Mode expansion modeling of rectangular integrated optical microresonators

Two dielectric waveguides that are evanescently coupled to a square or rectangular region of increased refractive index can serve as a very compact integrated optical microresonator. We consider these devices in a spatial two-dimensional setting, where a rigorous mode expansion technique enables accurate and quite efficient numerical simulations of these configurations. The paper is concerned with single resonator units as well as with an add-drop filter constructed by cascading two square cavities. Besides calculating the power transmission spectra, we try to document as far as possible the characteristic electric field patterns that occur at major and minor resonance wavelengths. The influence of the various geometrical parameters on the resonator performance is investigated in detail

Lichtführung in rechtwinkligen integriert magnetooptischen Bauelementen

By means of numerical simulations, the thesis aims at improvements in the understanding of light propagation in dielectric optical waveguides, with emphasis on nonreciprocal integrated magnetooptic devices. The results include: Proposal, implementation, and assessment of the WMM mode solver (Wave Matching Method) For waveguides with piecewise constant, rectangular permittivity profiles, the calculation of guided modes can be based on a local expansion into factorizing harmonic or exponential trial functions. A least squares expression for the mismatch in the continuity conditions at dielectric boundaries connects the fields on neighbouring regions. Minimization of this error allows to compute propagation constants and mode fields. The procedure has been implemented both for semivectorial and fully vectorial mode analysis. The piecewise defined trial fields are well suited to deal with field discontinuities or discontinuous derivatives. Numerical assessment shows excellent agreement with accepted previous results from other methods. The WMM turns out to be effective especially for structures described by only a few rectangles. It yields semianalytical mode field representations which are not restricted to a computational window. The fields are therefore perfectly suited for further processing, e.g. in the framework of various kinds of perturbation theory. Perturbational geometry tolerancing procedure Shifting the location of a dielectric boundary in the cross section of a 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, perturbational expressions for the derivatives of the propagation constants with respect to geometry parameters are discussed. The approach provides direct access to wavelength dependences. Comparison with rigorously calculated data shows that the accuracy is sufficient to yield reasonable tolerance estimates for realistic integrated optical devices, at almost no extra computational cost. This perturbational approach allows to establish and to quantify guidelines for geometry tolerant devices. Numerical assessment of nonreciprocal wave propagation The coefficients of coupled mode theory for the magnetooptic permittivity contribution allow a classification of the influences of gyrotropy on guided wave propagation. For mirror symmetric waveguides, one identifies the dominant effects of TE phase shift, TM phase shift, and TE/TM polarization conversion, for polar, equatorial, and longitudinal magnetooptic configurations, respectively. Layered equatorial magnetooptic profiles lead to the well known phase shifters for TM modes. Analogously, sliced asymmetric polar magnetooptic profiles yield phase shifts for TE polarized modes. Simulations of rib waveguides with a magnetooptic domain lattice predict effects of the same order of magnitude as the phase shift for TM modes. Phase matching as a condition for complete polarization conversion in longitudinally magnetized waveguides can be realized with selected geometries of raised strip waveguides or embedded square waveguides. Based on coupled mode theory for hybrid fundamental modes, the analysis of the performance of such devices in an isolator setting includes birefringence, optical absorption, and an explicit perturbational evaluation of fabrication tolerances. A magnetooptic waveguide which is magnetized at a tilted angle may perform as a unidirectional polarization converter. The term specifies a device that converts TE to TM light for one direction of propagation, while it maintains the polarization for the opposite direction. A double layer setup with two magnetooptic films of opposite Faraday rotation is proposed and simulated. Designs of three waveguide couplers for applications as isolators/circulators and polarization splitters Three-guide couplers with multimode central waveguides allow for a remote coupling between the outer waveguides. While the power transfer is a truly multimode interference process, one can identify two different regimes where either two or three supermodes dominate the coupling behaviour. Numerical simulations show reasonable agreement between the main coupling features in planar an three dimensional devices. The specific form of the relevant modes suggests the design of integrated optical isolators and circulators. Both planar and three dimensional concepts are investigated. A radiatively coupled waveguide polarization splitter should be designed such that the entire dynamic range of the coupling length variations is exploited. This is easily possible with a three dimensional raised strip configuration. Combination of two magnetooptic unidirectional polarization converters and two radiatively coupled waveguide based polarization splitters leads to a concept for a polarization independent integrated four port circulator device. The simulation predicts a total length of about three millimeters

