Mach Zehnder nerferomeer for Wavelengh Division Muliplexing Ary Syahriar Pusa Pengkajian dan Penerapan Teknologi nformasi dan Elekronika Badan Pengkajian dan Penerapan Teknologi e-mail : ary@inn.bpp.go.id Absrac A heoreical analysis of muliplexing based on Mach-Zehnder inerferomeer is presined. The oupu characerisics and TU channel separaion variaion of an equal arm-lengh inerferomeer are analyzed. The heory and numerical simulaion resuls have some direc fu n c i o n fo r p r a c i c a fab r i c a i on of h e d ev i c e s 1. nroducion n modern communicaion sysems narrow band informaion services and high-speed daa and video informaion services are expeced o be inegraed in one-cofiununicaion neworks l]. Wavelengh Division Muliplexing (WDM) is believed o be one of he mos pracical ways o achieve ransmission capaciies of a few era bi per second (Tb/s). Devices such as opical filers and wavelengh muliplexers (MUXER) and demuliplexers (DEMUXERS), which manipulae opical properies in wavelengh domain, are essenial o WDM opical communicaion sysems. One of he mos useful device is he Mach Zehnder nerferomeer (MZ) l2l. consiss of wo 3-dB coupler which has been bu spliced o build he inerferomeers. The mos imporan parameers in MZ is he difference in pah lengh which basicay wi deermine he MZ's characerisics. n his paper he analysis of MZ based on coupled mode heory and marix ransmission mehod is presened. A number of is feaures wi also be explained. 2. The MZ Srucure A Mach-Zehnder device consiss of wo 3 db fused couplers, beween which a phase difference is inroduced in he wo pahs by increasing one of he pah lenghs wih respec o he orher as shown in Figure 1. The fused couplers are wavelengh sensiive; hence he characerisics of he device are deermined by he 3 db crossover wavelengh of he couplers, he coupling srengh and he inroduced pah difference. up v Co ler 2 npu 1 Oupu npu 2 Ouou 2 Figure. Schemaic diagram of Mach-Zehnder inederomeer For modeling purposes he device can be divided ino hree consiuen pars: he wo 3 db couplers and a phase shifing secion beween hem. The characerisic of each of he comporibns
A-46 Proceedings, Kompuer dan Sisem nelijen (KOMMT 2002) Audiorium Universias Gunadarma, Jakara, 2l -22 Agusus 2002 pars of he device can be represened by he operaion of marix in a vecor which represens he ampliude of he signals in each of he wo fiber a he inpu o ha secion based on he coupled mode heory as [3]: cos(@) -7sin(o)-l J---\ ' M :l ' (l) - couper ysin(o) [- cos(o) here (D = KZ r= coupling coefficien, and z: 3 db coupler lengh' The field in he wo differenial pah lenghs inroduces a phase shif represened by [4] where d = f M, f eio o M rn,*-s, =1, "-r, ) and pis he effecive index of he opical fiber. A is he phase differen beween he wo arms. As is we known, he pvalue can be calculaed by solving he characerisic equaion for LPor mode [3]: (2) wj, (u) K (w) = uj (u) K (w " ) (3) where Jo and J1 arebessel funcions and K, and K1 are modified Bessel funcions. For single mo& operaion V<<2.4048. U and Whave is usual meanings [3]' For fiber couplers he coupling coefficien ris given by [3]: o rr2 x"(y!) /L \J A_ K = e) 27Tq a'zy2v@ here dis he separaion beween he fiber axes, d is fiber diameer, / is a normalized frequency, 'l fo he wavelengh and n1 is core refracive index of he fiber' The response of Mach-Zehnder hen is given by [5] l7f = M "orrlerm phase'shifm "oup"' and he oupu ampliude can be described by Eou,ou,=ME,nou, u Where he inpu ampliude is represened by a vecor l-l "*' = Lo.J n his calculaion a perfec 3 db coupler has been assumed and ha he fiber has no propagarb loss. 3. The MZ Characerisics he To opimize he design of '{rz, i is imporanocalculae andpredic performance. The firs calculaion is o find he effecive refracive index of fiber opics c'd
