Physics of elliptical reflectors at large reflection and divergence angles II: Analysis of optical beam distortions in integrated ultra-large-angle elliptical curved reflectors

In this work, we study the behavior of elliptical reflectors in nanophotonic integrated circuits in the context of two-dimensional multimode Gaussian beam. We show that the transformation of the beam profile at the input/output waveguide mouths, and the transformation of the beam profile at the reflector can be described in terms of 2D Hermite-Gaussian (HG) beam modes under first order approximation (FOA), referred to as HG-FOA. Due to the wavelength-scale waveguides in nanophotonic integrated circuits, the beams incident on the elliptical reflector have large diffraction angle which will result in asymmetric amplitude distortion upon non-normal reflection even for ideal elliptical reflecting surfaces. The amplitude distortion can be illustrated in the oscillation of the peaks of the reflected beam profiles around the propagation axis of the reflected beam. The amplitude distortion can also be shown by the deterioration in the coupling efficiency from the input waveguide to the output waveguide due to the excitation of higher order HG modes during the reflection. These two observations can both be explained by the HG-FOA method and are verified with Finite-Difference Time-Domain (FDTD) method. Moreover, we show that the coupling loss from the input waveguide to the output waveguide due to the higher order modes excited can be eliminated via insertion of a second reflector. Two specific arrangement of the second reflector are discussed and verified by the FDTD simulation.