An improved design of an integrated optical isolator based on non-reciprocal Mach±Zehnder interferometry N. BAHLMANN, M. LOHMEYER, M. WALLENHORST, H. DO È TSCH, P. HERTEL University of Osnabru È ck, 49069 Osnabru È ck, Germany Received 4 November 1997; revised and accepted 16 March 1998 Non-reciprocal rib waveguide structures can be used to realize integrated optical iso- lators. In this paper, we propose a concrete design for a Mach±Zehnder interferometer type isolator for TM modes. Just one of the arms, which are of equal length, is a non- reciprocal magneto-optic waveguide. The rest of the interferometer is reciprocal. Required fabrication tolerances are estimated, and the entire isolator is simulated by applying a ®nite difference beam propagation method. 1. Introduction Magneto-optic isolators play an important role in optical communication techniques. They are used to protect the semiconductor lasers from re¯ected light. At present only bulk isolators are available. To realize cheap integrated optical isolators, magnetic garnet ®lms can be used. They have low absorption and high Faraday rotation in the near infrared. The Faraday rotation, which is the basis for non-reciprocal eects, can be en- hanced by bismuth substitution. Various kinds of optical isolators have been proposed by a number of researchers [1±6]. The most promising concepts of integrated optical isolators rely on non-reciprocal Mach- Zehnder interferometry [7, 8]. The distinction between forward and backward propagation is achieved by the dierential non-reciprocal phase shift (NRPS) Db, the dierence be- tween the forward and backward propagation constants Db  b TM forw  b TM back of TM modes in magneto-optic waveguides [9]. In the forward direction, waves propagating along both arms of the Mach±Zehnder interferometer are in phase, in the backward direction a phase shift of p occurs. In former papers no concrete design for an isolator with one non- reciprocal arm was suggested. Here we present detailed design and fabrication consider- ations for the realization of such an isolator based on non-reciprocal Mach±Zehnder interferometry. We show how the intrinsic phase of the interferometer can be adjusted to zero in the forward propagation direction. Furthermore, we simulate the new design by a ®nite dierence beam propagation calculation. 2. Non-reciprocal waveguides The following analysis is performed for the basic rib geometry sketched in Fig. 1. Mode propagation is assumed along the z axis and the magnetization ~ M is adjusted in the ®lm Optical and Quantum Electronics 30 (1998) 323±334 0306±8919 Ó 1998 Chapman & Hall 323