New integrated programmable optical diffractive element

Transcription

1 New negaed pogammable opcal dffacve elemen Bzhan Rashdan * and Sna Khoasan Dep. of leccal ngneeng Shaf Unvesy of Technology P. O. Box Tehan Ian ABSTRACT In hs pape a new negaed pogammable dffacve opcal elemen s descbed whch s composed by sackng of he plasma wave opcal modulao/swch sucue. Ths sucue has he possbly of hgh densy negaon by means of he sae-of-he-a fabcaon echnologes. The devce has he n-desgn capably o be ehe pogammed eleccally o opcally. Boh he opcal and eleccal pogammng eque ansvese DC bases acoss he wavegude modulaos. Pogammng me n boh appoaches could be as low as 0ps. As poposed n he pape he devce has numeous applcaons n dffeen aeas ncludng decson makng paen ecognon hgh densy opcal soages pogammable gangs and hologams and opcal compung. Keywods: Inegaed Opcs Pogammable Opcal lemen Dffacon Plasma Wave Modulao Opcal Soage. INTRODUCTION The auhos had exploed he feasbly of a new negaed opcal modulao and swch whch s capable of opeaon beyond 00GHz. The basc sucue of he devce s a delecc wavegude along whch an opcal beam popagaes. I has a plana and vecal layeed sucue whch may be ealzed easly by he exsng mco-fabcaon echnology. The plasma wave opcal modulao/swch s based on he neacon of a guded lgh beam by he fee neface chages. The wo-dmensonal fee chages ae nduced a he delecc nefaces va he Mulle effec. The desgn and analyss deals ae also epoed -4. Recenly an applcaon of he above devce as an opcal memoy and even an opo-ansso s pesened 5. Ths memoy s bascally he same as he opcal modulao/swch wh he man dffeence beng n he chage/dschage me consan and usage of phoo-conducve popey of he semconducos. The nfomaon of hs memoy cell may be also wen opcally. In hs case he ansvese volage should be appled pemanenly n ode o manan a bas. Howeve he coespondng wavelenghs should be smalle han he wavelengh of he eadng opcal wave. A vaaon of hs memoy cell has he ably o conol he flow of a hgh powe guded opcal beam by a shoe wavelengh conol beam. Ths would esul n an opcal anssong effec whch povdes a bass fo he developmen of opcal anssos o opoanssos. Hee anohe applcaon of he plasma wave modulao/swch s poposed whch s obaned by sackng hs modulao n a vecal manne. In hs devce each of he modulaos has a sepaae volage bas so ha ndependen conol on he modulaos s possble. In he absence of he applyng volages he devce s smla o a delecc dffacon gang. If a lgh beam s popagang along one of he modulaos hen couplng beween neghbong wavegudes esuls n he nechange of opcal powe among he modulaos. The devce behaves hen as a deconal couple. Snce he applcaon of volage o a modulao n geneal affecs s gudng popees can be deduced ha he couplng among he wavegudes s possble only fo hose wavegudes who have a smla gudng mode ( should be poned ou howeve ha s possble o desgn he modulao so ha he pesence of chage layes has no such effec. Theefoe hee s a possbly o have a conol on he enegy ansfe among he wavegudes. Ths phenomenon povdes a means fo pogammng he dffacve elemen. By pope pogammng of he dffacve elemen ha s he applcaon of pope volages o ndependen wavegude modulaos vaous funconales can be ealzed as dscussed n moe deals below. In hs conex a heoecal appoach o analyze he efacon and eflecon of TM and T polazed waves ncden on a delecc neface s descbed when a wo-dmensonal conducng fee chage laye s pesen. Ths esuls n expessons * Coespondence: mal: ashda@sna.shaf.ac.; Telephone: ; Fax: Inegaed Opcs Devces V Gancalo C. Rghn Seppo Honkanen dos Poceedngs of SPI Vol. 477 (00 00 SPI X/0/$5.00 Downloaded fom SPI Dgal Lbay on 9 Sep 0 o Tems of Use: hp://spedl.og/ems

