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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Appl. Opt. (2)

Appl. Phys. Lett. (2)

Y. L. Pan and R. K. Chang, �??Highly efficient prism coupling to whispering gallery modes of a square µ-cavity,�?? Appl. Phys. Lett. 82, 487-489 (2003).
[CrossRef]

C. Y. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83, 1527-1529, (2003).
[CrossRef]

CLEO 2004 (1)

C. Y. Fong and A. W. Poon, �??Corner-cut square microcavity coupled waveguide crossing,�?? in proceedings of Conference on Lasers and Electro-Optics (CLEO), San Francisco, California 16-21 May 2004.

IEEE J. Quantum Electron. (2)

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, �??Modes in square resonators,�?? IEEE J. Quantum Electron. 39, 1563-1566 (2003).
[CrossRef]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus and J. D. Joannopoulos, �??Coupling of modes analysis of resonant channel add-drop filters,�?? IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

R. Grover, T. A. Ibrahim, T. N. Ding, Y. Leng, L. C. Kuo, S. Kanakaraju, K. Amarnath, L. C. Calhoun and P. T. Ho, "Laterally coupled InP-based single-mode microracetrack notch filter," IEEE Photon. Technol. Lett. 15, 1082-1084(2003).
[CrossRef]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling and W. Greene, �??Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,�?? IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, �??Vertically coupled glass microring resonator channel dropping filters,�?? IEEE Photon. Technol. Lett. 11, 215-217, (1999).
[CrossRef]

J. Lightwave Technol. (1)

OFC 2004 (1)

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, P. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo and J. Shantona, �??Compact full C-band tunable filters for 50 GHz channel spacing based on high order micro-ring resonators,�?? in proceedings of Optical Fiber Communication Conference (OFC), Los Angeles, California, 22-27 February 2004.

Opt. Express (2)

Opt. Lett. (6)

Other (3)

N. Ma, C. Li and A. W. Poon, �??Laterally coupled hexagonal micro-pillar resonator add-drop filters in silicon nitride,�?? to be published in IEEE Photonics Technol. Lett.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Boston: Artech House, 2000), Chapter 16.

FullWAVE, Rsoft Inc. Research Software, <a href="http://www.rsoftinc.com.">http://www.rsoftinc.com."</a>

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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.

Fig. 2.
Fig. 2.

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

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).

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.

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).

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.

Fig. 7.
Fig. 7.

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

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.

Fig. 9.
Fig. 9.

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

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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