcrostructured Polymer Fber ragg Gratngs: Smulaton and Expermental Overvew Carlos A.F. Marques, Lúca lro, Lutful Kahn, Roberson A. Olvera, Davd J. Webb, Member, IEEE, and Rogéro N. Noguera, Member, IEEE Abstract A fne control of the mcrostructured polymer fber ragg gratng spectrum propertes, such as maxmum reflected power and 3-d bandwdth, through acousto-optc modulaton s presented. For smulaton purposes, the devce s modelled as a sngle structure, comprsng a slca horn and a fber ragg gratng. For smlar szed structures a good correlaton between the numercal results and the expermental data s obtaned, allowng the stran feld to be completely characterzed along the whole structure. It s also shown that the mcrostructured polymer fber ragg gratng requres less effort from the pezoelectrc actuator to produce modfcaton n the gratng spectrum when compared wth a slca fber ragg gratng. Ths technque has potental to be appled on tunable optcal flters and tunable cavtes for photonc applcatons. Index Terms Mcrostructured polymer optcal fbers, Acousto-optc modulaton, Fber ragg gratngs. P I. INTRODUCTION OLYMER optcal fbers (POFs) are startng to be consdered a vable alternatve to slca fbers (SF) n applcatons such as short dstance transmssons [1, 2], sensng [3, 4], Terahertz wavegudes and flters [5], manly due to ther flexblty, larger core and smple connecton. One of the major drawbacks ponted to POFs s the greater attenuaton coeffcent comparng to SF, a fact that lmts ther applcatons. However, recent studes show that the use of fluornated polymers as core materals sgnfcantly reduces losses [6]. In-fber ragg gratngs (FGs) are ponted out as an nterestng devce for performng all-optcal sgnal processng Manuscrpt receved November14, 2012; revsed XXXX XX, 2012, XXX XX, 2012; accepted XXX XX, 2012.Date of publcaton XXX XX, The Fundação para a Cênca e a Tecnologa (FCT) Projects PTDC/EEA- TEL/114144/2009 and PTDC/EEA-TEL/122792/2010 are acknowledged. Carlos A. F. Marques and L. lro were supported by FCT under the SFRH/D/70661/2010 and SFRH/PD/78205/2011 scholarshps). Carlos A. F. Marques, Lúca lro, Rogéro N. Noguera are wth the Insttuto de Telecomuncações, Pólo de Avero, Avero, Portugal (emal: cmarques@av.t.pt, luca.blro@av.t.pt, rnoguera@av.t.pt). Lutful Kahn, Davd J. Webb are wth the Aston Insttute of Photonc Technologes, Aston Unversty, rmngham, 4 7ET, UK (e-mal: khanmlh1@aston.ac.uk, d.j.webb@aston.ac.uk). Roberson A. Olvera s wth the Volvo GTT - Advanced Technology & Research, Av. Juscelno K. Olvera, 2600, , Curtba, razl (emal: roberson.olvera@volvo.com). and sensng, however most FGs referenced n the lterature are nscrbed n SFs. On the other hand, for very short dstance transmssons, POFs present advantages compared wth conventonal optcal fbers, such as easy non-sklled handlng and ruggedness. The scentfc communty has been nvestgatng the possblty of nscrbng FGs n such fber. A specal type of POF s the mcrostructured POF (mpof). Its geometry provdes dfferent propertes compared to a step ndex fber, such as an endlessly sngle-mode, ar-gudng operaton and the ablty to expose the optcal feld of the guded modes to substances present n the holes. The frst FG nscrbed n mpof was obtaned usng a low-power helum cadmum (HeCd) laser at 325 nm [7]. The resultng ragg gratng had a ragg wavelength (λ ) of 1536 nm and a length of 10 mm. On the other hand, the acousto-optc (AO) effect s an mportant, fast and accurate mechansm that can be used to change and control several of the propertes of ragg gratngs n SF and tapered fbers. It has been successfully appled n the desgn and constructon of varous low nserton loss alloptcal processng devces such as a tunable optcal notch flter [8], tunable mode coupler [9], complex ragg gratng wrtng [10], gan equalzaton flter [11], among others. Concernng ts mechancal propertes, t s expected that the AO effect n mpof would be more evdent due to ts lower acoustc mpedance so mprovng the performance compared to the SF based devces. Therefore, ths work demonstrates a fne control of the mpof ragg gratng (mpofg) spectrum propertes through the AO modulaton. The nteracton between an acoustc wave (AW) generated by longtudnal exctaton and the wrtten ragg gratng s presented. For smulaton results, we apply the Fnte Element Method (FEM) and Transfer Matrx Method (TMM) for desgnng an mpofg acousto-optc modulator (mpofg-aom). The FEM approach allows the complete characterzaton of the stran feld caused by the acoustc wave along the structure whle the TMM s used to obtan the spectrum of the correspondng chrped gratng. A smlar theoretcal approach s used to calculate the spectral response of an mpofg embedded n a host materal system. Followng the theoretcal consderatons, expermental results are also presented.