2 fo he eflecon and efacon ampludes and phases. In he nex secon he effec of chage layes on he gudng modes of an ndependen modulao s suded. I s concluded ha he applcaon of volage o a wavegude can desoy s gudng popees so ha he couplng fom an adjacen wavegude becomes mpossble. In he nex secon applcaons of hs effec ae noduced whee we show demonsae he feasbly of consucng a pogammable dffacve elemen and dscuss s pobable applcaons. Fnally a sho concluson appeas.. RFLCTION AND RFRACTION AT A CONDUCTING INTRFAC I s possble o compue he eflecon and ansmsson coeffcens of a layeed delecc sucue by dec soluon of Maxwell's equaon. In a epo 6 hese coeffcens ae calculaed fo a plana sysem composed of hgh ndex glass MgF and Slve. Thee exss an exac analycal equvalen appoach 7 whch makes use of he so-called Fesnel coeffcens fo hs pupose. Meanwhle a geneal numecal appoach fo he compuaon of hese coeffcens when he nefaces ae conducng.e. hee exss a moble wo-dmensonal fee chage laye a he neface has been used pevously by he auhos. None of he above epos addess a deep heoecal undesandng of he eflecon and efacon phenomena a a conducng neface. Hee he eflecon and ansmsson coeffcens a such neface when llumnaed by a polazed TM o T wave s suded. I s shown ha he eflecon and efacon behave essenally he same when he neface s non-conducng e.g. obey he Snell's eflecon and efacon laws whle havng dffeen complex expessons fo he coespondng coeffcens. We exac he phase and amplude of hese coeffcens analycally... TM polazed lgh The aangemen of wo adjacen delecc sem-nfne slabs s llusaed n Fg.. Hee he y-axs s nomal and ouwads and he z=0 o x-y plane s equvalen o he neface of he medum n he z<0 and he medum n he z>0 egons. We suppose ha he eflecon and efacon of an ncden plane wave fom he z<0 egon wh he decon waveveco s elecc and magnec felds and H and angle of ncdence s popely descbed by he addon of wo plane waves. The fs plane wave eflecs back fom he neface wh he felds and H and decon waveveco s makng an angle wh he z-axs. The second plane wave efacs no he second delecc n he z>0 egon wh he felds and H and decon waveveco s makng an angle wh he z-axs. Lae we shall obseve ha hs assumpon leads o a conssen soluon. Snce he soluon of Maxwell's equaons s unque hs heefoe would be he only possble descpon of he eflecon and efacon a a conducng neface. Fo he ncden feld n he z<0 egon we have ( x z = ( sn zˆ ( x sn + z (a H ( x z = yˆ ( x sn + z (b whee = µ ε s he nnsc mpedance of he medum β s he popagaon consan whn he medum and he amplude of he elecc feld. Fo he efleced feld we have ( x z = ( + sn zˆ ( x sn z (a H ( x z = yˆ ( x sn z. (b The efaced feld n he medum s expessed smlaly by he elaons ( x z = ( sn zˆ ( x sn + z (3a H ( x z = yˆ ( x sn + z. (3b The applcaon of he connuy condon of he angenal componen of he elecc feld a he neface wh z=0 gves Poc. SPI Vol Downloaded fom SPI Dgal Lbay on 9 Sep 0 o Tems of Use: hp://spedl.og/ems

