A New Optical Waveguide for Implementation of Multi-wavelengths Narrowband Filters for DWDM Systems

Transcription

1 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.6 No.8B, August 6 39 A Nw Optical Wavguid for Implmntation of Multi-wavlngths Narrowband Filtrs for DWDM Systms A. Rostami [a, b] a)- Dpartmnt of Elctrical and Computr Enginring, Univrsity of Toronto, 1 King s Collg Road, Toronto, M5S 3G4, Canada b)- OIC Rsarch Lab., Faculty of Elctrical Enginring, Univrsity of Tabriz, Tabriz 51664, Iran Summary W invstigat th possibility of optical wavguid with multi-lvls indx of rfraction in th cor rgion (mor than two-lvls) for multi-wavlngths applications analytically and numrically. W show that with slowly varying apodization all of dns wavlngth division multiplxing (DWDM) applications with 3-dB sidband supprssion and insrtion losss of lss than 1-dB can b implmntd. Th coupld wav quations and coupling cofficint for gnral tratmnt and approximatd cass ar rviwd. Th apodization functions for obtaining narrowband filtring spcially for DWDM filtrs ar dtrmind. Also, th capability of our proposal for implmntation of suprimposd gratings with constant gomtry and only with suitabl apodization is illustratd. Finally, som DWDM filtrs basd on our proposal ar dsignd. Ky words Optical wavguid, Suprimposd Gratings, Multiwavlngths Filtrs, Optical wavguid with multi-lvls indx of rfractions 1. Introduction Th rapid dvlopmnt of dns wavlngth division multiplxing (DWDM) systm, which is a ncssary dmand of optical communication, has producd grat dmand for compact and r-configurabl slctiv multi-wavlngths tuning lmnts. Whr high fficincy and slctivity ar rquird, an intrsting altrnativ is th Bragg Gratings. Th Bragg Gratings hav important applications in optical communications including snsors, signal conditionrs such as filtrs, mod convrtrs, splittrs and many othr applications and signal gnration such as distributd fdback lasrs [1-4]. Multi-band optical filtrs hav ky rol in DWDM systms. Also, optical signal procssing, computing and communication ar dpnds on progrss in asy implmntation of multi-wavlngth building blocks. Thr ar many altrnativs for ralization of multiband optical filtrs basd on quasi-priodic structurs and ring rsonators [5,6]. Also, rcntly implmntation of multi-band optical filtrs basd on suprimposd gratings has bn discussd [7,8], owing to its powrful capacity offring a high numbr of channls of idntical spctral prformanc for filtring or chromatic disprsion compnsation in th xisting long-haul fibr link. Currntly, thr is a high lvl of intrst in th fabrication of filtrs to provid wavlngth slctivity and nois filtring in DWDM systms. Th tight spcifications of ths filtrs, rgarding th rquird nar squar amplitud rspons and th xtrmly low group dlay variations in th passband, pos a tchnological challng to any of th availabl tchnologis, for xampl, multi-layr dilctric thin film filtrs, arrayd wavguid gratings or fibr Bragg Gratings. In this dirction, suprimposd Bragg Gratings has bn found important and ky rol in ralization of multichannl DWDM applications and many rsarch rports prsntd for dscription of ths applications [9-14]. But, all of ths rsarchs limitd to constant prdfind suprimposing componnts and th rsulting wavguiding structurs for two diffrnt dsigns ar diffrnt from togthr from structural point of viw. Finally, thy couldn t prsnt a unifid wavguiding structur for implmntation of suprimposd gratings at last for spcial applications without gomtry changing. In this fild of rsarch, for ach cas, thr is an algorithm for inscription on optical mdiums. In this papr, a novl optical wavguid structur including multi-lvls indx of rfraction in th cor rgion with constant gomtry and possibility for asy apodization to obtain all DWDM applications and spcially from narrowband optical filtrs dsign point of viw and many othr intrsting optical transfr functions is prsntd. In th proposd wavguid, w hav mor than -lvls (maximum fiv lvls without apodization in ach priod) of th indx of rfraction, which looks diffrnt from traditional gratings. Basd on this

