A modulator is reported in which an extensional acoustic wave is launched along a fiber Bragg grating. The acousto-optic superlattice effect causes an enhancement in reflectivity within a narrow spectral region on both sides of the Bragg wavelength. For a fixed acoustic propagation direction, the Doppler shift can be either positive or negative, depending on whether the wavelength of the incident light lies above or below the Bragg condition. The device can function as a Bragg cell and a tunable filter

Dong, L.

Liu, W.F.

Russell, P.St.J.

English

Southampton (e-Prints Soton)

1Southampton SO17 1BJ,  UKTelephone: +44 1703 593150e-mail:   light@orc.soton.ac.ukOptoelectronics Research CentreUniversity of SouthamptonAcousto-optic superlattice modulator using a fiber Bragg grating W.F.Liu, *P.St.J.Russell and L.Dong *Optoelectronics Group, School of Physics, University of Bath, Bath BA2 7AY, UK AbstractA modulator is reported in which an extensional acoustic wave is launched along a fiber Bragggrating. The acousto-optic superlattice effect causes an enhancement in reflectivity within a narrowspectral region on both sides of the Bragg wavelength. For a fixed acoustic propagation direction, theDoppler shift can be either positive or negative, depending on whether the wavelength of the incidentlight lies above or below the Bragg condition. The device can function as a Bragg cell and a tunablefilter. All-fiber acousto-optic devices have potential uses as frequency shifters, multiplexers, modulators,and tunable filters. The ease with which these devices can be spliced into systems, and theconsequent low insertion loss, make them an attractive alternative to pigtailed bulk Bragg cells.Previous designs of intermodal coupler include dual-mode fibers supporting an acoustic flexuralwave [1,2], coupling between the polarization normal modes of a high-birefringence fiber  bymeans of a torsional acoustic wave [3], and a high-performance device based on a four-portfused-taper null coupler [4]. All these devices share the requirement that the acoustic wavelengthmust match the intermodal beat ength, L = 2B/)$, where )$ = *$   - $ * and $  and $  are theB      2   1   1  2propagation constants of the modes. In this Letter we describe a modulator (briefly reported for the fist time in Ref. 5) in which a fiberBragg grating is excited by an axially propagating extensional acoustic wave. The underlyingprinciple is acousto-optic superlattice modulation (AOSLM), first proposed in 1986.[6,7]   IAOSLM the counterpropagating optical modes (the Bloch waves [8]) of the fine-pitch Bragggrating are coupled by a course-pitch acoustic wave, the superposition of the two forming asuperlattice. Coupling is maximum when the inter-Bloch-wave beat period matches the acousticwavelength. The forward-travelling (group velocity in the +z direction) Bloch wave in a fiber Bragg gratingcan be closely approximated as a constant superposition of two coupled counterpropagatingguided modes with wave vectors k in the form [8]k = {±K + h [1 - (26 / h) ] } /2, (1)2 ½where K = 2B/7 is the Bragg grating vector and 7 is its physical pitch. Coupling constant 6 anddephasing parameter h are defined as 6 = Mk/4 and h = 2k - K, where k = Tn /c is the averageo     o    o  owave vector in the Bragg grating, n is the modal phase index, and M is the modulation depth ofOthe dielectric constant, i.e.,  = n (l + M cos Kz). Reversing the sign of h i  Eq. (1) yields ther  O2wave vectors of the complementary backward-travelling Bloch wave. The presence of two wavevectors in each Bloch wave, combined with their strong dispersion with fr quency (forming a stopband in the range -26 <h < 26), yields three different acousto-optic resonance conditions asopposed to one in normal fiber. Two of these conditions are at approximately the usual Brillouinfrequencies (~10GHz at 1530nm). The third, which concerns us in this Letter, is indicated on theT - k diagram in Fig. 1.  This condition occurs between the two forward (and the two backward),(z)& n 2oMn 2o' cos[Kz % asin(ksz)]' Jo(a) cosKz % jxn'1Jn(a)[cos(Kz %nksz)% (&1)n cos(Kz & nksz)],2Fig. 1. Frequency wave-vector diagram for a Bragggrating. The group velocity is proportional to theslope of the curves. In case A, a forward-travellingacoustic wave [(T , k ) vector shown by the arrows  sfrom b  to f ] couples a forward-travelling Blochl  lwave (f ) into a downshifted backward one (b ).  