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Planar corner-cut square microcavities: ray optics and FDTD analysis

Chung Yan Fong and Andrew W. Poon

Open Access Open Access

Abstract

We analyze corner-cut square microcavities as alternative planar microcavities. Ray tracing shows open-ray orbits that are 90°-rotated can oscillate between each other upon reflections at the 45° corner-cut facets, and have the same sense of circulation. Our two-dimensional finite-difference time-domain simulations suggest that a waveguide-coupled corner-cut square microcavity with an optimum cut size supports traveling-wave resonances with desirable add-drop filter responses. The mode-field pattern evolutions confirm the concept of modal oscillations. By applying Fourier transform on the mode-field patterns, we analyze the modal composition in k-space. The add-drop filter responses can be optimized by fine-tuning the waveguide width.

©2004 Optical Society of America

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Figures (10)
Fig. 1.
Fig. 1. Ray tracing in a 45°-corner-cut square microcavity with cavity size of a and cut size of (a), (b) 0.1 a, and (c), (d) 0.15 a. The wavefront-matched 4-bounce open-ray orbits (red solid) in (a) and (c) have the same θ = tan-1 (8/7) = 48.81°, assuming a (mx, my) = (7, 8) mode. The ray (blue dashed) is partially reflected from the cut facet and partially transmitted (gray dashed). The wavefront-matched 4-bounce open-ray orbits (blue solid) in (b) and (d) are reflected from the cut facet. The ray orbits have an incidence angle of 90°-θ = 41.19°, corresponding to a (mx, my) = (8, 7) mode, and preserve the same sense of circulation prior to the reflection.

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Fig. 2.
Fig. 2. Schematic of a planar parallel waveguide-coupled corner-cut square microcavity channel add-drop filter.

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Fig. 3.
Fig. 3. FDTD simulated TM-polarized throughput (blue solid), drop (red dashed) and add (green dotted) spectra of parallel waveguide-coupled corner-cut square microcavity. a = 2.2 μm, c = (a) 0 μm, (b) 0.1 μm, (c) 0.2 μm, (d) 0.3 μm, and (e) 0.4 μm. w = 0.2 μm and g = 0.2 μm. Insets show the device schematics. We identified mode A0 as (6, 9) and mode B0 as (7, 8).

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Fig. 4.
Fig. 4. Analysis of the add-drop filter performance for modes B0 - B4 as a function of the cut size. (a) Drop/add ratio and on/off ratio. (b) Coupling efficiency and Q.

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Fig. 5.
Fig. 5. (a) FDTD simulated steady-state electric-field pattern of mode A1. We denote the mode field pattern as (mx, my) = (6, 9). (b) Fourier transform (FT) of the cavity mode-field pattern. Zoom-in view shows the FT peak is shifted from the mode (6, 9).

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Fig. 6.
Fig. 6. FDTD simulated steady-state electric-field pattern evolution of mode B1. Field patterns are taken at time (a) t = t0, (b) t ≈ t0 + T/8, (c) t ≈ t0 + T/4, (d) t ≈ t0 + 3T/8 and (e) t ≈ t0 + T/2. t0 is an arbitrary time and T is the period. We denote (a), (e) as (7, 8) mode and (c) as (8, 7) mode.

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Fig. 7.
Fig. 7. Fourier transform of mode B1 field patterns at (a) t = t0 and (b) t ≈ t0+T/4.

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Fig. 8.
Fig. 8. FDTD simulated steady-state electric-field pattern of mode B2. The pattern is vortex-like and travels in a clockwise manner. (a) t = t0, (b) t ≈ t0 + T/8, (c) t ≈ t0 + T/4, (d) t ≈ t0 + 3T/8, and (e) t ≈ t0 + T/2. The dashed lines represent a wavefront traveling in the near 45° direction.

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Fig. 9.
Fig. 9. Fourier transform of mode B2 field pattern at (a) t = t0 and (b) t ≈ t0+T/4.

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Fig. 10.
Fig. 10. FDTD-simulated TM-polarized spectra of a parallel waveguide-coupled corner-cut square microcavity of w = (a) 0.1 μm, (b) 0.15 μm, and (c) 0.25 μm. c = 0.2 μm, a = 2.2 μm and g = 0.2 μm. Throughput (solid blue), drop (dashed red) and add (dashed green).

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