N. Bahlmann

Applications of magneto-optical waveguides in integrated optics: review

Magnetooptical garnets combine high Faraday rotation with low optical losses in the near infrared region where optical communication via glass ?ber is established. In this spectral range garnets are the only materials discussed to realize nonreciprocal devices as optical isolators and circulators. Although such devices are available as microoptical components, practical versions of their integrated counterparts are still lacking. Numerous concepts have been developed theoretically many of which are tested experimentally. This paper presents an overview of the state of the art of the applications of garnet films in integrated optics. Also the technique of combining garnets with semiconductor materials is shortly discussed.

Improved design of magnetooptic rib waveguides for optical isolators

Garnet films of the following compositions (Lu,Bi)/sub 3/(Fe,Ga,Al)/sub 5/O/sub 12/ and (Tm,Bi)/sub 3/(Fe,Ga)/sub 5/O/sub 12/ are grown by liquid-phase epitaxy on [111]-oriented substrates of gadolinium gallium garnet. Double layers with opposite signs of Faraday rotation and single layers are prepared. Optical monomode rib waveguides are realized using such films. The nonreciprocal phase shift of the fundamental TM-mode is studied both theoretically and experimentally at a wavelength of 1.3 /spl mu/m. The maximum nonreciprocal effect of double layer films is about 1.7 times larger than that of similar single layer waveguides. Agreement between experiments and calculations is excellent.

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.

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.

Analysis of nonreciprocal light propagation in multimode imaging devices

We investigate a structure consisting of a magneto-optic multimode waveguide and two monomode waveguides serving as in- and outlets. The geometrical dimensions of the multimode waveguide can be adjusted such that the guided modes interfere constructively in forward direction and destructively for backward propagation. In this paper we present concepts for a circulator and two isolators based on multimode imaging.