M. Lohmeyer

Analysis of polarization independent Mach-Zehnder-type integrated optical isolator

This paper proposes, for the first time, an integrated optical isolator independent of light polarization. A Mach-Zehnder interferometer (MZI) with two nonreciprocal phase shifters, one for transverse electric (TE) modes and another one for transverse magnetic (TM) modes can be adjusted so that it blocks the fundamental modes of the waveguides constituting the interferometer propagating in one direction and is transparent for the modes propagating in the opposite direction. If the interferometer branch waveguides are in single mode regime, the performance of the device will not depend on the polarization of incoming light. The nonreciprocal phase shifters can be realized on structures with magnetization tangential to the propagation direction. Three geometries of nonreciprocal phase shifters are discussed and tolerances are estimated.

Nonreciprocal coupled waveguides for integrated optical isolators and circulators for TM-modes

Magneto-optic rib-waveguides can be utilized to construct the main component of devices like nonreciprocal Mach-Zehnder interferometers or nonreciprocal directional couplers. In this paper we present detailed investigations of nonreciprocal couplers formed by double layer rib-waveguides with alternating sign of the Faraday rotation. The performance of the proposed devices is simulated by normal mode theory and simple beam propagation calculations which include the incoming and outgoing dividing parts of the directional couplers. It is shown that the device length can be reduced by a factor of 6 as compared to former designs.

Phase-matched rectangular magnetooptic waveguides for applications in integrated optics isolators: numerical assessment

Phase matching between the fundamental TE and TM modes is an essential condition for complete polarization rotation in magnetooptic waveguides with longitudinally directed magnetization. This condition can be satisfied with embedded square waveguides or with raised strip waveguides, provided that the core dimensions are suitably chosen. Based on coupled mode theory for the vectorial modes of rectangular isotropic waveguides, we numerically simulate the performance of such devices in an experimental isolator setup, including birefringence and optical absorption. Fabrication tolerances with respect to all relevant parameters can be evaluated by simple perturbational expressions. Numerical verification shows that these formulas are accurate enough for practical purposes. The tolerances qualify the traditional polarization rotator setup as competitive to recent proposals for integrated optical isolators based on nonreciprocal interferometry.

Magnetooptical waveguides with polarization-independent nonreciprocal phase shift

Magnetooptical waveguides having nonreciprocal phase shift for both TE and TM modes can be prepared by properly adjusting the spatial variation of the Faraday rotation. Such waveguides are attractive to realize optical isolators. We investigate four concepts of magnetooptical waveguides which yield equal nonreciprocal phase shifts for the fundamental TE and TM modes. A polarization-independent Mach-Zehnder-type integrated optical isolator is presented. All the calculations are performed using material parameters typical for garnet films.

Finite-element analysis of nonreciprocal phase shift for TE modes in magnetooptic rib waveguides with a compensation wall

The nonreciprocal phase shift for TE modes in magnetooptic rib waveguides supporting a domain lattice was recently predicted. Using a single magnetic compensation wall in the symmetry axis of the waveguides, the nonreciprocal phase shift can be enhanced by a factor up to 1.8. The nonreciprocal phase shift is calculated by perturbation theory. The electromagnetic fields are determined by a semivectorial finite-element method, which properly handles the required field discontinuities.

Vectorial wave-matching mode analysis of integrated optical waveguides

For mode fields of integrated optical waveguides with piecewise constant and rectangular permittivity profile, Maxwells equations reduce to the two-dimensional Helmholtz wave equation, supplemented by continuity requirements on the boundaries between different media. Two basic components of the mode field are expanded into factorizing harmonic or exponential functions, separately on each rectangular region. We determine approximations for guided modes and propagation constants by means of a minimization procedure based on a least squares expression for the mismatch in the continuity requirements. Results for the hybrid mode fields of typical sample waveguides classify this approach as competitive with and superior to alternative methods for vectorial mode analysis, although some open questions remain.

Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory

Alteration of a geometry parameter in the cross section of a dielectric waveguide with piecewise constant permittivity profile can be regarded as a refractive index perturbation in a layer along a dielectric discontinuity line. Starting from these thin layer perturbations, we derive explicit expressions for partial derivatives of propagation constants with respect to the transverse waveguide dimensions, both for hybrid modes and for fields calculated in the semivectorial approximation. The perturbational formulas allow to estimate fabrication tolerances for realistic integrated optics devices at almost no extra computational cost. We demonstrate this by the example of a simple directional coupler and compare the perturbational results to numerically calculated tolerances.

Radiatively coupled waveguide polarization splitter simulated by wave-matching-based coupled mode theory

Coupled mode theory is applied to an arrangement of three raised strip waveguides with a multimode central strip. We use semivectorial numerically computed modes of the three single isolated waveguides as a basis for propagating supermode analysis of the entire structure. The pronounced polarization dependence of the raised strip guides allows for the design of a conveniently short polarization splitter. We discuss design guidelines and estimate the fabrication tolerances. The accuracy of the coupled mode approach is assessed by comparison with rigorously computed supermodes for comparable two waveguide couplers. Both types of structures indicate the limits in the applicability of the coupled mode model.

Unidirectional magnetooptic polarization converters

Inclination of the bias magnetization in a magnetooptic waveguide yields both nonreciprocal phase shifts and polarization conversion. This enables the design of unidirectional polarization converters, i.e., waveguides that switch between orthogonal polarizations for one direction of light propagation, but keep the polarization state for light propagating in the opposite direction. Simulations of double layer raised strip waveguides show that these constraints can be met with properly adjusted geometries. The results lead to the proposal of a polarization independent integrated optical circulator based on two unidirectional polarization converters between a front and a back polarization splitter.

An improved design of an integrated optical isolator based on non-reciprocal Mach-Zehnder interferometry

Non-reciprocal rib waveguide structures can be used to realize integrated optical isolators. 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 finite difference beam propagation method.