2 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMER (DOULE-CLICK HERE TO EDIT) < 2 II. THEORETICAL ACKGROUND The FEM was ntroduced n the late 1950s n the arcraft ndustry [12]. The man advantages of the method are: the capablty of modellng complex geometres, the consstent treatment of dfferental-type boundary condtons, and the possblty to be programmed n a flexble and general purpose format [13]. As the structure modelled here presents a varable shape along the longtudnal axs, the FEM s best suted to study the problem wth the requred accuracy. Fg. 1 shows the 1-D dscretzaton of the FG-AOM, whose man parts are the slca horn and fber contanng FG. The structure s composed of N one-dmensonal elements of length Δz = L D /N separated by nodes, where L D s the total length of the FG- AOM. Each element s assocated wth a value that represents the area of the structure at that secton. Fg. 1. Dscretzaton of the FG-AOM n lnear elements. Each element has a characterstc functon area. The dfferental equaton of moton that represents the acoustc wave propagaton n the structure s known as: 2 u( z, t) u z, t E A( z) Az 0, 2 (1) z z t where u s the axal dsplacement, whch s dependent on the poston z and on the tme t, and du / dz s the longtudnal stran ɛ. The term Az () accounts for the varable sze of the structure along the z axs. E and ρ are the Young modulus and densty, assumed to be 72.5 GPa and 2200 kg/m 3 for the slca and 3GPa and 1180kg/m 3 for the polymer, respectvely. One assumpton establshed was to neglect the dampng of the acoustc wave n the structure. The ntal and boundary condtons are defned as: du AE Pt PDC P0 exp( jwt) dz (2) z0 u LD, t 0 The external exctaton Pt () s appled as the combnaton of a constant load (P DC ) and a harmonc load of frequency w and ampltude P 0 generated by the pezoelectrc transducer (PZT). A classcal lnear approach for the fnte elements s employed. After the one-dmensonal dscretzaton, the fnal matrx form of the problem s gven by: Mu Ku P, (3) where u and u represent the nodal dsplacement and acceleraton vectors, respectvely. The vector P s the nodal generalzed force and has a null value, except for the frst component, assocated wth the node at z = 0. In ths expresson, M and K are the mass and stffness matrces of the structure, respectvely, obtaned by the superposton of the mass and stffness matrx of each element, whch are expressed as: e e A z 1 0 Mj and e e AE1 1 Kj, z 1 1 where superscrpt e represents an element wth partcular propertes. For the smulaton, the appled load s assumed as beng a concentrated pont load at the base (larger dameter) of the slca horn. Consderng the exctaton n the form of PPDC Pexp 0 ( jwt) and assumng a lnear system, the soluton of the problem can be found by solvng the equatons: Mu Ku P (6) DC DC DC, Mu Ku P exp jwt (7) t t 0. Eq. (6) represents the contrbuton of the component, P DC, whch s understood as a statc pre-tenson appled to the structure before the onset of the acoustc wave. Therefore, the acceleraton s null and (6) can be reduced to: 1 udc PDC. (8) K Snce the tme dependent load generated by the pezoelectrc s harmonc and u 0, the soluton for (7) has the form ut t u0 exp( jwt ). After replacng t n (7) one obtans: (4) (5) w M K u P (9) Note that u 0, the dsplacement vector soluton, s hghly dependent on the ampltude P 0 and frequency w of the acoustc wave. Thus, the complete soluton wll be gven by: u u u (10) DC 0. Once the dsplacement feld s obtaned, the stran feld n each of the fnte elements can be found by dfferentaton, as: e 1 e e u u. (11) z In ths case, as the fnte element s lnear, u e+1 and u e are the dsplacements n the local nodes e+1 and e, respectvely. On the other hand, the result for a unform gratng s an effectve refractve ndex (n eff ) perturbaton n the core descrbed by: 2π neff z n eff z1 υcos z Λ (12) where n eff s the average change of the effectve refractve ndex, s the frnge vsblty (assumed untary n ths work) and Λ s the gratng nomnal ptch. As the gratng mposes a delectrc perturbaton to the wavegude, t forces the couplng between the propagatng modes. The theory of coupled-modes [14, 15] s a useful and very well proven tool for descrbng ths behavor. The set of coupled frst-order dfferental equatons used to descrbe the propagaton s gven by: dr j ˆ Rz S z (13) dz

