FDTD simulation of hexagonal micropillar cavities Frankie Kin Lam Tung, Ning Ma and Andrew W. Poon Department of Electrical and Electronic Engineering Hong Kong University of Science and Technology Clear Water Bay, Hong Kong, China Tel: (852)-2358-7905, Fax: (852)-2358-1485, Email: eeawpoon@ust.hk ABSTRACT Hexagonal micropillar (µ-pillar) cavities have been studied using 2-D finite-difference time-domain (FDTD) method. Singlemode resonances have been observed from a 2-µm sized hexagonal µ-pillar cavity that is selectively input- coupled. The simulated resonance wavelengths are consistent with the wavefront-matching condition based on ray- optics. The resonant field distribution has an integer number of field maxima along the cavity rim similar to whispering-gallery modes. Laterally waveguide-coupled hexagonal µ-pillar cavity channel add/drop filters with parallel and non-parallel waveguides have also been designed and simulated. Preliminary simulation of a 20-µm sized hexagonal µ-pillar cavity laterally coupled with 0.4-µm wide parallel waveguides demonstrated an extinction ratio of ≈ 8 dB, a signal/background ratio of ≈ 11 dB and a finesse of ≈ 5. Keywords: Hexagonal micro-pillar cavity, channel add-drop filter, waveguide-coupled, FDTD 1. INTRODUCTION Micro-pillar (µ-pillar) resonators have been gaining increasing interest for photonic integrated circuit applications because of the resonator compact size (<100 µm lateral dimension and ≈ µm height) and high Q-factor. Light can be partially confined by total internal reflection (TIR) at the dielectric resonator sidewalls. Resonances can be excited only when the cavity round-trip wave is wavelength-matched with the input-coupled wave. Circular-shaped µ-pillar cavities that are laterally and vertically-coupled with waveguides have been investigated for wavelength-division multiplexing (WDM) channel add/drop applications [1, 2]. However, the short interaction length between the curved cavity sidewall and the flat waveguide sidewall imposes a sub-micrometer air-gap distance for the evanescent coupling. Polygonal- shaped µ-pillar cavities that have a long interaction length along the entire flat cavity side-wall have been proposed as an alternative to ease the air-gap fabrication tolerance [3, 4, 5, 6]. In this paper we report our latest studies of the optical resonances of hexagonal µ-pillar cavities using 2-D finite- difference time-domain (FDTD) simulation. Singlemode resonances have been observed from a 2-µm sized hexagonal µ-cavity. The simulated resonance wavelengths are consistent with the wavefront-matching condition based on ray- optics. The mode field distributions at the singlemode resonances reveal an integer number of field maxima along the cavity rim similar to whispering-gallery modes. We also studied the feasibility of laterally waveguide-coupled hexagonal µ-pillar cavities for WDM channel add/drop applications. 2. WAVEFRONT-MATCHING CONDITION IN HEXAGONAL µ-CAVITIES Here we first review the wavefront-matching condition in hexagonal µ-cavities [6]. Figure 1 (a) shows six-bounce closed-loop trajectories (solid and dashed lines) with an incident angle θ = 60º. The trajectories have the same total path length of 3a, where a is the distance between the two parallel cavity sidewalls, and thus have the same cavity modes. Figure 1 (b) shows typical six-bounce trajectories with θ ≠ 60º that do not close upon themselves in each cavity round trip. However, resonances can be excited when the round-trip wave is wavefront-matched with the input-coupled wave. For instance, the ray AB and GH are wavefront-matched, as shown in Fig. 1 (b). The six-bounce trajectories can be partially confined by TIR at the cavity sidewall when θ c < θ < 120º - θ c , where θ c is the TIR critical angle.