2 4 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.6 No.8B, August 6 proposal, w show th capabilitis of this wavguid for DWDM and gnral optical applications. Hr, w prsnt a dsign procdur for obtaining spcial apodization functions for a givn multi-wavlngths rflction profil. Our mthod is basd on discrt invrs Fourir Transform of th dsird output Fourir domain componnts and r-construction of th indx of rfraction in position domain. Using th obtaind indx of rfraction, w dtrmin th apodization functions for th proposd grating. Also, our proposd mthod can b implmntd using Elctro-optically within th intgratd circuits. Our approach is prsntd in th following sctions with diffrnt topics as follows. In sction II, th mathmatical modling and formulation is prsntd. Also, simulation and rsults of dsignd xampls ar prsntd in sction III.. Mathmatical Modling Fig. 1 shows an spcial optical slab wavguid. In this figur, Λ = 4( d 1 + d ), d1, d,h, F j and n j ar grating priod, duration of high and low lvls of th indx of rfraction in th grating, duration of constant indx of rfraction, hight of slab, amplituds of high and low lvls of th indx of rfraction and th indx of rfractions for substrat, cor and cladding rgions rspctivly. As it is shown in this cas w hav mor than -lvls of th indx of rfractions vn in th sam amplituds ( F 1 = F ) compard to two lvls for traditional cas. In this cas w assum that thr is only on mod for propagating through cor in th forward and backward dirctions, for simplicity of formulation and w ignor from all radiation mods. Th amplituds ar small and can b considrd as prturbation. Now, in this sction for this spcial cas w rviw th Maxwll quations and coupld mod thory for analysis of our proposd optical wavguid. Th Maxwll wav quation for without prturbation and tim harmonic cas is as follows. [ + K n ( x, y)] Ψ( x, y, =, (1) whr n and K ar th indx of rfraction without prturbation and wav vctor rspctivly. With assuming singl mod and travling wav in Z- dirction, w hav [ t + K n ( x, y) β ] Ψt ( x, y) =, () whr indx t shows transvrs componnt and frquncy dpndnt β is th propagation wav vctor. If w considr TE mod for invstigation, for xampl, in prsnc of prturbation w hav i t EY ( x, y, z, t) = ω [ A( + B( ] Ψt ( x, y), (3) whr miβ ( ω) Z ω A(, B( and β ( ω) = nff = nff K. c If w apply this grating as prturbation into Maxwll quations, w obtain th following coupld wav quations as da( i( β + D( ) A( = id( B(, dz db( + i( β + D( ) B( = id( A(, dz (4) whr D( is givn in th following rlation. D( = δnk, (5) Fig. 1. A proposal for optical wavguid with multi-lvls indx of rfractions whr δn is prturbation and shown in Fig.. According to Fig., δ n can b writtn in diffrnt rgions in trms of rlvant apodization functions. d For d z, z d d 1 +, d d d 1 + z d1 + d +, d d d 1 + d + z d1 + d +,

3 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.6 No.8B, August 6 41 d d d 1 + d + z d1 + d +, d d d 1 + d + z 3d1 + d +, d d 3d 1 + d + z 3d1 + 3d +, d d 3d 1 + 3d + z 4d1 + 3d +, d 4d 1 + 3d + z 4d1 + 4d th prturbd indx of rfraction ar δ n =, F ( ), 1 z, F ( z ),, F 3 (,, F 4 ( and rspctivly. Whr F j and d j ar constant amplituds within ach priod and th indx of rfraction charactristics, which ar introducd in Fig. 1 rspctivly. π i z Λ Λ A( = a(, (8) π i z Λ B( = b(, Eq. (4) can b simplifid as da( = iδβ. a( + iξ (. b(, dz (9) db( * = iδβ. b( iξ (. a(, dz π whr δβ = β. For obtaining multiwavlngths rflction profil, it is ncssary that th coupling cofficint ξ ( or η( can b suprposition of slowly varying nvlop harmonic functions, in which ach of thm can b in rsonant with incidnt spcial wavlngths. So, η( should hav th following form gnrally as iα 1z iα z iα z 1 η ( =... + η + η + η +..., (1) 1 1 Fig. Th indx of rfraction as Prturbation If w hav priodic grating with amplituds F j, which ar constant in whol grating, th Fourir xpansion can b usd. Els th Fourir transform or discrt Fourir Transform can b usd. Howvr δn should b xpandd in trms of harmonic functions. Sinc δ n is small and oprats as prturbation and for Max F j Fi << F, thn, it can b xprssd as follows. π π i Z i Z Λ n z * Λ = η( ) + η ( δ, (6) whr η( and F ar slowly varying amplituds (it can b dtrmind for spcial and givn F j cass) and th avrag amplitud in whol grating. Now, if Eq. (6) substitutd into Eq. (5), w obtain th following rlation as π π i Z i Z Λ D Z z * Λ ( ) = ( ) + ξ ( ξ, (7) whr ξ ( = Kη(. Using Eq. (8), and nw variabls, which ar givn in Eq. (9), whr η j and α j ar coupling strngth for ach wavlngth and small and fixd numbrs dmonstrating th rsonant frquncis rspctivly. Using this quation for η ( th output paks can b obtaind in th rflction cofficint at Λ (1 α Λ j = Λ j ). (11) π In th sction III, w illustrat th suitabl apodization functions for obtaining spcials Λ j s. Now, basd on coupld wav quation, which is obtaind and givn by Eq. (9), w can introduc a diffrntial quation including th rflction cofficint as follows. r = b a Z, (1) dr dz = iδβ. r iξ. r iξ. (13) Using this quation, w can obtain th proposd optical wavguid rflction and transmission cofficints basd on xact or numrical mthods. Now, for dsigning a spcial multi-wavlngths rflction profil th following procdur should b prformd. For this purpos, w should obtain th Fourir domain ncssary information for ths multi-wavlngths. So, th Fourir componnt *