3 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMER (DOULE-CLICK HERE TO EDIT) < 3 ds * j ˆ S z Rz (14) dz where Rz () and Sz () represent the propagatng and counterpropagatng modes, respectvely; and the parameter k s defned as n eff. (15) In these equatons ˆ represents the general dc self-couplng coeffcent, whch s wrtten as a sum of two terms: ˆ 2 neff neff. (16) D In the frst term called detunng, 2 n s the desgn wavelength for a ragg scatterng wthn an nfntesmal varaton of the effectve ndex ( n 0),.e., a gratng that s nfntely weak. Ths above descrbed theory s applcable to unform gratngs, where the average refractve ndex change s constant. However, an acoustc wave wll lead to a chrp n the gratng, makng ts ptch non-unform. Therefore, the reflecton and transmsson spectra from the two-mode couplng theory can be calculated by consderng a pecewse approach, whereby the gratng s dvded nto dscrete unform sectons that are ndvdually represented by a matrx. The soluton s found by multplyng the matrces assocated wth each one of the sectons. The characterstc equaton s solved by equatng to zero the matrx determnant. The resultng polynomal enables the determnaton of the egenvalues. The gratng of length L can be treated as a quadrpole, as shown n Fg. 2. R and S represent the co-propagatng and counter-propagatng modes, respectvely. Fg. 2. ragg gratng n the core of an optcal fber. For convenence, the ampltude R (0) of the ncdent wave s normalzed, n such a way that the maxmum value s equal to the unt at the orgn (z = 0). Splttng the gratng n M unform sectons and defnng R and S as ampltudes of the felds across the secton, the propagaton s descrbed by: R R (17) T 1 S S1, where T s a 2x2 matrx gven by T ˆ cosh( Δ z) j snh Δ z j snh Δz, ˆ j snh Δ z cosh Δ z j snh Δz eff D eff (18) where z s the length of the th ˆ 2 2. The coeffcents ˆ unform secton and and k have local values at the th secton. Snce the matrces for each secton are known, the applcaton of the boundary condtons, R (0) 1 for z 0 L, causes the fnal equaton to be: and SL 0 for z R(0) R(L) 1 R(L), (0) T S(L) S(0) T 0 S where T M 1 T T T21 T 22 T and wrtng T n the form of T and smplfyng the Eq. (19), the result s: 1 T RL ( ) 11 (0) 12 ( ) S T R L (19). (20) The T 11 ~T 22 terms represent the gratng ampltude and phase response of the frst segment. From (20) one concludes that 1 RL. Therefore, the reflected ampltude for each T 11 wavelength can be found as (0) (0) 21 S S T, R(0) 1 T (21) 11 and the reflected power wll be gven by r ( ). III. COMPUTATIONAL SIMULATION Fg. 3 shows the steps of the algorthm for the acousto-optc effect smulaton. Frst, one s concerned wth the nput of the FG-AOM dmensons, such as the radus and the length of the slca horn and the length of the ragg gratng. In the second step the FEM s used to model the devce, whereby a desred load s appled to the base of the slca horn. The result s the stran feld calculated along the structure. However, only the stran feld n the FG regon s used as the nput to the Transfer Matrx method. The shft of the desgn wavelength along the z-axs as a functon of the stran feld s assumed as: D z D0 1 1 pe z (22) where p e s the photoelastc coeffcent and () z s the stran feld calculated n the prevous step through Eq. (11). It s mportant to note that ths equaton establshes the connecton between the two methods. Fnally, n the fourth step the TMM method gves the reflected and transmtted FG spectra. The structure s desgned usng nodes/m. Each pont along the structure corresponds to one element node. The quantty of nodes n the FG regon depends on ts length. For example, for L Gratng = 10 mm, there are 260 elements n the gratng regon, whch s enough to obtan an accurate stran feld for resonance frequences n study. The number of sectons n the TMM s chosen to be the same as the number of elements used n the FEM for the gratng regon. In the example, the dscrete 2

