Mach Zehnder Interferometer for Wavelength Division Multiplexing Ary Syahriar Pusat Pengkajian dan Penerapan Teknologi Informasi dan Elektronika Badan Pengkajian dan Penerapan Teknologi e-mail : ary@inn.bppt.go.id Abstract A theoretical analysis of multiplexing based on Mach-Zehnder interferometer is presented. 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 practical fabrication of the devices. 1. Introduction In modern communication systems narrow band information services and high-speed data and video information services are expected to be integrated in one-communication networks [1]. Wavelength Division Multiplexing (WDM) is believed to be one of the most practical ways to achieve transmission capacities of a few tera bit per second (Tb/s). Devices such as optical filters and wavelength multiplexers (MUXER) and demultiplexers (DEMUXERS), which manipulate optical properties in wavelength domain, are essential to WDM optical communication systems. One of the most useful device is the Mach Zehnder Interferometer (MZI) [2]. 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 will determine the MZI s characteristics. In this paper the analysis of MZI based on coupled mode theory and matrix transmission method is presented. A number of its features will also be explained. 2. The MZI Structure A Mach-Zehnder device consists of two 3 db fused couplers, between which a phase difference is introduced in the two paths by increasing one of the path lengths with respect to the other as shown in Figure 1. The fused couplers are wavelength sensitive; hence the characteristics of the device are determined by the 3 db crossover wavelength of the couplers, the coupling strength and the introduced path difference. L 1 Coupler 1 Coupler 2 Input 1 L 2 In p ut 2 Ou tput 2 Figure 1. Schematic diagram of Mach-Zehnder interferometer For modeling purposes the device can be divided into three constituent parts: the two 3 db couplers and a phase shifting section between them. The characteristic of each of the components A-45
A-46 Proceedings, Komputer dan Sistem Intelijen (KOMMIT 22) Auditorium Universitas Gunadarma, Jakarta, 21 22 Agustus 22 parts of the device can be represented by the operation of matrix in a vector which represents the amplitude of the signals in each of the two fiber at the input to that section based on the coupled mode theory as [3]: here cos( Φ) j sin( Φ) M coupler = (1) j sin( Φ) cos( Φ) Φ = κ z, κ = coupling coefficient, and z = 3 db coupler length. The field in the two differential path lengths introduces a phase shift represented by [4] jφ e M Phase Shift = jφ (2) e where φ = βδl, and β is the effective index of the optical fiber. ΔL is the phase different between the two arms. As is well known, the β value can be calculated by solving the characteristic equation for LP 1 mode [3]: WJo ( U) K1( W ) = UJ1( U) Ko ( W ) (3) where J o and J 1 are Bessel functions and K o and K 1 are modified Bessel functions. For single mode operation V<< 2.448. U and W have its usual meanings [3]. For fiber couplers the coupling coefficient κ is given by [3]: Wd 2 K o ( ) λ U κ = a (4) 2 2 2 2πn a V K ( ) 1 1 W here d is the separation between the fiber axes, a is fiber diameter, V is a normalized frequency, λ is the wavelength and n 1 is core refractive index of the fiber. The response of Mach-Zehnder then is given by [5] M = M M M (5) coupler phase shift coupler and the output amplitude can be described by Where the input amplitude is represented by a vector E output = M E input (6) 1 E input = (7) In this calculation a perfect 3 db coupler has been assumed and that the fiber has no propagation loss. 3. The MZI Characteristics To optimize the design of MZI, it is important to calculate and predict the device performance. The first calculation is to find the effective refractive index of fiber optics as a
Mach Zehnder Interferometer for Wavelength Division Multiplexing A-47 function of wavelength. Figure 2 shows the effective refractive index of fiber as a function of wavelength. This is derived by finding root of Equation (3) which can easily be done using bisection method. The linear response of refractive index shows that the fiber acting in single mode region. Furthermore it can be used to predict the change of output characteristic as function of wavelength. Effective refractive inde 1.46733 1.46732 1.46731 1.4673 1.46729 1.46728 1.46727 1.46726 1.46725 1.46724 1.46723 Figure 2. Effective refractive index as a function of wavelengths Figure 3. shows ΔL change as function of λ on π phase shift different of the two arms. It shows that ΔL change as linear function which can be used to predict exact path difference in designing multi/demultiplexing devices. 2.14118 2.14116 2.14114 L ( m) 2.14112 2.1411 2.1418 2.1416 2.1414 2.1412 Figure 3. Arm length different of MZI as function of Wavelength for π/2 phase shift
A-48 Proceedings, Komputer dan Sistem Intelijen (KOMMIT 22) Auditorium Universitas Gunadarma, Jakarta, 21 22 Agustus 22 The typical output spectra of an MZI are shown in Figure 4 with different path length. As we can see, this bi directional multi-window WDM acts as a special multiplexer which combine/separates two sets of wavelengths, which are interleaved by each other. Because the transfer function is actually periodic in the frequency domain, once the first and the last desired wavelengths are set at the ITU frequency, the rest of the wavelength peaks in between will automatically sit at their respective ITU wavelengths. Because the 3-dB couplers have a broad bandwidth, this device also shows superior uniformity on the insertion loss of the wavelength peak. -1 Power (db) -2-3 -4-5 ΔL =.15 μ m -6 (a) -1 Power (db) -2-3 -4-5 ΔL =.3 μ m -6 (b)
Mach Zehnder Interferometer for Wavelength Division Multiplexing A-49-1 -2-3 -4-5 ΔL =.5 μ m -6 (c ) -1 Power (db) -2-3 -4-5 ΔL =.78 μ m -6 (d) Figure 4. MZI spectra with different ΔL length
A-5 Proceedings, Komputer dan Sistem Intelijen (KOMMIT 22) Auditorium Universitas Gunadarma, Jakarta, 21 22 Agustus 22 4. Conclusion We 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 to improve device performance a phase length different can be tuned to comply with ITU grid. 5. Reference [1] R. Ramaswami, Optical fiber communication: from transmission to network, IEEE. Commun. Mag., 5 th Anniversary comm. Issue, 138-147, 22. [2] M.J. Yadlowsky, E.M. Deliso, V.L. Da Silva, Optical fibers and amplifiers for WDM systems, Proc. IEEE, vol. 85, 1765-1779, 1997. [3] D. Marcuse, Theory of dielectric waveguides, Academic Press, New York 199. [4] R. Adar, C.H. Henry, M.A. Milbrodt, R.C. Kistler, Phase coherence of optical waveguide, IEEE J. of Lightwave Technol., vol. 12, 63-66, 1994. [5] 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 grating exposure, Appl. Optics. Vol. 36, 7838-7845, 1997.