Mach Zehnder nerferomeer for Wavelengh Division Muliplexing A-47 funcion of wavelengh. Figure 2 shows he effecive refracive index of fiber as a funcion of wavelengh. This is derived by finding roo of Equaion (3) which can easily be done using bisecion mehod. The linear response of refracive index shows ha he fiber acing in single mode region. Furhermore i can be used o predic he change of oupu characerisic as funcion of *'avelengh. C).li H c) li C) (),!2.* rrl r.46733 r.46732 r.4673r r.4673 r.46729 1.46728 r.46721 r.46726 r.4672s r.46724 1.46723 528 1536 1s44 1552 Wavelengh (nm) Figure 2. Effecive refracive index as afuncion ofwavelenghs Figure 3. shows A change as funcion of 1" on n phase shif differen of he nvo arms. shows ha M change as linear funcion which can be used o predic exac pah difference in designing muli/demuliplexing devices. 2.14118 2.4T6 2.44 E 2.ra2 S z.4l { { z.+ros 2.r406 2.4r04 2.402 1528 1536 s44 T552 1560 Wavelengh (run) Figure 3. Arm lengh differen of MZ asfuncion of Wavelenghfor d2 phase shif
A48 Proceedings, Kompuerdan Sisem nelijen (KOMMT 2002) Audiorium Universias Gunadarma, Jakara, 2l -22 Agusus 2002 The ypical oupu specra'of an MZ are shown in Figure 4 wih differen pah lengh. As we can see, his bi direcibnal muli-window WDM acs as a special muliplexer which combine/separaes wo ses of wavelenghs, which are inerleaved by each oher. Because he ransfer funcion is acuay perio$ic in he frequency domain, once he firs and he las desired wavelenghs are se a he TU frequency, he res of he wavelengh peaks in beween wi auomaicay si a heir respecive TU wavelenghs. Because he 3-dB couplers have a broad bandwidh, his device also shows superior uniformiy on he inserion loss of he wavelengh peak. ^ -20 b -30 - -40 A,L=0.15 pm r528 1536 1544 1552 1560 Wavelengh (nm) (a) ^ _20 b -30 F< -40-50 -60 1528 L,L:0.3 pm 1536 544 1552 Wavelengh(nr 1560 (b)
Mach Zehnder nerferomeer for Wavelengh Division Muliplexing A-49 0-20 -30-40 l! oupu i ii r -50 LL--0.5 pm ul -60 1528 1536 r544 r552 l 560 l la l a, ' rf al ( Ț (c) 0 E i B -20-30 -40 1 l { l f \l l l a l lr -50-60 528 1536 1544 1552 Wavelengh (nnr) LL:0.78 pm 1560 (d) Figure 4. MZ specra wih dffiren AL lengh
A-50 Proceedings, Kompuer dan Sisem nelijen (KOMMT 2002) Audiorium Universias Gunadarma, Jakara, 2l - 22 Aeusus 2002 4. Conclusion We have demonsraed a WDM device based on fiber opics Mach Zehnder inerferomeer. We invesigaed he specral change as a funcion of wavelengh in S-band region. Addiionay o improve device performance a phase lengh differen can be uned o comply wih TU grid. Reference L2) 3l l4l l5l R. Ramaswami, "Opical fiber communicaion: from ransmission o nework", EEE. Commun. Mag., 50'h Anniversary comm.ssue, 138-147,2002. M.J. Yadlowsky, E.M. Deliso, v.l. Da Silva, "opicar fibers and amplifiers for wdm sysems", Proc. EEE, vol. 85, 1765-1779,1997. D. Marcuse, Theory of dielecric waveguides, Academic press, New york 1990. R. Adar, C.H. Henry, M.A. Milbrod, R.C. Kisler, "Phase coherence of opical waveguide''. EEE J. of Lighwave Technol., vol. 12, 603-606,1994. T. Erdogan, T.A. srasser, M.A. Milbrod, E.J. Laskowski, c.h. Henry, G.E. Kohnke. "nergraed Mach-Zehnder add-drop filer fabricaed by a single UV-induced graing exposure", Appl. Opics. Vol. 36, 7838-7845, 1997.