4 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMER (DOULE-CLICK HERE TO EDIT) < 4 structure s excted wth dfferent acoustc wave frequences of load ampltudes P 0 = 1.5 N and P DC = 0 N, where P 0 wll vary. Fg. 3. lock dagram of the FG-AOM smulaton. The mechancal propertes of the mpof can be acheved applyng the theory of homogenzaton [16] or applyng concepts of mxture rules of composte materals [17] used n ths work. In order to adjust the FEM appled to a conventonal FG, the effectve Young's modulus s calculated for the mpofg subtractng the equvalent amount of materal on the homogeneous polymer fber. Thus, the effectve transversal area s gven by: 2 Aeff An ( dh) (23) 4 where n s the number of holes, d h s the dameter of each hole and A s the transversal area of a crcle wth the same dameter of the fber. Ths way, the effectve Young's modulus for the mpof s gven by: Aeff E E, (24) A eff Aeff eff, (25) A where ρ s the densty of the polymer. Knowng the effectve area, the effectve Young's modulus and the effectve densty, one can calculate the stffness and mass matrces, used n the FEM analyss, treatng the mpofg as a homogeneous conventonal fber [18]. The applcaton of FEM to the mpof model can be performed assumng geometrcal symmetry for both man drectons wthn transversal secton. Here, we also consder the dmensons of the fber used (SF or mpof). IV. SIMULATION RESULTS AND DISCUSSION When an acoustc wave s coupled nto a fber where an FG s nscrbed t generates a standng mechancal wave. A detaled study of the natural vbraton modes of the mechancal structure can be found n lterature [22] and the man results wll be summarzed brefly here for completeness. The FEM modal analyss usng a commercal software (ANSYS) showed that: () most low frequency resonant modes generate flexural acoustcal waves; () longtudnal resonant modes are mostly observed n hgh frequency regmes (the acoustc longtudnal wavelength s small and the structure does not support the exstence of flexural waves); () at low frequency regmes, n an hybrd mode the flexural regme s domnant but there s also an nteracton wth a low frequency longtudnal acoustc wave. Flexural acoustc waves cause mcrobendngs n the fber and reduce the FG reflectvty consequently. The effect of the longtudnal wave n the FG modulaton plans depends on ts frequency namely the relatonshp between the acoustc wavelength and the FG length. If the acoustc longtudnal wavelength s lower than the FG length, the stran feld transferred to the FG has both compresson and rarefacton and addtonal bands appear on both sdes of the gratng reflecton spectrum. When the longtudnal wave s equal or longer than the FG length the compresson and/or rarefacton stran feld wll result n a shft of the ragg wavelenght or even cause a lnear varaton n the gratng perod (chrp). A. Stran feld behavour Fg. 4 shows the modulator response (PZT s coupled to the horn-fber system) n terms of fber dsplacements, whch s decomposed nto axal (z drecton) and transversal dsplacements (xy drecton). Although all analyzed acoustc modes have both components of the dsplacement feld, the longtudnal acoustc waves are characterzed by the larger dsplacements n z drecton. The transversal dsplacements are due to lower ampltude flexural oscllatons whch are polarzed n xy plane, transversally to the fber axs. Also, at