Inl       lcase B, forward Bloch wave f  is coupled into2anomalously downshifted backward Bloch wave b2by backward-travelling acoustic wave.  The thickhorizontal dashed lines join the (T, k) points of theforward and backward fiber modes of each Blochwave.wave vectors of the two Bloch waves and has an associated frequency shift that can lie between 0 and several hundredmegahertz (for clarity, acoustic frequency shift T  is exaggerated in Fig. 1).  Note that insone-dimensional photon-photon scattering the two-vector (T, k) must be conserved, i.e., (T ,outk ) - (T , k ) = (T , k)~ where the frequency components must all be positive (acousticout   in  in   S  sparameters have the subscript ); we ensure this by choosing the input and output two-vectors sosas to make T  - T  = T  0.  The group velocity of each Blo mode is given by *T/*k = ±(c/n)out  in  s >               o[1 -(26/h) ]  which tends to zero at each stop-band edge and changes sign on opposite sides of2 ½the lines k = ±K/2. An intriguing feature of superlattice coupling is that the direction of theDoppler shift can be reversed. On the upper stopband banch, n acoustic wave travelling into theincident Bloch mode will produce a frequency-upshifted reflected Bloch mode. On the lowerstop-band branch, however, thereflected mode will be anomalouslyfrequency downshifted. As we showbelow, these predictions areconfirmed by experiment. An acoustic wave of average powerP will produce a peak strain of s =s       O[2P /(EA< )] ~ where E is Young'ss gs½modulus, A is the fiber area, and <gsis the acoustic group velocity.  Thisstrain field will sinusoidally modulateboth the average index and the pitchof the grating. Close to thestop-band edges, where the groupvelocity is very small, both of theseeffects are significant.  Further fromthe stop-band edges, however, pitchmodulation dominates. Since thacoustic wave travels some 10 x5more slowly than the light, weignore its temporal dependence(while remembering the Dopplershift). For a strain field in the forms(z) = s cos (kz)~ the resultingO  srelative dielectric constant ,(z) isgiven by (2)c)882. )< ' c2nofs<s2%6B2½.cfs2no<s,3Fig. 2. Experimental setup for monitoring the responseof AOSLM. Light from a tunable single-frequencydiode laser (TL) is divided at a fused taper coupler(FC1), one half going to the fiber Bragg grating (FBG)and the other to a bulk Bragg cell (BC).  The lightreflected from the AOSLM is combined with thefrequency-shifted light from the Bragg cell at a secondcoupler (FC2), and the mixed signal is detected at asquare-law detector (D); the redundant light in thesecond arm of FC2 is eliminated in an index-matchingcell (IMC). A piezoelectric transducer (PZT) and afused-silica horn (SH) are used to excite the AOSLM.Fig. 3. Reflectivity spectrum of the undistributedBragg grating (top) and the spectrum of theenhancement in reflectivity due to the acoustic wave(bottom). here a = Ks/ks.  It is clear that aOsequence of ghosts of the originalfiber grating forms at spatialfrequencies given by successivespatial sidebands of K.  Theamplitudes of these sidebands aregiven, for small argument *a* <<1,by J (a) . a/ (2n!).  The AOSLMn n  nresonance occurs when the acousticwave vector matches thewave-vector difference between twoBloch waves. This leads to thecondition(3) where f and <  are the acoustics  sfrequency and the phase velocity and)< and )8 are the optical frequencyand wavelength shifts from theBragg condition of the fiber grating.The approximate expression on theright-hand side of Eq. (3) is validwhen the AOSLM condition occursfar from the Bragg condition. Forbulk silica <  is 5760 m/s, and givensour experimental value of 6 =1.3/mm, Eq. (3) shows that AOSLMresonance will occur, e.g., at NMfrom the Bragg wavelength if theacoustic frequency is 15MHz (NB:<  falls when the acousticswavelength is comparable with thefiber radius [9]).  It can be shownthat the coupling constant betweenthe counterpropagating Bloch wavesat the first sideband in Eq. (2) isgiven approximately by 6 =16J (Ks /k) . 6Ks /(2k).  Figure 21 0 s   0 sshows the experimental setup. Thefiber grating was written with aphase mask in a boron-codopegermanosilicate fiber (N.A., 0.115;cutoff, 1300nm).  The UV sourcewas an ArF excimer laser at 193nm.The grating was 3mm long, with a4Fig. 4. RF spectra at the detector for sidelobesat 8 > 8  (top) and 8 < 8  (bottom).  The peakB     Bat 8MHz is caused by beating between theunshifted and the shifted Bragg gratingreflections.  