(A) wavelength-scale SOI microdisk exceptional point filter based on two unequal scatterers

Abstract

The appearance of exceptional point involving the coalescence of both eigenvalues and eigenfunctions of non-Hermitian Hamiltonian in an open quantum system is investigated in a resonator-waveguide system. In particular, asymmetric backscattering in a two-port optical filter is observed using Finite Element Method (FEM) and Finite-Difference Time-Domain (FDTD) numerical simulations with only two unequal Rayleigh scatterers placed at certain lateral positions in the evanescent field of the cavity on silicon-on-insulator (SOI) platform. Field incidence that adheres to the structure’s chirality causes the incident photons to ‘tunnel through’ along the resonator as though the scatterers are absent. Incidence at the opposite port however induces significant backreflection which field is then coupled back to the input port. The backscattering at the input port suggests the existence of a simultaneous ‘drop’ port without introducing a second waveguide

besides being asymmetric in behavior at exceptional point contrary to the current typical filters. While the ‘through’ port remains steadily unruffled and symmetric, the backscattering can be fine-tuned by simply shifting one of the scatterers, which to a certain displacement extent exhibit a complete reversal of asymmetric behavior at the ports. Rigorous theoretical model based on the temporal coupled mode theory framework is developed to set the governing dynamical properties of the filter system. This work introduces a novel form of filter, which is proposed as the ‘Exceptional Point Filter’ with concurrently symmetric and asymmetric ports

and can be a new addition to the current family of filters we have today.