Nanowire-array-based photonic crystal cavity by finite-difference time-domain calculations

Abstract

Stimulated by recent reports on successful preparation of periodic nanowire arrays, we propose a class of photonic crystal (PC) cavities based on such nanowire arrays. This concept combines the advantages of PC's for tight confinement of light with the demonstrated suitability of nanowires for fabricating lasers. Unlike a previously used two-dimensional analysis, the three-dimensional finite-difference time-domain technique employed here allows us to study real spatial structures with nanowires of finite length. We discuss the realistic aspects of the cavity design, including the leakage in the vertical direction, aspect ratio of the wires, and thickness of the insulating layer between wires and substrate. The results show it is feasible to achieve microcavites with mode volumes from $\ensuremath{\sim}10{(\ensuremath{\lambda}∕n)}^{3}$ to $\ensuremath{\sim}2{(\ensuremath{\lambda}∕n)}^{3}$ and $Q$ values as high as ${10}^{4}$ using only about 80 nanowires with a proper design. The electromagnetic field of the mode concentrates in the nanowires, allowing their use as possible active materials for lasing and nonlinear operation. In addition, we analyze the influence of optical properties of the materials on the performance of the cavities, including absorption and dispersion. A simple formula is derived to calculate the $Q$ value with the presence of absorption. We predict a frequency splitting in dispersive materials based on numerical simulation. The results reported here establish the viability of the concept of using nanowires as building blocks to design microcavities and provide guidelines for designing compact and tightly confined optical modes in these cavities.