Journl of Th-Qr Unversty No.3 Vol.4 December/008 Investgton phse n cse of Brgg couplng Hder K. Mouhmd Deprtment of Physcs, College of Scence, Th-Qr, Unv. Mouhmd H. Abdullh Deprtment of Physcs, College of Scence, Dyl, Unv. Sf F. Hssun Deprtment of Physcs, College of Educton, Almustnsyrh, Unv. Abstrct These results of nvestgton hve show hgher controllng possblty by lght wves dffrcton phses n cse Brgg couplng Dffrcton of sotropc, nsotropc ntercton whch tke plce smultneously. The occurrence source These dstncton cse of ntercton produced from ddtonl phse shft of lght pss through the ultrsonc wves meshes s dffrcton grtng,nd controllng by prmeters dul ntercton Through (Rmn-Nth) Prmeters. Ths evdent vrton n lght wves dffrcton phses ( 0,, ) whch rech to () wth wde rnge vlue of Rmn-Nth Prmeters (.95 > v, >.7 ) nd unppernce of jump n phse of dffrcted wve lght n ny order of dffrcton must be to tke n to consderton when the modern (Acousto-optcs) devces desgn. 48
Journl of Th-Qr Unversty No.3 Vol.4 December/008. Introducton The lser nventon hs led the development of cousto-optcs ntercton nd ts pplcton, mnly for grtng phse, deflecton, modulton nd sgnl processng. Techncl progresses n utlzton of effcent brefrngent crystls nd hgh frequency pezoelectrc trnsducer hve brought vluble beneft to cousto-optcs components mprovement[,,4]. In these types of nterctons cn show the lght dffrcton by ultrsound n crystls n usully s ccompned by chnge n optcl polrzton nd ntenstes, wth mportnt chnge n mtchng phse. All ths mportnt chnges cn be descrbe s sum of sngle collson, ech of whch nvolves the nnhlton of one ncdent photon t frequency (ω ) nd one phonon t frequency (Ω ) nd smultons creton of new (dffrcted) photon t frequency (ω d ) s. ω d = ω + Ω..() Whch propgtes long the drecton of scttered bem? The conservton of momentum requres tht the momentum ħ(k+k) of colldng prtcles be equl to the momentum ħk d of scttered photon,so tht. k d = k + K...() Therefore the dffrcted bem s shfted n frequency by n mount equl the sound frequency (Ω ) ths led ω d < ω. But were reversed the drecton of the sound bem, the sctterng process could be consdered s on n whch new photon (dffrcted photon ) nd new phonon re generted whle the ncdent photon s nnhlted. In ths cse, the conservton of energy from the two cse s [-5]. ω d = ω Ω..(3) Ths relton between the sgn of frequency chnge nd sound propgton drecton s consstent wth Doppler-shft. Ths phenomen whch occurs n sotropc nd nsotropc med smultneously lso n brefrngent crystls only or homogenous crystls [7,6]. The present nvestgton concentrtes on phses ddtonl n cse Brgg Couplng mtchng tht s tke plce durng so-clled mxed sotropc nsotropc dffrcton. As couplng ddtonl phses n up-down shfted regmes of ntercton, 48
Journl of Th-Qr Unversty No.3 Vol.4 December/008 n two orders dffrcton. Ths mter cqures the property of n optcl phse grtng for perod to the coustc wvelength.. Theory Prt Under The supposton of plne wves, the lght phse n ll dffrcton orders durng the ntercton of Brgg couplng phse ( ) n sotropc-nsotropc dffrcton whch occurs smultneously s ddtonl phse-shft.my be determne from system of coupled wves equton (s known) s functon of Rmn Nth prmeters ( v v nd v ) [,5 ]. l M P.......(4) Equton (4) show The Rmn-Nth prmeter s proportonl to the squre root of cousto optc fgure mert ( v M ). M 6 p n....(5) 3 V It s know tht ( M ) proportonl to the second power of effectve photoelstc constnt ( p or p ) provdng the sotropc or nsotropc cousto optc ntercton, M p nd ( ) M p [, 7]. ( ) Therefore the rto of Rmn-Nth prmeters durng the combned nterctons s equl The rto of effectve photoelstc constnts ( v effectve photoelstc constnts ( p, coeffcents of optcl ndctrx [3,6]. where v p p ).The vlues of p ) were found from the chnges of the The Brgg couplng phse n ddton to the ddtonl phses-shft (, ) (,) referrng to the sotropc nd nsotropc dffrcton respectvely. Correspondng system of couplng wves equton [].esly to obtn t where [ = tn - (y/x)] therefore the system of coupled wves Eg. Cn be wrtten s. 48