3 β sn β sn = β = sn. (4 Ths esuls n he Snell eflecon and efacon angles = (5 n sn = sn. n (6 Theefoe fo he elecc felds ampludes of he ncden eflecon and ansmed waves we have ( + cos =. (7 If a conducng wo-dmensonal fee chage laye wh he suface conducvy σ exss a z=0 an neface cuen densy s geneaed accodng o J s ( x σ ( = x0. (8 Ths cuen wll noduce a dsconnuy n he angenal magnec feld veco H so ha Theefoe n whch σ σ. ( H H = J s zˆ. (9 z =0 ( = + σ (0 Usng he defnons fo he eflecon and ansmsson coeffcens equaon esuls R and T he followng sysem of R T + σ TM TM = ( whch has he soluon ( + ( + R TM = ( + T TM =. (3 + ( + I s smple o check ha he above esuls elax o he nomal expessons n he absence of he chage laye σ=0 8. Moe neesngly n he lm of nfne conducvy σ + one may show R TM =- and T TM =0. Theefoe a conducve neface wh nfne conducvy would oally eflec back he ncden lgh jus as he medum was a pefec conduco. The above elaons may be exaced fom he σ=0 case by makng he eplacemen ( + σ cos. Thus he pesence of neface cuen J s has esuled n an appaen ncease n he nnsc mpedance of he medum. 430 Poc. SPI Vol. 477 Downloaded fom SPI Dgal Lbay on 9 Sep 0 o Tems of Use: hp://spedl.og/ems

4 .. T polazed lgh Wh he ad of Fg. fo he T polazed ncden wavefon we have ( x z = yˆ ( x sn + z (4a ( x z = ( + sn zˆ ( x sn + z H. (4b and especvely fo he eflecon and efacon wavefons ( x z = yˆ ( x sn z (5a ( x z = ( + sn zˆ ( x sn z H (5b ( x z = yˆ ( x sn + z (6a H ( x z = ( + sn zˆ ( x sn + z. (6b The coespondng eflecon and ansmsson coeffcens would be heefoe ( + ( + R T = (7 + T T =. (8 + ( + Agan smla o he TM mode n he lm of nfne neface conducvy σ + we have R T =- and T T =0. In conas o he TM mode howeve he elaons (7 and (8 can be exac fom he σ=0 case by makng he eplacemen ( +. Thus fo boh ncdence polazaons he nnsc mpedance of he medum has appaenly nceased bu o dffeen mulplcaon facos. 3. FFCT OF TH CONDUCTIV INTRFAC ON GUIDING PROPRTIS In ode o sudy he effec of conducve neface n guded modes s necessay o deve he eflecon phase when a oal eflecon occus. Snce a guded mode s chaacezed by he fac ha s oal oundp phase eadaon conssng of he pah delay and he eflecon phase a he up and down nefaces should be an nege mulple of π. 3.. Phase of he eflecon coeffcen In he case ha a oal eflecon happens a he neface hen sn > and heefoe s complex valued. Unde such condons we would have evanescen waves n medum and he magnude of he eflecon coeffcen R uns ou o be equal o uny egadless of he polazaon. I s possble o show afe some algebc manpulaons ha he eflecon phases coespondng o he TM and T modes ae R R TM T = π + an = an n σ n sn an sn n n n n (9 n n + sn an sn n n σ n n + σ 0 0 (0 Poc. SPI Vol Downloaded fom SPI Dgal Lbay on 9 Sep 0 o Tems of Use: hp://spedl.og/ems

5 n whch 0 s he nnsc mpedance of he vacuum. Hee we have supposed ha he meda ae non-magnec wh µ =µ 0 n = ε ε and n = ε ε. The elaons (9 and (0 show ha he phase of he efleced wave s dependen on he 0 0 neface conducvy. Ths concluson wll be of mpoance n he nex subsecon. 3.. Dspeson equaon of he wavegude As can be obseved fom (9 and (0 may be shown ha s mpossble fo a conducve neface of wo sem-nfne medums o manan he same TM o T eflecon phase when σ=0 9. Howeve fo a sysem conssng of wo o moe delecc slabs nsead of he maeal hs condon may be volaed. Ths means ha s sll possble o keep a gudng mode unaffeced by he pesence of neface fee chage layes f a pope desgn s woked ou. I should also be menoned ha he pesence of chage laye can no conbue an angle equal o geae han π o he eflecon phase. The oundp phase of a plane wave opcal beam popagang n a slab wavegude conssng of hee consecuve layes and 3 especvely called as cove flm and subsae wh n > n and n > eads 0 Φ + Φ + β νπ ν Z ( = 3 n whch s he hckness of he delecc s he popagaon angle (0<<π/ and Φ and Φ 3 ae he T o TM eflecon phases coespondng o he eflecon a he flm-cove neface and he flm-subsae nefaces especvely. In pncple s possble o fnd a numecal soluon of ( fo o