Coupled-waveguide exchange-Bragg resonator filters: coupled-mode analysis with loss and gain

Novel resonator filters made of two closely coupled asymmetric waveguides with phase-shifted exchange-Bragg grating, are investigated. Coupled-mode theory based on the normal modes is used to examine the effects of loss and gain on the filter spectral responses. The filter exhibits a total transmission at central wavelength and a rejection to the adjacent waveguide with high extinction ratio for other signals in the absence of loss and gain. Material loss reduces the transmitted power level and increases the filter bandwidth. With a certain amount of optical gain, good transmission can still be maintained in the presence of material loss. Proper control of the optical gain can lead to the amplification of both the transmitted and reflected powers at the central wavelength