lower frequences (flexural regme) the flexural acoustc waves are mostly characterzed by the larger dsplacements n xy drecton however, some dsplacements n z drecton are observed. Fg. 4. AOM frequency response n terms of the fber transversal and axal dsplacements. A numercal comparson of the mechancal propertes along mpofg-aom and the smlar structure wth slca FG (SFG) s performed. Fgs. 5 (a) and (b) detal the dmensons of the FG-AOM used n the FEM model (smlar to the expermental structure). A comparson of the stran feld along the mpofg-aom length and the smlar structure wth SFG-AOM s shown n Fgs. 5 (c,e)-(d,f), when the gratng length s L Gratng = 2 mm and 10 mm, respectvely. The stran feld was acheved by FEM consderng a snusodal exctaton source appled on the base of the slca horn wth resonance frequences (f R ) of 302 khz and 1 MHz, and load ampltudes

5 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMER (DOULE-CLICK HERE TO EDIT) < 5 P 0 = 1.5 N and P DC = 0 N. Accordng to the results presented n Fg. 4 and also consderng a decomposton of the stran feld, for 302 khz and 1 MHz the stran feld s presented by ts transversal and longtudnal component, respectvely. As can be seen n Fg. 5, the stran feld ampltude s hgher for the mpofg than for SFG due to ts smaller stffness. It s also verfed that the acoustc wavelength s shorter for the mpof, as expected. The behavor of the structure can be studed under the nfluence of parameters such as the frequency of the acoustc wave, the appled load or ts dmensons. Usng the dmensons gven n Table 1 the followng sectons detal the behavor of the reflected gratng spectrum as these parameters are vared. functon of the PZT exctaton frequency for the dmensons detaled n Table 1 (n ths case for 72 mm of nteracton length). When a longer pece of mpof s added on the set (the case of 80 mm nteracton length Table 1), t reduces the stffness of the fber, and a small shftng of the resonance frequences range happens. Also, comparng these data wth the results obtaned n [21] for SF, the resonance frequences are dstnct for mpof, as expected, due to the dfferent mechancal propertes (mpof and SF). The stran felds are much hgher than for SF, wth more than two orders of magntude. L Gratng = 2 mm L Gratng = 10 mm Fg. 6. Stran varaton versus the PZT exctaton frequency. Fg. 5. Dameter of the AOM structure as functon of the FG length: (a) 2 mm and (b) 10 mm. Superposton of stran felds for mpofg and SFG under the nfluence of the AO effect when gratng length s (c,e) 2 mm and (d, f) 10 mm. TALE I. FG LENGTH AND RESPECTIVE ACOUSTIC WAVE INTERACTION LENGTH OF THE HORN-FIER FG length (mm) 2 10 Interacton length: horn-fber (mm) For a gven devce dmenson the stran also vares wth the PZT exctaton frequency. The acousto-optc effect n the fber wll be enhanced when the exctaton of the natural resonant modes of the slca horn fber structure are best matched to the frequences delvered by the PZT. Prevous results show that all resonant modes measured n the PZT are agan observed n the combned structure, but wth slght changes n frequency values because the ansotropc constants used n smulatons dd not nclude the PZT losses [22]. Those losses reduce the mpedance-phase ampltude, whch affects the localzaton of some resonances by the condton of mnmum mpedance and null phase. Fg. 6 shows stran varaton as a. Frequency and load varaton Fg. 7 shows the gratng reflecton spectra calculated usng the theory and computatonal smulaton descrbed n Sectons II and III. y exctng the structure wth acoustc waves of dfferent frequences the gratng spectrum shows other characterstc wavelengths. We smulated the gratng reflecton spectra n mpof for three dfferent scenaros: () usng flexural regme at 126 khz (Fg. 7 (a)); () usng longtudnal regme at 1 MHz (Fg. 7 (b)) and 3.5 MHz (Fg. 7 (c)); () to obtan smlar spectral