Abstract

Adapting the concept of solid immersion lenses, we numerically study a micro-optical scheme for conventional high-index and photonic-crystal waveguide coupling by using a combination of different numerical methods such as ray tracing, angular-spectrum propagation, finite-difference time-domain simulations, and finite-element-method simulations. The numerical findings are discussed by means of impedance, group- or energy-velocity, spot-size, and phase-matching criteria. When fabrication constraints for high-index immersion lenses made of silicon are taken into account, a coupling efficiency of $\sim 80\%$ can be reached for monomode silicon-on-insulator waveguides with a quadratic cross section of the core and rectangular cross sections of moderate aspect ratio. Similar coupling efficiencies of $\sim 80\%$ can be obtained for silicon-on-insulator photonic-crystal waveguides. Tolerances that are due to misalignments and variations of the substrate thickness of the silicon lens are discussed.

© 2006 Optical Society of America

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