Diffraction characteristics of high-spatial-frequency (HSF) gratings are evaluated for application to polarization-selective computer-generated holograms by the use of two different approaches: second-order effective-medium theory (EMT) and rigorous coupled-wave analysis (RCWA). The reflectivities and the phase differences for TE- and TM-polarized waves are investigated in terms of various input parameters, and results obtained with second-order EMT and RCWA are compared. It is shown that although the reflection characteristics can be accurately modeled with the second-order EMT, the phase difference created by form birefringence for TE- and TM-polarized waves requires the use of a more rigorous, RCWA approach. The design of HSF gratings in terms of their form birefringence and reflectivity properties is discussed in conjunction with polarization-selective computer-generated holograms. A specific design optimization example furnishes a grating profile that provides a trade-off between the largest form birefrin gence and the lowest reflectivities.
Dual resonance in a waveguide-coupled ring microresonator j iříč t y r o ký 1, * , i va n r i c h t e r 2 a n d m i l a nš iň o r 2 Abstract. Eigenmodes of an isolated circular ring or disk microresonator are degenerate because of its rotational symmetry. Coupling of the microresonator to a straight bus guide breaks the rotational symmetry of the device. As a result, two slightly different resonant frequencies occur. While this effect is known in microring lasers, it is usually neglected in microring-based filters and add-drop de/multiplexers for telecom applications. Resonant frequency splitting does not follow from the usual 'optical circuit' analysis of the microring devices in which the coupling between the bus guide and ring is described by the 2 × 2 coupling matrix. It is shown here that the full 4 × 4 scattering matrix that takes into account also the back-reflections in the coupling region has to be used in order to include this effect into consideration. The magnitude of the resonant frequency splitting due to coupling to the bus guides in small high-contrast structures is estimated by two-dimensional numerical modelling based on bi-directional mode expansion and FDTD algorithms.
Properties of reflection and transmission spectral filters based on Bragg gratings in subwavelength grating (SWG) metamaterial waveguides on silicon-on-insulator platform have been analyzed using proprietary 2D and 3D simulation tools based on Fourier modal method and the coupled-mode theory. We also demonstrate that the coupled Bloch mode theory can be advantageously applied to design of Bragg gratings in SWG waveguides. By combining different techniques, including judiciously positioning silicon loading segments within the evanescent field of the SWG waveguide and making use of its dispersion properties, it is possible to attain sub-nanometer spectral bandwidths for both reflection and transmission filters in the wavelength range of 1550 nm while keeping minimum structural features of the filters as large as 100 nm. Numerical simulations have also shown that a few nanometer jitter in the size and position of Si segments is well tolerated in our filter designs.
High-quality cavities in hybrid material systems have various interesting applications. We perform a comprehensive modeling comparison on such a design, where confinemen in the III-V material is provided by gradual photonic crystal tuning, a recently proposed method offering strong resonances. The III-V cavity couples to an underlying silicon waveguide. We report on the device properties using four simulation methods: finite-di ference time-domain (FDTD), finite-elemen method (FEM), bidirectional eigenmode propagation (BEP) and aperiodic rigorous coupled wave analysis (aRCWA). We explain the major confinemen and coupling effects, consistent with the simulation results. E.g. for strong waveguide coupling, we fin quantitative discrepancies between the methods, which establishes the proposed high-index-contrast, lossy, 3D structure as a challenging modeling benchmark. References and links
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