fnd he popagaon mode. Of couse hee may be seveal soluons o even no soluon a all. Needless o say he soluons ae affeced fo he above wavegude by he pesence of neface chages. Ths s due o he fac ha each ncden wavefon on he nefaces sees a sem-fne slab on he ohe sde of neface beng ehe cove o subsae. Thus accodng o he dscusson n he begnnng of hs subsecon he eflecon phases ae ceanly affeced. Snce oal of he eflecon phases can no change moe han π due o he conducng nefaces he gudng angle and coespondngly he guded mode mus be peubed by neface chages. I s emphaszed ha hs concluson s ue fo he hee laye slab wavegude as supposed above. Ths means ha s sll possble fo a sysem wh dffeen confguaon o have a guded mode unchanged by he chage layes. 4. PROGRAMMABL DIFFRACTIV LMNT The undelyng dea n he pogammable dffacve elemen s vey smple. If wo smla slab wavegudes ae pu close enough n paallel ogehe and an opcal beam s le o popagae n one of hem he coespondng evanescen waves of he guded beam would leak no he second wavegude. Afe some dsance along he popagaon n he fs wavegude he opcal powe s hus ansfeed o he second wavegude. Smlaly he ansfeed enegy wll be geng back no he fs wavegude afe he same dsance beng efeed o he couplng dsance. So he popagang elecomagnec enegy oscllaes back and foh beween wo wavegudes wh a spaal peod equal o wce of he couplng dsance. In ohe wods he pesence of he second wavegude peubs he guded mode n he fs one. Ths phenomenon s named couplng and s an elecomagnec dual of he unnelng beween wo neghbong poenal wells n quanum mechancs ndeed. The close he wavegudes he songe he couplng and he shoe he couplng dsance. By nceasng he numbe of dencal wavegudes beng n paallel ogehe he couplng among he wavegudes becomes much complcaed and he oal flowng elecomagnec enegy dvdes among all wavegudes exchangng ndefnely among hem. If hs sucue s peodc would be compaable o a gang fom anohe pon of vew. Howeve n geneal s possble o desoy he gudng popey of all wavegudes excep wo and le an opcal beam o popagae n one of hem. I s obvous ha he enegy would be exchangng only beween he emanng wo wavegudes. Snce he ohes ae no capable o gude an opcal beam. Now he desoyng effec can be accomplshed hough he neface chages. If each of he wavegudes has an ndependen on/off bas (Fg. 3 he ansfe of enegy beween he wavegudes wll be fully n conol eleccally. To llusae hs dea suppose ha each wavegude can cay an opcal beam when no neface chage s pesen o he wavegude s n s on sae. Now suppose ha he applcaon of he bas volage dsubs he gudng popey of he wavegude so ha hee emans no guded mode; hs case may be ealzed hough a pope desgn. Afe passage of a me and fomaon of neface chage layes he wavegude s uned off and becomes nvsble o he couplng pocess. Theefoe s possble o 43 Poc. SPI Vol. 477 Downloaded fom SPI Dgal Lbay on 9 Sep 0 o Tems of Use: hp://spedl.og/ems

6 conol he oupu nensy of each ndependen wavegude by he ndependen volages. I should be menoned ha he me consan of fomaon of chage layes can be as low as 0ps as s so fo he case dscussed n ou eale epos. Ths pems a conol on he opcal sysem beyond 00GHz. If he layeed sucue of wavegudes s peodc o almos peodc and he hckness of deleccs s smalle o compaable o he wavelengh we oban a dffacve elemen whose popees may be conolled effecvely by he applcaon of a gd of volage souces. Such dffacve elemen fnds mpoan applcaons n decson makng paen ecognon and compue geneaed hologams. If each of he wavegudes can be llumnaed ndependenly by wo sho wavelenghs enough o exce he