Physics of elliptical reflectors at large reflection and divergence angles I: Their design for nano-photonic integrated circuits and application to low-loss low-crosstalk waveguide crossing

In this work, we study the formulation of beam propagation in an elliptical reflector in nanophotonic integrated circuits (NPICs). We introduce a Gaussian beam mode analysis with Effective Refractive Index Approximation (EIA) applied to planar waveguides. The wavelength-scale waveguides in NPICs lead to large diffraction angle of the input beam and phase aberration in the reflected beam. However, this aberration can be shown to be negligible under first order approximation (FOA). With the Gaussian beam formulation, we study the Near Field and Far Field scenarios in the incident and reflected beams and propose a design methodology that utilizes the two scenarios to minimize footprint of associated devices. Specifically, we use Finite-Difference Time-Domain (FDTD) simulation to show that applying such methodology in designing a waveguide crossing using elliptical reflectors not only minimizes the device footprint but also creates a novel crossing that outperforms the conventional Direct Waveguide Crossing (DWC) in terms of the lowest order mode transmission efficiency and crosstalk.