Optik 122 (2011) 2199–2202 Contents lists available at ScienceDirect Optik jou rnal homepage: www.elsevier.de/ijleo Design and simulation of magneto-optic Mach-Zehnder isolator M. Khatir ∗ , N. Granpayeh Faculty of Electrical and Computer Engineering, K. N. Toosi University of Technology, Tehran, Iran a r t i c l e i n f o Article history: Received 2 September 2010 Accepted 4 February 2011 Keywords: Magneto-optic Isolator Mach-Zehnder Beam propagation method Effective index method a b s t r a c t In this paper, we have designed, optimized and simulated the magneto-optic Mach-Zehnder isolator. The waveguide isolator is based on a nonreciprocal phase shift in the magneto-optic branch of the MZ isolator. We have used the finite difference beam propagation method for numerical solution of the scalar wave equation. We have also used the transparent boundary condition. The propagation constant has been achieved by using the effective index method. We have calculated the design parameters to decrease the insertion loss in the forward direction and increase return loss in the backward direction and achieved a 40 dB isolation ratio. © 2011 Elsevier GmbH. All rights reserved. 1. Introduction In optical communication systems, the optical isolators are essential devices to protect optical active devices from undesired reflected light. A waveguide optical isolator is integrable to the optical sources and therefore reduces the cost of total system. The nonreciprocal properties of magneto-optic waveguides have been studied since 1985 [1]. Various types of magneto-optic waveguides have been proposed and some of them have been experimentally tested. Zeats and Watanabe [2] demonstrated that a magneto-optic film of a diluted magnetic semiconductor Cd 1-x Mn x Te grown on GaAs substrate can operate as a waveguide. A guided wave optical isolator using a four layer leaky yttrium iron garnet (YIG) waveg- uide with a YIG guiding layer was proposed and analyzed by Priye et al. [3]. The effect of nonreciprocal loss/gain of a waveguide optical amplifier covered by an absorbing magneto-optic layer was stud- ied in 1999 [4]. A nonreciprocal phase shift occurs in the waveguide geometry with the magnetic field applied transversely to the mate- rial. Z-independent magneto-optic waveguides have been analyzed and simulated by several methods such as: finite elements [5], finite differences (FD) [6,7], periodic Fourier transform [8] and the Galerkin method [9]. The beam propagation method (BPM) is one of the most popular approaches used in the modeling and simulation of electromagnetic wave propagation in guided-wave optoelec- tronic and fiber optic devices. ∗ Corresponding author. E-mail address: khatir@ee.kntu.ac.ir (M. Khatir). An important structure for isolators is the Mach-Zehnder type. The basic schematic of the Mach-Zehnder isolator with recipro- cal and nonreciprocal branches is shown in Fig. 1. A nonreciprocal phase shift of 90 ◦ between the two arms of the isolator together with a reciprocal phase shift of 90 ◦ have been achieved which result in optical blockage of the backward light and full transmission in the forward direction. The condition of 2h ≫ 2d is necessary for reduc- ing the coupling between two parallel branches. The dimensions and other parameters of the isolator must be determined so that a -90 ◦ and 90 ◦ phase shift can be achieved for the nonreciprocal branch in the forward and backward directions, respectively, but a +90 ◦ phase shift in reciprocal branch in both directions. Thus in the forward and backward directions the total phase shift between the fields in branches 1 and 2 are zero and 180 ◦ , respectively. In this paper, we have used the finite difference beam propa- gation method (FD-BPM) for simulation of the performance of a Mach-Zehnder isolator. Section 2 describes the optical waveguide theory. Then the effective index method (EIM) is described in Sec- tion 3. In Section 4, the FD-BPM and the EIM is proposed as a fast algorithm for simulation. The results are demonstrated in Section 5 and finally the paper is concluded in Section 6. 2. Optical waveguide theory If in the planar waveguide of Fig. 2 n f > n s > n c , where n c , n f and n s are the refractive indices of cover, waveguide layer and substrate, respectively, then the light wave is guided in the waveguide layer. It is assumed that the waveguide has a step-index profile. All mate- rials are considered to be lossless. The substrate and cover region are assumed to be isotropic. 0030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2011.02.009