## Abstract

A method based on Yeh’s rigorous $4\times 4$ matrix algebra and a fast perturbation-theory-based method are proposed for modeling and optimization of an integrated magneto-optical (MO) waveguide isolator. The transverse MO Kerr effect in ferromagnetic ${\mathrm{Co}}_{90}{\mathrm{Fe}}_{10}$ is used to design the integrated isolator. Waveguide losses introduced by absorption in the MO metallic film are compensated for by optical gain in an InP-based semiconductor optical amplifier with a tensile strained multiple-quantum-well (MQW) active region. The desired device isolation, which originates from the nonreciprocity of the transverse MO effect, is obtained by operation of the device under appropriate current injection, leading to zero modal net gain in the forward direction while the device remains lossy in the backward direction. In the approach based on Yeh’s matrix formalism, phenomena such as the MO effects described by anisotropic permittivity tensors, waveguide losses in absorbing layers, and optical gain in the active layer are explicitly included. Numerical aspects of the resonant condition solution for waveguide modes are discussed. In the perturbation theory method, the MO nonreciprocal waveguide effects are calculated in a first-order scheme. The general models are applied in an example of a realistic InP-based MQW isolator with a ${\mathrm{Co}}_{90}{\mathrm{Fe}}_{10}$ MO layer, indicating that practical isolation ratios are achievable within reasonable levels of necessary material gain. Rigorous and perturbation models are compared, and good agreement is obtained. This result indicates that first-order perturbation theory modeling of integrated magneto-optics is accurate enough, even for devices that employ MO materials with relatively strong Voigt parameters.

© 2005 Optical Society of America

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