Abstract
We report a numerical and analytical study of mode field patterns and mode coupling in planar waveguide-coupled square microcavities, using two-dimensional (2-D) finite-difference time-domain (FDTD) method and k-space representation. Simulated mode field patterns can be identified by k-space modes. We observe that different mode number parities permit distinctly different mode field patterns and spectral characteristics. Simulation results suggest that k-space modes that nearly match the waveguide propagation mode have a relatively high coupling efficiency. Such preferential mode coupling can be modified by the mode number parity.
Highlights
Planar waveguide-coupled microcavities (μ-cavities) in the form of circular ring and disk [14], racetrack [5], and square [6,10,11,13] have been attracting considerable interest for channel add-drop applications in wavelength-division multiplexed (WDM) networks
Lightwave can be partially confined by total internal reflection (TIR) at the μ-cavity sidewalls, so that optical resonances can be excited when the cavity round-trip lightwave is wavefront-matched with the input-coupled lightwave
A number of research groups have proposed square μ−cavities that have high-Q resonances and long interaction length along the entire flat cavity sidewalls as an alternative resonator to ease the air-gap spacing tolerance [6,7,8,9,10,11,13]
Summary
Planar waveguide-coupled microcavities (μ-cavities) in the form of circular ring and disk [14], racetrack [5], and square [6,10,11,13] have been attracting considerable interest for channel add-drop applications in wavelength-division multiplexed (WDM) networks. Multimodes of square μ−cavities, which are attributed to k-space modes of the cavity with mirror-like boundaries [7,8], have been experimentally demonstrated by Gaussian beam coupling [7,8] and by prism coupling [9]. Planar waveguide-coupled square and rectangular μ−cavities have been investigated analytically using coupled mode theory by modeling the cavity as a singlemode standing wave resonator [6] and directional coupler segment [11], and numerically by finite-difference timedomain (FDTD) [6] and mode expansion method [10,11]. Multimode spectra and mode field patterns of planar waveguide-coupled square μ-cavity channel add-drop filters are numerically simulated using two-dimensional (2-D) FDTD method. Simulation results show that k-space modes that nearly match the waveguide modes can in general be preferentially input-coupled
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