Abstract
In this work, a dielectric waveguide mode solver is presented considering a general nonreciprocal permittivity tensor. The proposed method allows us to investigate important cases of practical interest in the field of integrated optics, such as magneto-optical isolators and anisotropic waveguides. Unlike the earlier developed mode solver, our approach allows for the precise computation of both forward and backward propagating modes in the nonreciprocal case, ensuring high accuracy and computational efficiency. As a result, the nonreciprocal loss/phase shift can be directly computed, avoiding the use of the perturbation method. To compute the electromagnetic modes, the Rayleigh-Ritz functional is derived for the non-self adjoint case, it is discretized using the node-based finite element method and the penalty function is added to remove the spurious solutions. The resulting quadratic eigenvalue problem is linearized and solved in terms of the propagation constant for a given frequency (i.e., γ-formulation). The main benefits of this formulation are that it avoids the time-consuming iterations and preserves the matrix sparsity. Finally, the method is used to study two examples of integrated optical isolators based on nonreciprocal phase shift and nonreciprocal loss effect, respectively. The developed method is then compared with the perturbation approach and its simplified formulation based on semivectorial approximation.
Highlights
Dielectric waveguides are fundamental components of optoelectronic and microwave devices.They have been extensively studied in the past and different kinds of materials have been considered
It is worth noting that the longer the waveguide, the larger the nonreciprocal effect. As it can be seen from the figure, a 25 nm-thick iron film will produce a nonreciprocal loss (NRL) of about −7 dB/mm, while a four times thicker layer generates an isolation of almost −12 dB/mm
It is worth noting that the proposed method allows us to directly compute the nonreciprocal phase shift effect (NRPS) and the NRL for complex structures based on new materials characterized by higher Faraday rotation constants like, for example, the bismuth iron garnet (BiIG) [64], in which the perturbation method could be rather inaccurate
Summary
Dielectric waveguides are fundamental components of optoelectronic and microwave devices. When KMx or KMy are purely imaginary numbers, the forward and backward modes differ only in the phase constant (i.e., the imaginary part of the propagation constant) and a nonreciprocal phase shift effect (NRPS) arises. By exploiting this effect, optical isolators have been designed using MachZehnder Interferometer (MZI) configuration in order to generate constructive interference for forward light and destructive interference for backward light [25, 26]. By exploring two examples of optical isolators based on magneto-optical waveguides for silicon compatible platform, we show how the shift between forward and backward propagation constants can be directly computed instead of using the pertubation theory [28]
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