48 Journl of Th-Qr Unversty No.3 Vol.4 December/008 tn tn 4 tn 0 Sn Sn Cos Remrkble the relton between Rmn-Nth prmeters present, the rto v v s evluted on the bsc of the used brefrngent crystls, whch dependent on the type of coustc mode nd on the chosen crystl cut. 3.Results nd Dssecton From Eg. (6), clculton the chnges of phses couplng, re presented n two fgures ( nd ) s functon of Rmn- Nth prmeter v (expressed n untes of ). The fgures shows the grph of the phses ( 0,, ) of zeroth nd sotropc, nsotropc dffrcton orders respectvely, where The zeroth phses 0 s represented by squre curve whle the nsotropc dffrcton phse s represented by sold nd the sotropc dffrcton phse s represented by dshed curve. Here observed mportnt dfference between ll the fgures from where the stremlned t ll curves to reches mxmum vlue for chnge n phse, versus vlue of v whch n rnge (.7-.95)..... (6)
Journl of Th-Qr Unversty No.3 Vol.4 December/008 Moreover, more mportnt observton the cutoff product of phses (, ) up to vlue ( v = 0.5 ) occurs only wth rto v v = tht mens tht the cousto-optcs ntercton wll vnsh t lower vlues of Rmn- Nth prmeter v. On the other hnd, from fgure () the chnge n phse of zeroth order rech to vlue ( ) s the stremlned unform progressve wthout jump to ( ) drectly, s well know the Brgg trdtonl condton. It s evdent tht durng Brgg sctterng pper to us the vlue of nsotropc - sotropc phse, they re meetng n hgh vlues t Rmn- Nth prmeter v. All ths dfferences s result of n ncrese of the rto of the Rmn-Nth prmeters v v from ( to 4). Remrkble the pek phses re obtned t hgh vlue of the Rmn-Nth prmeters. Fgs. (),() shows tht the vlues of prmeters v nd v t mxmum phses ( 0,, ) re lwys observed n rnge (.95 > v, >.7 ). 6. Concluson The study shows tht n cse of Brgg couplng n nsotropc sotropc of cousto-optcs ntercton the chnge of lght phse s tke plce wth the two nterctons smultneously. The ddtonl phse s consstent wth Doppler-shft, n ddton the mgntude of the chnge phse depended on the rto of Rmn- Nth prmeters effectve photoelstc constnts ( v v whch depended on coustc power P nd The rto of p, p ).Tht chnges gven possblty controlled phse of lght wve n sotropc or nsotropc dffrcton smultneously, wth wde rnge vlue. 44
Journl of Th-Qr Unversty No.3 Vol.4 December/008 3.5 3.5.5 0.5 0.7.9 0 0.5.5 () For the rto 3.5 (b) For the rto 3.5.5 0.5 0 0 0.5.5.9.95 Fg.() Phse chngng for combned processes. 48
Journl of Th-Qr Unversty No.3 Vol.4 December/008 89
Journl of Th-Qr Unversty No.3 Vol.4 December/008 REFERENCES [] Yrv A nd Yeh P, 984, Optcl Wves n Crystls, Wley, New York. [] Hssen J.A. 99 "Addtonl phse shft effect n cousto- optcl ntercton", Ph.D thess, College of Physcs, Moscow Stte, Unv. [3] Blkshy V., Hssn J.A. 993 "Polrzton effect n cousto-optcs ntercton" Optcl Eng., Vol.3, No.4, U.S.A. [4] Voloshnov V nd Tchernytn A, 000 "Smultneous up-shfted nd down-shfted Brgg dffrcton n brefrngent med" Journl of Optcs A: Pure nd Appled Optcs, Vol., No. 5. [5] Blkshy V. I., Nknorv E. A. nd prygn V. N., 983 Phse relton n Brgg dffrcton, Moscow Unv. Phys. Bull, Vol. 4,No. 6. [6] Bzhcnov V.Yu.,Vsnctsov M.V. Soskn M.S. 984 Optcl nsotropy of volume phse grtngs " Opt. Commun,Vol.50, No. 6. [7] Ptrov V.V., Lpn S.A. 003" Hgh Frequency n Brgg Cell Acousto-Optcs" September, Srtov Stte Unversty, Srtov Russ. 89