shape n SF and mpof (Fg. 6 (d)). For these scenaros the preload P DC s chosen to be null and the ampltude of the harmonc load P 0 s changed. The FG length s L Gratng = 2 mm. In the frst scenaro the PZT actuator works n the bendng regme at 126 khz as seen n Fg. 6 (a). It shall be noted that P 0 s much lower for mpofg due to smaller stffness n comparson wth the SFG (nset of Fg. 7 (a)). As expected, a decrease of the gratng reflectvty was acheved. In the second scenaro the PZT actuator works n the stretchng and compresson regme, wth symmetrc dsplacement ampltude as seen n Fg. 7 (b) and (c). Fg. 7 (b) shows also the gratng reflecton spectrum when P 0 = 0 N s appled at 1 MHz showng one central peak, λ 0. Applyng load, sde bands appear and f P 0 s ncreased, more sde bands appear but the central band s attenuated. The wavelength dfference between the central band and the sde bands s estmated as Δλ = λ 2 -λ 0 = λ 1 -λ 0 = λ 3 -λ 1 = λ 4 -λ 2 = 1.08 nm. The same dfference s obtaned between consecutve sde bands. Fg. 7 (c) shows a smlar behavor wth a hgher resonance frequency. The fgure also shows a greater dfference between the sde bands due to the frequency ncrease. To obtan smlar spectral shape n the SF and mpof, t was necessary to apply a lower resonance frequency as well as lower PZT load to the mpof as shown n the Fg. 7 (d). It shows that the mpofg requres less effort from the PZT actuator.

6 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMER (DOULE-CLICK HERE TO EDIT) < 6 Fg. 8. Stran behavor versus the slca horn (a, b, c) dameter and (d) length. Fg. 7. Reflected spectra when exctatons are appled wth frequency at (a) 126 khz, (b) 1 MHz and (c) 3.5 MHz. (d) Smlar spectral shape SF and mpof. The FG length s 2 mm. C. Influence of the dmensons The nfluence of the horn dmensons on the stran observed along the structure allows the optmzaton of each of ts parts. Applyng dfferent resonance frequences and PZT loads, the stran feld seen by the gratng can be modfed through changes n the dmensons of the slca horn. Fg. 6 shows the stran behavor as a functon of the dameter and of the length of the slca horn for SF and mpof. A modfcaton of the horn dmensons causes changes n the resonance frequences of the devce. Numercal results show that an ncrease of the slca horn base dameter causes an ncrease n the stffness and mass of the system, leadng to a decrease of the dsplacement and stran felds along the FG (Fgs. 8 (a) and (b)). Fg. 8 (c) shows the results when a low ampltude load of P 0 = 0.05 N s appled and we concluded that the stran felds are hgher for mpof, regardless of the appled voltage and resonance frequency. y smulaton results, the slca horn wth 1 mm of base dameter presents the best result n terms of stran feld. On the other hand, a change of the slca horn length does not cause sgnfcant varatons n these felds, as shown n Fg. 8 (d), and, once more, the mpof stran felds are much hgher than for SF regardless the resonance frequency and FG length. The stran feld s also hgher (more than one order of magntude n relaton to Fg. 8 (a)) when long FGs are used as shown n Fg. 8 (b). In fact, the observaton of the AO effect n a 2 mm gratng s already a sgnfcant result when compared to the same effect n a SF, whch requres a length of few centmeters to be notced. Furthermore, from the smulaton results we can observe effects of the dfferent FG lengths (such as 10mm length), allowng optmsaton for POF applcatons that requre FGs wth dfferent characterstcs such as bandwdth and/or reflected power, among others. V. EXPERIMENTAL REALIZATION AND RESULTS The ragg gratngs used to perform the experments were nscrbed n PMMA-based few mode mpof through the phase mask technque, usng a contnuous wave HeCd laser wth an output wavelength of 325nm and a power of 30mW. The mpof has an outer dameter of 150 μm and a core dameter