4 4 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.6 No.8B, August 6 should b dtrmind prcisly (amplituds and bandwidths). Thus, using invrs Fourir Transform, th position distribution of th indx of rfractions can b obtaind as N 1 k = kn iπ δ n( n) = δnn( k) N, (14) whr δ nn and N ar th Fourir domain componnt (dtrmind from rflction profil, which is ncssary in dsign) and numbr of sampls rspctivly. Th following procdur can b applid to dsign of multi-wavlngths narrowband filtrs basd on our proposd grating. 1. According to multi-wavlngths rflction profil (as an input to dsign problm) th Fourir domain paks, and wavlngths can b dtrmind. Using ths information and Eq. (- 1) η or ξ can b calculatd. Using Eq. (-6), th δ n in th Fourir domain ( δ nn ) can b obtaind and can b convrtd to discrt form with imagination of th amplituds in th grating structur as discrt sampls.. Using invrs Fourir Transform, th position dpndnt prturbd indx of rfraction should b calculatd. 3. Using our introducd Grating structur, th amplituds F, F, F, ) ar obtaind. ( 1 3 F4 Using proposd algorithm, th indx of rfraction in position and finally th apodization functions could b dtrmind. harmonic, which is dominant in our considration and calculations, can b dtrmind as follows. ( ) 1.5 n π n z = + δ sin( z ), (15) 1 Λ whr δn1 for ths cass ar obtaind as δ n 1 =.795,.658. If w apply th Transfr Matrix Mthod (TMM) or any othr numrical mthods, th following rsults can b obtaind. Fig. (3-1) shows our simulatd rsults for this cas with constant amplituds. Fig. (3-1-a) shows xampl for.35, which is narrowband filtr and Fig. (3-1-b) is corrspond to scond xampl for.75, which is widband compard to first xampl. a 3. Rsults and discussion In this sction, w will driv som of spcial faturs of our proposd optical wavguid. In this invstigation, w considr two gnral cass. 1. Constant Amplituds ( F 1 = F ). Modulatd Amplituds (Similar or diffrnt rflction profils) ( F1 F F3 F4 ) Cas 1) In this cas w considr th sam amplituds for all high and low lvls of th indx of rfractions and is givn in th following, as dsign xampls. This is thr lvls optical wavguid and similar to traditional cas. F 1 = F =.35,.75 In this cas, th prturbd indx of rfraction could b xpandd in trms of Fourir sris and first b Fig. 3 a)- Th Rflction Cofficint for constant Amplituds (Grating Lngth =3.6 mm, and Amplituds: F 1 = F =.35, Priod of Grating =.5167 um, Rflction Pak= and BW (-1dB)=.15 nm) b)- Th first harmonic of th indx of rfraction profil

