Photonic crystal defect mode cavity modelling: a phenomenological dimensional reduction approach

Abstract

A phenomenological dimensional reduction approach (PDRA) for the cavity characteristics in defect mode based photonic crystal (PC) lasers is presented. Based on the fully vectorial three-dimensional finite-difference time-domain (3D FDTD) technique, simultaneous enhancement and suppression in spontaneous emission and absorption were obtained in an absorptive photonic crystal slab (PCS) cavity. Effective index perturbation (EIP) was proposed for fast and accurate determination of the effective index and the dominant resonant cavity frequency in a 3D PCS structure, with two-dimensional (2D) FDTD simulation. Further dimensional reduction from 2D to one-dimensional planar cavity enables phenomenological modelling of lasing characteristics via the effective reflectivity calculation and rate equation analysis. Very fast and accurate results have been achieved with this PDRA approach. A high spontaneous emission factor and cavity quality factor Q were obtained in a single defect cavity, which led to over an order reduction in lasing gain threshold. The model offers a fast and accurate tool for the design and modelling of PC defect mode cavity based devices and aids the research in the proposed novel defect mode based devices such as ultra-compact light sources on Si and spectrally resolved PC infrared photodetectors.