of 15μm. The core s bounded by four rngs of holes as shown n Fg. 9 (a). Detals of the producton process of the mpof are descrbed n [19]. The laser beam was focused vertcally downward usng a 10-cm focal length cylndrcal lens, through a 1061nm perod phase mask and onto the fber. The mpof was lad on a v-groove and taped down usng polymde tape. Ths type of fber has a typcal nscrpton tme of 40 to 60 mn. The ragg wavelength of the nscrbed gratng was n the regon of 1570 nm wth a length of 2 mm, determned by the wdth of the UV laser beam. The nscrpton process was montored usng a 1550nm multmode μm slca fber coupler, a broadband lght source, and an optcal spectrum analyzer (OSA). For the nscrpton, a temporary connecton was made usng a FC/APC contact connector on a μm slca fber whch was then butt coupled to the bare POF usng an x-y-z translaton stage. A small amount of ndex matchng gel was used n the couplng to reduce Fresnel reflectons. After the nscrpton, the gratng was splced to a SF usng UV curable glue [20]. (a) (c)

7 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMER (DOULE-CLICK HERE TO EDIT) < 7 Fg. 9. (a) Mcroscope mage of end face of few mode mpof. (b) Acoustooptcal modulator desgn and geometrc propertes. (c) Schematc apparatus used to excte acoustc waves n the slca horn structure. The AOM s composed of a PZT (PZ26 model dsc - a slca horn and the mpof contanng the ragg gratng (see Fg. 9 (b)). The AOM s the same used n our prevous works [10,11]. The slca horn length s L horn = 50 mm, wth a base dameter Φ = 3 mm, a tp dameter Φ = 1 mm and central hole dameter Φ=150.5 μm. The ntal tenson of the FG s adjusted usng mcroresoluton translaton stages. The end of the fber s fxed n a holder, whch enables the generaton of an acoustc standng wave. The acoustc wave nteracton length of the horn-fber s 72 mm and 80 mm when the FG length s 2 mm and 10 mm, respectvely, as shown n the Table 1. It should be note that the acoustc wave nteracton length s the total length of the FG-AOM, L D. The set was swept over the range from 1 khz to 1.5 MHz to nvestgate the acoustc effects on the mpofg and to compare wth FG n slca fber. As one can see n Fg. 9 (c), the AOM s connected to an arbtrary functon generator and the reflected spectrum was montored by an OSA wth wavelength accuracy of 1 pm. Fg. 10 (a) shows that the acoustc exctaton at 77 khz leads to a broadenng of the FG spectrum, whch can be controlled by means of the PZT load (V PZT ). When the PZT load s set at 20V, the FG ampltude s totally suppressed. Ths result can be explaned consderng the couplng mechansm of the propagatng modes. The lower reflectvty of the gratng s due to changng perod along the gratng length that dsrupts the phase matchng, leadng to a lower couplng to the counter-propagatng mode [22]. For example, ths behavor can be used for add-drop multplexers n low frequency regmes. It should be noted that maxmum ampltude measurement of each spectrum s made between the values of nose background and man peak (Fg. 10 (a)). Fg. 10 (b) shows the spectral behavor of the gratng when the appled V PZT s changed between 0 V and 20 V and wth the acoustc wave frequency set at 77 khz. It s possble to control the 3-d bandwdth of the reflected spectrum by tunng the appled V PZT. As the PZT load s ncreased the phase msmatchng effect also ncreases. In the case of 3-d bandwdth measurements, results are presented for PZT loads up to 17 V, the maxmum measurable 3-d bandwdth value. For hgher loads, the FG s suppressed. Fgs. 10 (c-e) show the measured-smulated FG spectra when the gratng s excted wth the 77 khz resonance for dfferent V PZT. The measured spectra are compared to the modelled TMM spectra obtaned from prevously assessed FEM smulatons. At V PZT = 10 V the ampltude of the harmonc load delvered by the PZT s P 0 = 0.63 N (verfed through smulatons). The