A theoretical analysis of multiplexing based on Mach-Zehnder interferometer is presinted. The output characteristics and ITU channel separation variation of an equal arm-length interferometer are analyzed. The theory and numerical simulation results have some direct function for practicaI fabrication of the device

Syahriar, Ary

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Mach Zehnder Interferometer for Wavelength Division MultiplexingAry SyahriarPusat Pengkajian dan Penerapan Teknologi Informasi dan ElektronikaBadan Pengkajian dan Penerapan Teknologie-mail : ary@inn.bpPt.go.idAbstractA theoretical analysis of multiplexing based on Mach-Zehnder interferometer is presinted.The output characteristics and ITU channel separation variation of an equal arm-lengthinterferometer are analyzed. The theory and numerical simulation results have some directfu n c t i o n fo r p r a c t i c a I fab r i c a t i on of t h e d ev i c e s1. IntroductionIn modern communication systems narrow band information services and high-speed dataand video information services are expected to be integrated in one-cofiununication networks Il].Wavelength Division Multiplexing (WDM) is believed to be one of the most practical ways toachieve transmission capacities of a few tera bit per second (Tb/s). Devices such as optical filtersand wavelength multiplexers (MUXER) and demultiplexers (DEMUXERS), which manipulateoptical properties in wavelength domain, are essential to WDM optical communication systems.One of the most useful device is the Mach Zehnder Interferometer (MZI) l2l.It consists of two 3-dB coupler which has been butt spliced to build the interferometers.The most important parameters in MZI is the difference in path length which basically willdetermine the MZI's characteristics.In this paper the analysis of MZI based on coupled mode theory and matrix transmissionmethod is presented. A number of its features will also be explained.2. The MZI StructureA Mach-Zehnder device consists of two 3 dB fused couplers, between which a phasedifference is introduced in the two paths by increasing one of the path lengths with respect to theorher as shown in Figure 1. The fused couplers are wavelength sensitive; hence the characteristicsof the device are determined by the 3 dB crossover wavelength of the couplers, the couplingstrength and the introduced path difference.Co ler 2Input 1Input 2Output IOutout 2upIvFigure I. Schematic diagram of Mach-Zehnder intederometerFor modeling purposes the device can be divided into three constituent parts: the two 3 dBcouplers and a phase shifting section between them. The characteristic of each of the comporiBntsparts of the device can be represented by the operation of matrix in a vector which represents theamplitude of the signals in each of the two fiber at the input to that section based on the coupledmode theory as [3]:I cos(@) -7sin(o)-lM : l  '  J--- \  |  ( l )' - couPter [- ysin(O) cos(O) Ihere (D = KZ t r= coupling coefficient, and z: 3 dB coupler length'The field in the two differential path lengths introduces a phase shift represented by [4]A-46 Proceedings, Komputer dan Sistem Intelijen (KOMMIT 2002)Auditorium Universitas Gunadarma, Jakarta, 2l -22 Agustus 2002f eio o IM rn,*-stt, =1, "-r, )where d = f M, and pis the effective index of the optical fiber. AI is the phase different betweenthe two arms. As is well known, the pvalue can be calculated by solving the characteristic equationfor LPor mode [3]:wJ, (u ) K | (w ) = uJ | (u ) K " (w ) (3)the(2)where Jo and J1 areBessel functions and K, and K1 are modified Bessel functions. For single mo&operation V<<2.4048. U and Whave its usual meanings [3]'For fiber couplers the coupling coefficient ris given by [3]:o rr2 x"(Y!)