phoo-conducvy of maeals a sack of opcal memoes s obaned 5. By ealzng a wo-dmensonal aay of channel wavegudes nsead of slab wavegudes a hgh densy opcal soage s feasble. Dealed analyss of he sacked Mulle effec plasma wave modulaos s o be epoed elsewhee 9. I s added ha he feasbly of opcal anssos s aleady nvesgaed by he auhos 5. A pope combnaon of such devces hough opcal neconnecs would lead o a majo developmen n he negaed opcal compung echnology whee all of he logc opeaons ae done fully opcal. Howeve such negaed sysems need o dsspae some eleccal enegy dawn fom he basng volage souces. 5. CONCLUSIONS An applcaon of he Mulle effec plasma wave modulao/swch was pesened based on he noducon of a new opcal dffacve elemen. Ths elemen s obaned by sackng he plasma wave modulao n a one- o wo-dmensonal aay each havng an ndependen volage bas. The basc dea behnd he sysem s he change of he eflecon phase due o he pesence of fee neface chages and has been houghly analyzed. In ode o make a heoecal analyss he ncden lgh has been decomposed no TM and T modes. I s dscussed ha he pesence of a conducve neface fee chage laye does no change he smple efacon and eflecon mechansm of a plane wave as s undesood fo a non-conducve neface. Howeve could seously affec he eflecon and ansmsson phases when oal nenal eflecon occus as well as he eflecon and ansmsson ampludes. The peubaon caused by he pesence of he neface chages necessaly changes he gudng popees of a smple ndependen slab wavegude fo example can affec he gudng angle o decease he numbe of guded modes even down o zeo (hs concluson can be volaed fo sysems conssng of moe sacked delecc layes as dscussed. The couplng beween he neghbong modulaos can be fully conolled by he eleccal bases of he wavegudes. Ths poduces an opcal mulplexe. If he feaue sze of he devce s shoe han o of he ode of he wavelengh a pogammable gang s obaned whch has mpoan poenal applcaons. The devce may be consdeed o seve as an opcal soage compue geneaed hologam and so on wh mno modfcaons. A pope combnaon of such devces hough opcal neconnecs would lead o a majo developmen n he negaed opcal compung echnology. RFRNCS. B. Rashdan A. Nojeh and S. Khoasan "A new plasma wave mco-opcal modulao/swch" Poc. MOMs'99 pp Manz A. Nojeh M. Sc. Dsseaon Depamen of leccal ngneeng Shaf Unvesy of Technology Tehan A. Nojeh S. Khoasan and B. Rashdan "leco-opc plasma wave lgh modulao" Poc. 8h IC Isfahan S. Khoasan A. Nojeh and B. Rashdan "Quanum mechancal analyss of a Mulle effec plasma wave opcal modulao/swch" Poc. SPI 3896 pp Sngapoe S. Khoasan A. Nojeh and B. Rashdan "New negaed opcal memoy based on he plasma wave modulao/swch " o be publshed n Poc. SPI 477 San Jose G. J. Kovacs and G. D. Sco "Opcal excaon of suface plasma waves n layeed meda" Phys. Rev. B 6 pp Fonana "A heoecal analyss of he couplng of lgh o suface plasma oscllaons a he edge of a slab wavegude" I Tans. Mcowave Th. Tech. 46 pp D. K. Cheng Feld and Wave lecomagnecs nd ed. Addson-Wesley Readng S. Khoasan Ph. D. Dsseaon Depamen of leccal ngneeng Shaf Unvesy of Technology Tehan T. Tam Inegaed Opcs Spnge-Velag New Yok 975. Poc. SPI Vol Downloaded fom SPI Dgal Lbay on 9 Sep 0 o Tems of Use: hp://spedl.og/ems

7 s H x s y σ H z s H Fg.. Confguaon of efleced and efaced wave fo TM mode. s H x H y σ s s z H Fg.. Confguaon of efleced and efaced wave fo T mode. V 4 n n V 3 n n V n n V n n Fg. 3. Sacked plasma wave modulaos wh ndependen bases. 434 Poc. SPI Vol. 477 Downloaded fom SPI Dgal Lbay on 9 Sep 0 o Tems of Use: hp://spedl.og/ems