Highly efficient photonic crystal-based multichannel drop filters of three-port system with reflection feedback

We have derived the general condition to achieve 100% drop efficiency in the resonant tunneling-based channel drop filters of a threeport system with reflection feedback. According to our theoretical modeling based on the coupled mode theory in time, the condition is that the Q-factor due to coupling to a bus port should be twice as large as the Q-factor due to coupling to a drop port and the phase retardation occurring in the round trip between a resonator and a reflector should be a multiple of 2pi. The theoretical modeling also shows that the reflection feedback in the threeport channel drop filters brings about relaxed sensitivity to the design parameters, such as the ratio between those two Q-factors and the phase retardation in the reflection path. Based on the theoretical modeling, a fivechannel drop filter has been designed in a two-dimensional photonic crystal, in which only a single reflector is placed at the end of the bus waveguide. The performance of the designed filter has been numerically calculated using the finite-difference time domain method. In the designed filter, drop efficiencies larger than 96% in all channels have been achieved.