Three-guide couplers with multimode central waveguides allow for remote coupling between optical channels. A simple three mode approximation turns out to be sufficient for the description of the main features of the power transfer behavior. The specific form of the relevant modes suggests the design of integrated optical isolators and circulators based on magnetic garnet materials. These novel devices are superior to conventional nonreciprocal couplers with respect to the total length and admissible fabrication tolerances. We characterize the isolation performance and the transmission loss for the proposed devices by propagating mode simulations and estimate the influence of geometry parameter deviations.

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.

A bimodal planar waveguide segment of specific length and thickness between two thinner single mode sections can serve as an interferometer. Depending on the phase gain of the two modes in the thick region, these fields can interfere destructively or constructively at the transition from the bimodal to the single mode section. We employ this geometry to realize a simple magnetooptic isolator configuration, using a wide strip that is etched into a double layer in-plane magnetized magnetooptic film. The magnetization is oriented parallel to the strip; the light traverses the strip perpendicularly. Then the magnetooptic effect causes the phase velocities of TM polarized waves to be different for opposite directions of light propagation, resulting in a nonreciprocal power transfer across the strip. For a properly selected geometry one can expect isolator performance. If the strip width varies slightly, then adjusting the beam incoupling position means to change the distance which the light travels in the two mode segment. This offers a convenient tuning possibility, which may be a means to overcome the strict fabrication tolerances that apply usually to interferometric integrated isolator concepts.

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.

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.

Shifting the location of a dielectric boundary in the cross section of an integrated optical waveguide with piecewise constant refractive index profile results in a permittivity perturbation in a layer along the discontinuity line. On the basis of these thin layer perturbations, we discuss perturbational expressions for the derivatives of the propagation constants with respect to geometry parameters, both for fully vectorial, hybrid and for semivectorial approximations to the basic mode fields. The expressions are numerically verified by comparison with rigorously calculated data for a common semiconductor rib waveguide. Applied to a more complex device, the perturbational approach allows to estimate its complete set of tolerances for the geometry parameters, including the wavelength, on the basis of a single mode analysis. This is exemplified with a two rib waveguide coupler. By comparison with conventionally computed tolerances we give some assessment for the applicability of the effective perturbational approach.

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.

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.

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.

One of the principal tasks of numerically simulating integrated optical devices is the accurate calculation of modal fields and propagation constants. Our recently proposed 'wave-matching-method' for dielectric waveguides with rectangular and piecewise constant refractive index profiles is based on expansions of the electromagnetic field into functions with harmonic and exponential dependence on the transverse coordinates. Local expansions for regions with constant permittivity are joined by minimizing a least squares expression for the remaining misfit at the discontinuity lines. For this paper the wave-matching analysis has been applied to a number of more complex structures: a conventional, deeply etched two-waveguide coupler, an ARROW- waveguide, a three dimensional four-waveguide coupler and three-waveguide coupler with multimode central rib (radiatively coupled waveguides). We have found good overall agreement where a direct comparison with published results is possible.

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.

Magnetic garnet films of composition (Nd,Lu,Bi)3(Fe,Al,Ga)5O12 are grown by liquid-phase epitaxy on [111] oriented substrates of gadolinium gallium garnet. They have positive uniaxial anisoptropy and support lattices of parallel stripe domains. A monomode optical rib waveguide is prepared by photolithography and ion-beam etching parallel to the (112̄) direction, which is the preferred direction of the stripe domains. A magnetic domain pattern can be created such that a domain wall is located at the rib center while the adjacent walls stick to the flanks of the rib. At a wavelength of 1.3 μm a nonreciprocal phase shift of the guided fundamental transverse electric mode is observed.

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.

The nonreciprocal effect is the difference Deltabeta = beta(forward)-beta(backward) between forward and backward-propagation constants of optical modes. This effect is analyzed for the fundamental TM00 mode of channel waveguides in epitaxially grown magnetic garnet films. To increase |Deltabeta|, double layers with opposite signs of Faraday rotation are used to prepare the waveguides. It is shown that the temperature dependence of Deltabeta can be reduced considerably if the layer with positive Faraday rotation, which is at room temperature close to the Curie point, is replaced by a paramagnetic layer with negligible Faraday rotation. Concurrently, however, |Deltabeta| is decreased by approximately 35% at 295 K.

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.

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.

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.

Nonreciprocal rib waveguide structures can be used to realize integrated optical isolators. The nonreciprocal phase shift is the difference between the forward and backward propagation constants of TM modes in magneto-optic waveguides. It can be optimized with respect to absolute value and temperature dependence if double layer waveguides with different magnetic and nonmagnetic layers are prepared. In this paper we propose an improved design for two different Mach-Zehnder interferometer isolators the nonreciprocal parts of which are formed by such double layer waveguides. One concept utilizes a nonreciprocal and a reciprocal arm. In the other case both arms are nonreciprocal but with opposite sign of the nonreciprocal phase shift. A particular property of both concepts is that the lengths of the nonreciprocal arms are well defined. The rest of the interferometer is made by reciprocal rib waveguides. Therefore, the nonreciprocal phase shift is well known. The concepts are compared with regard to isolation ratio, forward losses and fabrication tolerances. Moreover, we simulate the entire isolator by a finite difference beam propagation calculation.

A concept for an integrated optical Mach-Zehnder interferometer isolator for TE modes is presented. Vertically magnetised magneto-optic rib waveguides with a compensation wall serve as nonreciprocal phase shifters for the fundamental TE mode. The nonreciprocal phase shifts in both interferometer arms add as the jumps of the Faraday rotation at the compensation walls have opposite sign.

Garnet films of composition (Lu, Bi) 3 (Fe, Ga, Al) 5 O 12 and (Tm, Bi) 3 (Fe, Ga) 5 O 12 are grown by liquid-phase epitaxy on [111]-oriented substrates of gadolinium gallium garnet. Ferrimagnetic films with positive or negative Faraday-rotation as well as paramagnetic films with negligible Faraday-rotation are produced by variations of the rare earth ion substitutions. The temperature dependence of Faraday-rotation is fitted with a molecular field model. Optical rib waveguides in single and double layer garnet films with different Faraday-rotations are realized. The nonreciprocal phase shift of the TM 0 -Mode is studied both theoretically and experimentally at a wavelength of 1.3 μm. Results show that the maximum nonreciprocal effect at room temperature of double layer films with opposite Faraday-rotation is 1.6 times as large as that of comparable single layer waveguides. But, because of the large temperature dependence of the Faraday-rotation of the positive rotating films, these waveguides show a large temperature dependence of the nonreciprocal phase shift. This problem can be avoided if the positive rotating layer is replaced by a paramagnetic layer. Agreement between calculations and measurements is excellent.