The presence of a band on thelow-frequency side of the 80MHz referencesignal indicates that the AOSLM signal isfrequency upshifted. bandwidth of 0.7nm, a Bragg wavelength of 1526.5nm, and a coupling constant 6 = 1.3/mm.  Apiezoelectric transducer, bonded to a silica horn and driven by a rf signal generator, was used asthe source of acoustic waves.  The diameter of the silica horn was tapered from 3mm to 125µmover a distance of ~7cm.  One end of the fiber grating was spliced directly to the horn.  To testwhether the light reflected from the grating is upshifted or downshifted, the light was mixed at asquare-law detector with light frequency shifted in a conventional Bragg cell.  We found that theinterface loss between the transducer and the silica horn is a very important factor in obtainingefficient coupling of the longitudinal acoustic wave to the fiber grating.  The light was detectedat one of the output ports of 3dB coupler FC2, with the remaining port being immersed inindex-matching oil. The reflectivity spectrum of the undisturbed Bragg grating and the spectrum of the enhancementin reflectivity due to the acoustic wave are plotted in Fig. 3.  AOSLM is observed on both sidesof the stop band.  The acoustic frequency was 8.02MHz, and the electrical drive power to thetransducer was 350mW.  The wavelengths of AOSLM reflection were at 1525.3nm on theshort-wavelength side and 1527.6nm on the long-wavelength side.  The magnitude of thewavelength s ift )8 from Bragg wavelength is in each case approximately 1.15nm, and thebandwidth ofthe AOSLM effect is ~0.2nm. In a series of measurements of wavelength shift )8as a function of acoustic frequency (4 to 15.2MHz in steps of 1MHz) the agreement betweentheory [Eq. (3)] and experiment was better than a few percent. The results showed that AOSLMcould be used to form a tunable filter with a tuning rate of 0.15nm/MHz. The results of the heterodyne experiment are shown in Fig. 4.  A tunable single-frequency laserwas used, and the acoustic drive frequency was 8MHz.  On the short-wavelength side of theBragg condition the reflected light wasfrequency upshifted (conventionalDoppler effect), whereas on thelong-wavelength side it was downshifted(anomalous Doppler shift) as predicteby theory. Since the spatial sidebands produced bythe acoustic wave [Eq. (2)] can beregarded as weak ghosts of the strongpermanent Bragg grating, the FWHMbandwidth of the AOSLM effect isexpected to be that of a weak Bragggrating of the same length, namely, )8opt= 1.398 /(BLn ) where L is the fiber2 olength and the numerical factor relates tosinc(1.39) = 1/2.  For L = 3mm at 8 =21530nm this equation predicts )8 =opt0.23nm, which is in reasonableagreement with the experimental results.For small acoustic powers, it can beshown that the efficiency of conversion0 can be approximated by 0 . (6  L) =12 [6LJ (Ks /k)] . For the parameters in1 o s25our experiment 0 ~ 15%, and using the relationship given in the paragraph above Eq. (2) to relateacoustic power to s , it can be shown that of the 350mW electrical drive power, only 57mW isOactually reaching the Bragg grating as acou tic power.  Since the efficiency scales linearly withthe power and as the square of length, there is clearly scope for improving the AOSLM efficiencyby better acoustic transducer design, increasing the grating length, or using thinner fibers.  Someadvantages would result if the core was offset from the centre of the fib r and lexural waves wereused. Substantial improvements are expected with better acoustic transducer design, a longer fibergrating, and thinner fiber. References 1. B.Y.Kim, J.N.Blake, H.E.Engan and H.J.Shaw, Opt. Lett. 11, 389 (1986). 2. J.N.Blake, B.Y.Kim, H.E.Engan and H.J.Shaw, Opt. Lett. 12, 281 (1987). 3. M.Berwick, C.N.Pannell, P.St.J.Russell and D.A.Jackson, Electron. Lett. 27, 713 (1991).4. T.A.Birks, S.G.Farwell, P.St.J.Russell and C.N.Pannell, Opt. Lett. 19, 1964 (1994);erratum, Opt. Lett. 21, 231 (1996).5. W.F.Liu, P.St.J.Russell, D.O.Culverhouse and L.Reekie, in Confere ce on Lasers andElectro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America,Washington, D.C., 1996), pp. 243-244. 6. P.St.J.Russell, Phys. Rev. Lett. 56, 596 (1986).7. P.St.J.Russell, J. Appl. Phys. 59, 3344 (1986). 8. P.St.J.Russell, J. Mod. Opt. 38, 1599 (1991). 9. H.Kolsky, Stress Waves in Solids (Oxford U. Press, London, 1953), Chap III. 

Acousto-optic superlattice modulator using Fibre Bragg grating

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