5 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.6 No.8B, August 6 43 a basd on TMM mthod and obtaind th multiwavlngths rflction profil, which is givn in Fig. 5. How, w can dtrmin ths amplituds, which ar so complicatd. For this purpos, w usd our procdur, which is givn in sction II. For xampl, hr, w considr th rflction cofficint profil with thr paks at 3-wavlngths from DWDM systm standard with approximatly (for satisfying th DWDM dmands spcifications, xact similarity is impossibl) similar charactristics (from rflction paks and Bandwidths point of viws and) at λ 1 = 1.55μm. 819nm, λ = 1. 55μm and λ 3 = 1.55μm nm, which is convrtd to discrt form with imagination of th amplituds ar our sampls and illustratd in Fourir domain in Fig. 5. According to our procdur prsntd in sction II, aftr slcting th frquncis including bandwidths (.75 nm) and amplituds (Rflction paks =.9346) (Fig. 5), th invrs Fourir Transform can b calculatd and th position dpndnt indx of rfraction can b dtrmind and illustratd in Fig.5. As it is shown, th amplituds ar suprposition of thr sinusoidal functions for gnrating thr paks in frquncy domain. In th nxt xampl, w will illustrat th diffrnt rflctd multi-wavlngths profils. b Fig. 4 a)- Th Rflction Cofficint for constant Amplituds (Grating Lngth =3.6 mm, and Amplituds: F 1 = F =.658, Priod of Grating =.5167 um, Rflction Pak=.9641 and BW (-1dB)=.35 nm) b)- Th first harmonic of th indx of rfraction profil In Figs. 3 th rflction cofficints (a, b) and first harmonic of th indx of rfractions (a, b) for ths cass ar illustratd. As it is shown in Fig. 3, with suitabl amplitud for prturbd indx of rfraction for our proposd optical wavguid, many dsird filtrs profil can b obtaind, which is important in optical communications, spcially for DWDM applications. Cas ) Modulatd amplituds for similar profils- In this cas w considr th diffrnt amplituds for ach high and low lvls of th prturbd indx of rfractions for gnration of multi-wavlngths in th rflctd signal with similar profils. For first xampl in this cas, th following curvs ar accptd for amplituds, which ar givn in Fig. 5. Using ths figurs for amplituds, in our proposd grating, of th indx of rfractions, w simulat th rflction cofficint a b

6 44 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.6 No.8B, August 6 c d f Fig. 5 a,b,c,d)- Amplituds of Grating )- Th rflction cofficint and f)- Th Spctral Charactristic in discrt Fourir domain (Priod of Grating =.5167 um, Rflction Pak=.9346 and BW (-1dB)=.75 nm) Cas ) Modulatd amplituds for diffrnt profils- According to our tratmnt for similar profils in th prvious xampl, hr, w will dsign two wavlngths rflction with diffrnt charactristics (rflction paks and bandwidths). For scond xampl in this cas, th following curvs (Fig. 6-a) ar accptd for amplituds. With ths slctions, w simulatd th rflction cofficint and obtaind th multi-wavlngths rflction profil with diffrnt shaps, which is givn in Fig. 6-b. For dtrmination of amplituds, our procdur, which is discussd in sction II, can b usd. For xampl, hr, w considr -wavlngths componnts, which is prsntd in discrt Fourir domain in Fig. 6-c with diffrnt spctral shaps and charactristics (rflction paks and Bandwidths) for having th rflction paks at λ = 1.55μm. 819nm and 1 λ = 1.55μm nm. According to our procdur prsntd in sction II, aftr slcting th frquncis including bandwidths (.35 and.15 nm) and amplituds (Rflction paks =.9641 and.65189) th invrs Fourir Transform can b calculatd and th position dpndnt indx of rfraction can b obtaind and illustratd in Fig 6-a. As it is shown, th amplituds ar suprposition of two sinusoidal functions.

7 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.6 No.8B, August 6 45 b c Fig. 6 a)- Amplituds of Grating b)- Th rflction cofficint (Priod of Grating =.5167 um, Rflction Pak=.9641, and BW (-1dB)=.35,.15 nm) c)- Th Spctral charactristic in discrt Fourir domain a So, th multi-wavlngths filtr dsign basd on our proposd grating prsntd. It is xplaind that basd on our proposd procdur, th narrowband filtr dsign for optical applications gnrally and DWDM spcially is possibl. Our proposal is suitabl for intgratd systms and optical intgratd circuits dsign. Also, our prsntd optical wavguid introducs a spcial wavguid for th first tim with constant gomtry for ralization of suprimposd gratings with diffrnt combinations, in which thr isn t a traditional structur for ralization of mor than two componnts with soft control. So, our mthod is gnral and can implmnt all suprimposd gratings. Hr, w introducd an optical wavguid including multilvls indx of rfractions with constant gomtry and capabl for implmntation of a larg numbr of

