JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 17, NO. 2, FEBRUARY 1999 243 A Rigorous Comparison of the Performance of Directional Couplers with Multimode Interference Devices M. Rajarajan, Student Member, IEEE, B. M. A. Rahman, Senior Member, IEEE, and K. T. V. Grattan Abstract— The authors report, for the first time, a direct comparison between a directional coupler and a multimode interference-based device, in relation to their performance characteristics such as crosstalk, polarization dependence and the effect of fabrication tolerances. The coupling efficiency for a nonidentical coupler, produced inadvertently due to problems with fabrication tolerances, is also demonstrated. The vector finite element (FE) and the least squares boundary residual (LSBR) methods are employed as the numerical tools used in this simulation study. Index Terms— Crosstalk, directional couplers, finite element method, least squares boundary residual method, multimode interference devices, photonic devices, polarization effects, power splitters. I. INTRODUCTION W ITH the maturity of a range of photonic devices, the emphasis on development is now in the design of compact optoelectronic integrated circuits, to exploit the full potential of available low-loss and high-bandwidth optical fibers. These optical systems use directional couplers [1], adiabatic Y-branches [2], free-radiating devices, and multi- mode interference couplers [3] for signal routing and signal processing. Even though directional couplers have proved to be efficient power routing devices, however, the development of multimode interference (MMI)-based devices has proceeded rapidly due to their having attractive properties [3] such as compactness, tolerance to a range of fabrication parameters, an inherent balance, and low optical loss and because they are particularly well suited to use with a moderate number of ports. In this paper, the authors present a rigorous numerical comparison of the performance of a directional coupler with that of a MMI-based device. To our knowledge, for the first time, the important properties such as crosstalk, polarization sensitivity and fabrication tolerances are directly compared for both types of devices and their performance characteristics, developed in this simulation, are discussed. To do so, the vector -field finite element method (FEM) is used to calculate the modal propagation constants and field profiles and the least squares boundary residual (LSBR) method is used to determine the modal excitation coefficients. The combination of these two methods has already been Manuscript received September 15, 1997; revised April 22, 1998. The authors are with the Department of Electrical, Electronic and Informa- tion Engineering, City University, London EC1V 0HB U.K. Publisher Item Identifier S 0733-8724(99)01203-7. proved to be more accurate than other available numerical techniques [4]. II. THEORETICAL BACKGROUND Directional coupler-based devices are important components in a wide range of integrated optic devices. When light is launched into one of the input guides, at the coupling length most of the power is coupled to the adjacent output guide. However, there may be a small amount of power remaining out the incident output port due to the incomplete cancellation of the modes, and this is responsible for the presence of crosstalk [5]. This may be due to the unequal coefficients of the excited even and odd supermodes, structural asymmetry, or the device length not being equal to the coupling length. The shorter the coupling length, the worse is the crosstalk, since the supermode coefficients become unequal due to the strong coupling between the guides. The coupling length of a directional coupler may be defined as (1) where and are the propagation constants of the even and odd supermodes. The performance characteristics of MMI-based devices are also evaluated in this study. The MMI devices consist of a lateral multimode waveguide where the interference between the modes leads to well defined images of the exciting field at specific imaging lengths. In this simulation study, “restricted resonance” MMI couplers are used. In these restricted interfer- ence devices, the access waveguides are positioned at points and where is the width of the MMI, in order not to excite some specific modes in the device. By using the restricted resonance condition, the device length can be reduced by some threefold. The beat length of a MMI may also be defined as (2) where and are propagation constants of the first and the second modes in the MMI section. Since the quadrature relationship of the propagation constants for the higher order modes is approximately holds [3], at one beat length, most of the input power appears in the cross state and produces a mirror-image of the input. At twice the beat length, the power 0733–8724/99$10.00  1999 IEEE