/L \J A_ e)K = 27Tq a'zY2V@here dis the separation between the fiber axes, d is fiber diameter, / is a normalized frequency, 'l fothe wavelength and n1 is core refractive index of the fiber'The response of Mach-Zehnder then is given by [5]l7f = M "orrlerM phase'shiftM "ouPI"'and the output amplitude can be described byEou,ou,=ME,nou, tutWhere the input amplitude is represented by a vectorl-t l"*' = Lo.J c'DIn this calculation a perfect 3 dB coupler has been assumed and that the fiber has no propagarbloss.3. The MZI CharacteristicsTo optimize the design of I'{rZI, it is important tocalculate andperformance. The first calculation is to find the effective refractive indexpredictof fiber opticsMach Zehnder Interferometer for Wavelength Division Multiplexing A-47function of wavelength. Figure 2 shows the effective refractive index of fiber as a function ofwavelength. This is derived by finding root of Equation (3) which can easily be done usingbisection method. The linear response of refractive index shows that the fiber acting in single moderegion. Furthermore it can be used to predict the change of output characteristic as function of*'avelength.r.46733r.46732r.4673rr.4673r.467291.46728r.46721r.46726r.4672sr.467241.46723I  528 1536 1s44 1552Wavelength (nm)Figure 2. Effective refractive index as afunction ofwavelengthsFigure 3. shows AI change as function of 1" on n phase shift different of the nvo arms. Itshows that M change as linear function which can be used to predict exact path difference indesigning multi/demultiplexing devices.C). l iHc)liC)(),!2.*r r l2.141182.I4TI62.I4t t4E 2.raII2S z. t4t l{{ z.t+ros2.r4t062.t4r042.t4t021528 1536 ts44 T552Wavelength (run)1560Figure 3. Arm length different of MZI asfunction of Wavelengthfor d2 phase shiftA48 Proceedings, Komputerdan Sistem Intelijen (KOMMIT 2002)Auditorium Universitas Gunadarma, Jakarta, 2l -22 Agustus 2002The typical output spectra'of an MZI are shown in Figure 4 with different path length. Aswe can see, this bi directibnal multi-window WDM acts as a special multiplexer whichcombine/separates two sets of wavelengths, which are interleaved by each other. Because thetransfer function is actually perio$ic in the frequency domain, once the first and the last desiredwavelengths are set at the ITU frequency, the rest of the wavelength peaks in between willautomatically sit at their respective ITU wavelengths. Because the 3-dB couplers have a broadbandwidth, this device also shows superior uniformity on the insertion loss of the wavelength peak.r528 1552 1560-60-10^ -20b -30--401536 1544Wavelength (nm)(a)-10^ _20b -30F< -40-501536 t544 1552Wavelength(nrtA,L=0.15 pmL,L:0.3 pm I I1528(b)1560Mach Zehnder Interferometer for Wavelength Division Multiplexing A-490-10-20-30-40-50-60152801536 r544 r552 l  560(c)EtiB-10-20-30-40-50-60t528 1536 1544 1552Wavelength (nnr)(d)Figure 4. MZI spectra with dffirent AL length1560i i  It r  IlaIIla,IIIt 'ut lr fa lt tt(T,IIl !I tl lIIttIIoutput i I lLL--0.5 pm\ lt lt tIIIII1tl lt lIII{I tt llrIttIItIILL:0.78 pmI Il lt lIaIIItIIt ll lI IIIItIIIIIfA-50 Proceedings, Komputer dan Sistem Intelijen (KOMMIT 2002)Auditorium Universitas Gunadarma, Jakarta, 2l - 22 Aeustus 20024. ConclusionWe have demonstrated a WDM device based on fiber optics Mach Zehnder interferometer.We investigated the spectral change as a function of wavelength in S-band region. Additionally toimprove device performance a phase length different can be tuned to comply with ITU grid.ReferenceR. Ramaswami, "Optical fiber communication: from transmission to network", IEEE.Commun. Mag., 50'h Anniversary comm.Issue, 138-147,2002.M.J. Yadlowsky, E.M. Deliso, v.L. Da Silva, "opticar fibers and amplifiers for wDMsystems", Proc. IEEE, vol. 85, 1765-1779,1997.D. Marcuse, Theory of dielectric waveguides, Academic press, New york 1990.R. Adar, C.H. Henry, M.A. Milbrodt, R.C. Kistler, "Phase coherence of optical waveguide''.IEEE J. of Lighwave Technol., vol. 12, 603-606,1994.T. Erdogan, T.A. strasser, M.A. Milbrodt, E.J. Laskowski, c.H. Henry, G.E. Kohnke."Intergrated Mach-Zehnder add-drop filter fabricated by a single UV-induced gratingexposure", Appl. Optics. Vol. 36, 783 8-78 45 , 1997 .t l lL2)t3ll4ll5l

Mach Zehnder Interferometer for Wavelength Division Multiplexing

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