dfferences n reflectvty and wavelength bandwdth between measured-smulated results are due to gratng varatons orgnatng n the gratng nscrpton process. The expermental results show a good agreement wth the smulated data. (a) Fg. 10. (a) Spectrum behavor when a 77 khz frequency acoustc wave exctes the mpofg, varyng V PZT from 0 to 20 V. (b) 3-d FG bandwdth behavor as a functon of the PZT load (expermental results and smulated data) for an acoustc exctaton of 77 khz. FG measured-smulated spectra when (c) AW s OFF, (d) V PZT s 7 V (correspondng an ampltude of the harmonc load P 0 = 0.5 N) and (e) V PZT s 15 V (P 0 = 0.8 N). Fg. 11 (a) shows an example of spectral shapng when an acoustc exctaton of 193 khz s turned ON. In ths example, the sde lobe of the reflecton spectrum of the FG s suppressed, due to an nduced apodzaton, leadng to a better flter response. At 193 khz, the acoustc wavelength (~ 3.09 mm) s larger than the gratng length (L GRATING = 2 mm). Once the length between the PZT and the begnnng of the FG (60 mm) and the acoustc wavelength are known, the wave poston relatvely to the FG can be estmated,.e. the rato between them gve us the wave poston relatvely to the FG as shown n Fg. 11 (b). When acoustc wave s turned ON there s a maxmum of the standng acoustc wave at z = 0. Takng nto account the calculated standng wave perod, t s possble to wrte the FG n a wave zone whch nduces an apodzaton such as the center of the FG s postoned n a node (zero dsplacement see Fg. 11 (b)). In Fg. 11 (c), the acoustc exctaton of 214 khz results n a spectral broadenng of the FG. Ths may be a result of the gratng beng n the transton between the compresson and rarefacton stran felds, correspondng to both blue and red shftng of the λ. Therefore, ths behavor demonstrates a bandwdth tunng structure as a functon of the PZT load. (a) (b) (c) Fg. 11. (a) Gratng reflecton spectrum behavor when the AW s swtched ON (20 V) and OFF consderng a frequency at 193 khz.. (b) Dagram

8 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMER (DOULE-CLICK HERE TO EDIT) < 8 showng the wave poston relatvely to the FG. (c) Reflected spectrum behavor when the AW s swtched ON and OFF consderng a frequency at 214 khz. In ths expermental work the acoustc exctaton s only observed n low-frequency regme,.e. when the longtudnal acoustc wavelength s longer that the FG length (2 mm). Indeed, from Fg. 6 we can conclude that for a devce usng mpof, mostly resonance frequences are located below 1 MHz (shorter acoustc wavelength). At ths partcular frequency and for 3.5 MHz, the appearance of addtonal bands on both sdes of the gratng reflecton spectrum should be expermentally observed. Therefore, further developments wll be focused n the ncreasng of the FG length n order to ncrease the acoustc-optc nteracton length and thus mprove the peak reflectvty of the secondary lobules. VI. CONCLUSION In summary, we have demonstrated that the exctaton of an FG wrtten n mpof through acoustc waves can be attaned. Results show that t s possble to dynamcally control the propertes of the gratng spectra even wth a gratng length of 2 mm through the AOM, whch has not been possble n SFs. The FEM and the TMM present the advantage of calculatng the stran along the whole structure allowng the determnaton of the nfluence of the structure dmensons (horn, fber and FG szes) on the gratng reflected spectrum when an acoustc wave propagates along ts axs. Furthermore, the physcal characterstcs of the structure can be adjusted n order to obtan the desred stran and FG spectrum. The approach takes nto account the load nduced by the acoustc wave, whch can be assocated wth the characterstcs of the PZT actuator used for ts exctaton. The smulaton results obtaned usng the method correlate well wth expermental data. 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