Wave-matching-method for mode analysis of dielectric waveguides

Abstract: Frequently the cross section of a longitudinally homogeneous dielectric waveguide may be decomposed into rectangles with constant permittivity. For points inside these rectangles the wave equation for modal fields is solved analytically by expanding into functions with harmonic or exponential dependence on the transverse coordinates. Minimization of a least squares expression for the remaining misfit on the boundary lines allows us to determine propagation constants and fields for guided modes. Semivectorial calculations for two sets of rib waveguides and the center sections of a directional coupler and a MMI device show very good agreement with results found in the literature

Integrated optical cross strip polarizer concept

Passing across an abrupt junction from a thick vertically bimodal waveguide to a thinner single mode segment, guided light can undergo complete destructive interference, provided that the geometry and the phases of the modes in the initial segment are properly adjusted. We propose to employ this effect to realize a simple polarizer configuration, using a strip that is etched from a planar waveguide. A beam of light is made to pass the strip perpendicularly. The light enters from the single mode waveguide outside the strip into the strip segment, which is configured to support two modes. At the end of the strip, apart from reflections, the amount of power that is guided in the following lower segment depends on the local phases of the two modes. These phases are different for TE and TM light, hence we may expect a polarization dependent power transfer, resulting in polarizer performance for a properly selected geometry. The paper describes in detail the modeling of the device in terms of rigorous mode expansion. Design guidelines and tolerance requirements for geometric and material parameters are discussed. For typical Si3N4/SiO2 materials, our calculations predict a peak performance of 34 dB polarization discrimination and 0.3 dB insertion loss for a device with a total length of about 1

Oncofetal antigen in Xiphophorus detected by monoclonal antibodies directed against melanoma-associated antigens

Monoclonal antlbodies (MAbs) directed against Xiphophorus melanoma cells were deve(oped and tested by lndirect immunofluorescence and Immunoperoxidase staining for reactivity with a panel of I 5 allogeneic tissues and 12 allogeneic cell llnes. The reactivity of such MAbs was restricted to melanoma cells from tumor biopsies and melanoma-derived cell lines. ln addition, all embryonie cells of all histiotypes from developmental stages later than mld·organogenesis and from corresponding short term in vitro cultures reacted with these MAbs. ln contrast, normal tissues and organs from adult fish dlsplayed no reactivity, thus implying that the melanoma-associated antigens detected by the MAbs described are oncofetal antigens

Integrated optical cross strip interferometer

A thick, bimodal segment of specific length and height between two single mode sections of a planar waveguide can serve as an integrated optical interferometer. It is realized by etching a wide strip form a guiding film. A vertically guided, laterally unguided beam of light is then made to traverse the strip perpendicularly. For a wide range of materials the structure can be dimensioned such that it shows the proper behavior of an interferometer: depending on the phase gain of the two modes in the thick region, the guided light interferes either almost completely destructively at the transition to the output segment, i.e. the power is radiated away into the substrate and cover regions, or constructively, i.e. most of the power passes the device. We believe that for certain applications structures of this kind can be a simple substitute for instruments like Mach-Zehnder interferometers or directional couplers. This is illustrated by two numerically simulated examples: A polarizer constructed from silicon based waveguides, which offers 30 dB polarization discrimination and 0.1 dB insertion loss with a total length of only 10 micrometers, and a proposal for an integrated magneto optic isolator experiment, where the freedom in the lateral direction can be exploited for a proper tuning of the device

Integrated magnetooptic cross strip isolator

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 in-coupling 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

Integrated optical polarizer based on the cross strip interferometer configuration

A bimodal segment of specific length and thickness between two single mode sections of a planar waveguide can serve as a simple interferometer. The configuration can be realized by etching a wide strip from a dielectric film and forcing a — vertically guided, laterally unguided — beam of light to traverse the strip perpendicularly. A TE-pass polarizer designed on the basis of this concept achieves more that 30dB polarization discrimination with a total length of only 5 micrometers, for air covered Silicon-Oxide/Nitride waveguides at a wavelength of 650 nanometers