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.

Wavelength division multiplexing (WDM) is essential for further enhancement of the transmission capacities of optical telecommunication systems. Key devices in WDM networks are multiplexing/demultiplexing components, which enable the combination/separation of several carrier waves with different wavelengths for the purpose of simultaneous transmission through one optical fibre. These components can be realized using Bragg diffraction from volume holographic gratings. Especially reflection holograms provide a pronounced wavelength selectivity which makes them attractive for free-space WDM applications. Holograms can be stored permanently in photorefractive lithium niobate crystals by the method of Thermal Fixing. Heating of the crystal during or after the recording process and subsequent development by homogeneous illumination at room temperature create nonvolatile holograms. The recording and development processes of Thermal Fixing in iron- and copper-doped lithium niobate crystals were investigated. Macroscopic Gaussian-shaped intensity patterns were used to analyse the origin of the fixing mechanism. Spatially resolved absorption measurements were performed to determine the concentration profiles of electron traps (Fe II/III) and protons. Results of computer simulations were compared with experimental results, which showed that protons can be found to work as compensators during hologram recording at temperatures around 180 degree C. Nevertheless thermal fixing without protons was possible, another compensation mechanism stood in. The obtained refractive-index changes were due to the electro-optic effect, other contributions could be neglected. With this detailed knowledge about thermal fixing, a two-channel demultiplexing unit was built by superposition of two thermally fixed reflection holograms in an iron-doped lithium niobate crystal. For this purpose a special two-beam interference setup with precisely adjustable writing angles was arranged in a vacuum chamber to eliminate thermally induced phase disturbances of the holographic recording procedure. Continuous development of the holograms by incoherent light was necessary. In the dark, the enhanced dark conductivity of the crystal used gave rise to a hologram degradation within about one day. Large diffraction efficiencies were attained (intensity losses between 2.3 and 5.2 dB only) uilizing crystals with high-quality polished surfaces. The crosstalk supression of the realized demultiplexer was > 25 dB, which is comparable with the performance of other multiplexing techniques like fibre Bragg gratings or arrayed-waveguide gratings. The low polarization dependence of the demultiplexer can be improved by superposition of two holograms for each channel.

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