TY - JOUR A1 - Lohmeyer, M. A1 - Shamonin (Chamonine), Mikhail A1 - Hertel, P. T1 - Boundary conditions for the finite difference beam propagation method based on plane wave solutions of the Fresnel equation JF - IEEE Journal of Quantum Electronics N2 - Each particular implementation of the beam propagation method (BPM) requires a special procedure allowing for radiation to leave the computational window. We propose a new approach to constructing the finite difference schemes of the BPM at the boundary of the computational window. These schemes are independent of the computed fields and allow for a similar treatment of both interior and boundary points. The new approach can be further improved by correcting the field values at the boundary points according to Hadley's method. The algorithm is easy to implement for both two- and three-dimensional structures. The new method considerably reduces computation times because the propagation matrices remain constant in longitudinally invariant sections, thus avoiding repeated LU-decompositions. The basic idea-establishing the finite difference scheme such that locally exact, approximate, or plausible solutions are recovered-may be of interest for other efforts to solve partial differential equations by the finite difference method. KW - Boundary conditions KW - Finite difference methods KW - Optical propagation KW - Matrix decomposition KW - Computational modeling KW - Refractive index KW - Maxwell equations KW - Sparse matrices KW - Partial differential equations KW - Shape Y1 - 1997 U6 - https://doi.org/10.1109/3.552269 SN - 0018-9197 VL - 33 IS - 2 SP - 279 EP - 286 ER - TY - JOUR A1 - Shamonin (Chamonine), Mikhail A1 - Lohmeyer, M. A1 - Hertel, P. T1 - Analysis of power-dependent switching between radiatively coupled planar waveguides JF - Journal of Lightwave Technology N2 - Effective coupling between two remote optical waveguides without branching sections can be achieved in a three-guide system with multimode central waveguide. We investigate the nonlinear power switching of c.w. laser radiation by such radiatively coupled waveguides. It is shown that effective all-optical switches with spatially well separated input/output channels can be realized although the influence of multimode interference on the switching characteristics becomes more pronounced for increasing thickness of the central guide. Different coupling regimes are specified, and the changes in switching characteristics during the transformation from one regime to another is studied. Numerical calculations for the critical power are compared with an approximate analytical expression. It is also shown that, at a moderate input power, a small number of modes determines the switching behavior. KW - Electromagnetic coupling KW - Planar waveguide KW - Optical waveguides KW - Nonlinear optics KW - Optical coupling KW - Optical surface waves KW - Optical refraction KW - Optical variables control KW - Refractive index KW - Optical switches Y1 - 1997 UR - 1558-2213 U6 - https://doi.org/10.1109/50.588671 VL - 15 IS - 6 SP - 983 EP - 989 PB - IEEE CY - New York ER - TY - JOUR A1 - Lohmeyer, M. A1 - Shamonin (Chamonine), Mikhail A1 - Bahlmann, N. A1 - Hertel, P. A1 - Dotsch, H. T1 - Radiatively Coupled Waveguide Concept for an Integrated Magneto-Optic Circulator JF - MRS Online Proceedings Library N2 - 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. Y1 - 1998 U6 - https://doi.org/10.1557/PROC-517-519 SN - 1946-4274 IS - 517 SP - 519 EP - 524 ER - TY - JOUR A1 - Shamonin (Chamonine), Mikhail A1 - Lohmeyer, M. A1 - Hertel, P. T1 - Directional coupler based on radiatively coupled waveguides JF - Applied optics (Appl. Opt.) N2 - We investigate a system of two waveguides with leaky modes sharing a common substrate (radiatively coupled waveguides). The main advantage of such a system is the possibility of remote coupling. A perturbation theory is developed for both TE and TM polarization. Numerical calculations of dispersion curves and of the coupling length allow us to determine the limitations of the perturbation theory. We study the influence of multimode interference on the process of beating by considering the propagation of a given initial field. Finally, we propose a new design for an effective, integrated optical TE-TM polarization splitter. Y1 - 1997 UR - https://opg.optica.org/ao/abstract.cfm?URI=ao-36-3-635 U6 - https://doi.org/10.1364/ao.36.000635 VL - 36 IS - 3 SP - 635 EP - 641 ER -