IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 13, NO. 9, SEPTEMBER 2001 969 Add–Drop Multiplexing by Grating-Induced Dispersion in Multimode Interference Device Mattias Åslund, Leon Poladian, Member, IEEE, John Canning, and C. Martijn de Sterke Abstract—We present the design for an add–drop multiplexer using a multimode interference device that supports two modes, and incorporates a Bragg grating. This device only exploits the dis- persive aspects of the grating in transmission. The grating induces a wavelength-dependent phase difference between the modes in- side the structure, effectively inverting the interference pattern at the output of the device over a small wavelength range whereby add–drop functionality is achieved. Index Terms—Couplers, gratings, multimode waveguides, wave- length-division multiplexing. I. INTRODUCTION A DD–DROP multiplexer devices allow access to single- wavelength channels and are crucial elements in wave- length-division-multiplexed (WDM) networks [1]. There is an interest in novel schemes that can overcome dispersion prob- lems and high component counts associated with add–drop de- vices based on the spectrally very narrow fiber Bragg grating reflections. The add–drop multiplexer proposed here combines low device dispersion and the spectrally narrow features of a Bragg grating in a single component. It utilizes the strong dis- persion just outside the bandgaps of an optical Bragg grating to alter the interference patterns of a multimode interference (MMI) device [2]. The interference pattern at the end of the de- vice is determined by the phase differences between the modes of the device. The phase difference, in turn, depends on the prop- agation constants of each mode. The grating is used to alter the effective propagation constant individually for each mode over a small wavelength range, which changes the interference pat- tern at the end of the device. In this letter, the basic principle is explored with two modes only. Similar and more complex ef- fects should occur if more than two modes are present. Grating generated spectral bandpass structures have been observed ex- perimentally in tapered waveguides supporting many modes [3]. II. DEVICE DESCRIPTION,MODELING, AND RESULTS The device is illustrated in Fig. 1. It consists of a dual-mode waveguide with a Bragg grating and two entry and two exit waveguide ports. The device is designed such that all wave- length channels enter through input port 1 and those wavelength channels outside the wavelength region affected by the grating Manuscript received February 13, 2001; revised May 24, 2001. M. Åslund, L. Poladian, and J. Canning are with the Optical Fiber Tech- nology Centre, University of Sydney, Eveleigh NSW 1430, Australia (e-mail: m.aslund@oftc.usyd.edu.au). C. M. de Sterke is with the School of Physics, University of Sydney, Eveleigh NSW 1430, Australia. Publisher Item Identifier S 1041-1135(01)07531-0. Fig. 1. Schematic of add–drop multiplexer device consisting of an MMI section with gratings incorporated (thin vertical lines) together with two input and two output ports. 5 cm, 12 m, 5 m, 531 nm, 1.46 1.4653. emerge from throughput port 4. The properties of the grating are designed such that signals within the band of the add–drop wavelength channel emerge from drop port 2, and for symmetry reasons, signals within the add–drop band entered in the add port 3 emerge from the common throughput port 4. The behavior of the device is analyzed both numerically (using the coupled mode equation for the grating) and analyt- ically (using the dispersion relation of the modes). An aspect of the device that simplifies the modeling is that it has one symmetric and one antisymmetric mode in the dual-mode section. There is, thus, no cross coupling of power between modes 1 and 2 if the grating is symmetric in the transverse direction. This simplifies the necessary calculations in that the modes can be considered separately. The wavelength dependent phase at the end of the two-moded section of the device for mode is therefore calculated by solving the coupled mode equation for each mode individually (1) where amplitude of the forward-propagating mode; amplitude of the backward-propagating mode; coupling coefficient of the grating; detuning (2) from the Bragg condition (2) Here, is the propagation constant in the absence of the grating. Although depends on waveguide and material dis- persion, it is taken to be constant for the narrow wavelength range considered here. The detuning for the second mode can 1041–1135/01$10.00 © 2001 IEEE