Digital signal processing in coupled photonic crystal waveguides and its application to an all-optical AND logic gate

Abstract

The realization of all-optical AND logic gates for pulsed signal operation based on the photonic bandgap transmission phenomenon is proposed. We are using realistic planar air-hole type coupled photonic crystal waveguides (C-PCWs) with Kerr-type nonlinear background medium. The novelty of our analysis is that the proposed AND logic gate operates with the temporal solitons, which maintain a stable envelope propagating in the nonlinear C-PCWs, enabling true ultrafast full-optical digital signal processing in the time-domain. The bandgap transmission takes place when the operating frequency is chosen at the very edge of the dispersion curve of one of the supermodes in the C-PCWs. In this regard, our original fast and accurate method is used to efficiently calculate the supermodes of the C-PCW system. The underlying semi-analytical full-wave modal analysis is based on the evaluation of the lattice sums for complex wavenumbers using the transition-matrix method in combination with the generalized reflection-matrix approach. As a proof of concept successful pulse operation of the all-optical AND logic gate is demonstrated in the framework of extensive full-wave finite-difference time-domain electromagnetics analysis.