8 46 IJCSNS Intrnational Journal of Computr Scinc and Ntwork Scurity, VOL.6 No.8B, August 6 suprimposd gratings only with soft control (apodization). This is a novl rsult, which prsntd in this papr and illustratd with som xampls in sction III. Our proposd wavguid will introduc soft controllabl optical dvics and systms. Conclusion Hr, a nw structur for optical wavguid including multi-lvls indx of rfraction with constant gomtry and asy capability for implmntation of multi-wavlngths transfr functions and spcially narrowband optical filtrs has introducd. Th capability of our proposal with thr dsigns in sction III has dmonstratd. Our proposal can b usd in optical DWDM systms as wll as for ralization of intrsting optical nginring transfr functions. Th similar and diffrnt rflction paks asily can b ralizd only with obtaind amplitud profils (soft control). So, th proposd structur is nw and will introduc soft control basd optical dvics and systms and will b basis for rconfigurabl dvics. Also, this structur can b intgratd asily and can b usd in optical intgratd circuits as basic blocks for complx optical systm implmntation. Th proposd structur can b ralizd using lctrooptically. rang smiconductor lasrs with sampld gratings, IEEE J. QE, Vol. 9, No. 6, Jun [9] A. Othonos, X. L and R. M. Masurs, Suprimposd multipl Bragg Gratings, Elctronics Lttrs, Vol. 3, No. 3, Nov [1] X. Fu, M. Fay and J. M. Xu, 1x8 Suprgrating Wavlngth division dmultiplxr in a Silica planar wavguids, Optics Lttrs, Vol., No. 1, Nov [11] I. A. Avrutsky, M. Fay and J. M. U, Multiwavlngth diffraction and Apodization using Binary Suprimposd Gratings, IEEE Photonic Tchnology Lttrs, Vol. 1, No. 6, Jun [1] R. Slavik and S. LaRochll, Larg Band Priodic Filtrs for DWDM using Multipl-suprimposd Fibr Bragg Gratings, IEEE Photonic Tchnology Lttrs, Vol. 14, No. 1, Dc.. [13] H. Li and Y. Shng, Dirct Dsign of Multi-channl Fibr Bragg Grating with discrt Layr-pling Algorithm, IEEE Photonic Tchnology Lttrs, Vol. 15, No. 9, Spt. 3. [14] H. Li, T. Kumagai, K. Ogusu and Y. Shng, Advancd dsign of a multichannl fibr Bragg Grating basd on a Layr pling mthod, J. Opt. Soc. Am. B, Vol. 1, No. 11, No. 4. Rfrncs [1] T. Erdogan, Fibr Bragg Grating Spctra, J. Lightwav Tchnology, Vol. 15, No. 8, Aug [] H. Nishihara, Y. Handa, T. Suhara, and J. Koyama, Microgratings for High-fficincy guidd bam dflction fabricatd by lctron bam dirct writing tchniqus, Appl. Optic. Vol. 19, PP , 198. [3] A. Kvorkian, A Si intgratd wavguiding polarimtr, Proc. SPIE, Vol. 8, PP , [4] T. Suhara, and H. Nishihara, Intgratd optics componnts and dvics using priodic structurs, IEEE J. QE-, PP , [5] A. Rostami and S. Matloub, Multi-band Optical Filtr Dsign Using Fibonacci basd Quasi-priodic Homognous Structurs, Procding of th AP- RSC4, Qing Dao, China, 4. [6] M. Raisi, S. Ahdrom, K. Alamh, K. Eshraghian, Multi-band MicroPhotonic Tunabl Optical Filtr, Scond IEEE Intrnational Workshop on Elctronic Dsign, Tst and Applications, January 8-3, 4, Prth, Australia [7] V. Minir, A. Kvorkian and J. M. Xu, Diffraction charactristics of suprimposd Holographic gratings in planar optical wavguids, IEEE Photonic Tchnology Lttrs, Vol. 4, No. 1, Oct [8] V. Jayaraman, Z. M. Chuang and L. A. Coldrn, Thory, Dsign and prformanc of Extndd Tuning