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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 20 — Oct. 4, 2004
  • pp: 4864–4874
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Planar corner-cut square microcavities: ray optics and FDTD analysis

Chung Yan Fong and Andrew W. Poon  »View Author Affiliations


Optics Express, Vol. 12, Issue 20, pp. 4864-4874 (2004)
http://dx.doi.org/10.1364/OPEX.12.004864


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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

1. Introduction

Polygonal type microresonators, in the form of square [12–19

12. 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]

], hexagon [20

20. 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.

], and octagon [21

21. C. Li, N. Ma, and A. W. Poon, “Waveguide-coupled octagonal microdisk channel add-drop filters,” Opt. Lett. 29, 471–473 (2004). [CrossRef] [PubMed]

], have the advantage of flat resonator sidewalls. N-bounce ray orbits can be partially confined by TIR at the N-polygonal microresonator flat sidewalls. These N-bounce ray orbits can be wavefront-matched with the input and output-coupled waveguide wave, thus exciting resonances. As compared with racetrack type microresonators, polygonal microresonators do not have the complications of straight-to-bend or bend-to-straight waveguide transition loss, waveguide bending loss, or microring inner sidewall scattering loss. The flat resonator sidewalls are also more favorable for fabrications employing standard microelectronics fabrication processes [20

20. 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.

, 21

21. C. Li, N. Ma, and A. W. Poon, “Waveguide-coupled octagonal microdisk channel add-drop filters,” Opt. Lett. 29, 471–473 (2004). [CrossRef] [PubMed]

]. However, it has been recognized that polygonal microresonators can have shortcomings of (i) multimode resonances due to different wavefront-matched ray orbit round-trip lengths, and (ii) cavity loss due to diffraction at sharp cavity corners.

2. Ray optics in 45°-corner-cut square microcavities

2.1 Review of wavefront-matched ray orbits and k-space representation in square microcavities

In order to appreciate the merits of the corner-cut square microcavity design, here we briefly review the essential concepts of wavefront-matched open-ray orbits and k-space modes in square microcavities. One of us previously proposed [13

13. A. W. Poon, F. Courvoisier, and R. K. Chang, “Multimode resonances in square-shaped optical microcavities,” Opt. Lett. 26, 632–634 (2001). [CrossRef]

] that square microcavities have 4-bounce closed or open-ray orbits that are TIR-confined at the flat cavity sidewalls, and the orbits can be wavefront-matched with the input-coupled wave upon each round trip. Closed-ray orbits with an incidence angle θ = 45° always return to the same starting point upon each round trip, enabling traveling-wave resonances. However, open-ray orbits with θ ≠ 45° do not return to the same starting point upon each round trip. Such open-ray orbits can subsequently walk-off and impinge on the orthogonal sidewall, resulting in ray orbits of the same θ but travel backward. Superposition of the forward and backward-propagating open-ray orbits of the same θ can form standing-wave resonances that are, however, undesirable for add-drop applications.

Using physical optics, we can quantitatively model square microcavity modes in k-space [13

13. A. W. Poon, F. Courvoisier, and R. K. Chang, “Multimode resonances in square-shaped optical microcavities,” Opt. Lett. 26, 632–634 (2001). [CrossRef]

, 15

15. C. Y. Fong and A. W. Poon, “Mode field patterns and preferential mode coupling in planar waveguide-coupled square microcavities,” Opt. Express 11, 2897–2904, (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2897 [CrossRef] [PubMed]

, 16

16. 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]

]. The mode k-vector components in the x and y directions, kx and ky, can be discretized in the form kx = mx π/a and ky = my π/a, where mx and my are integer number of field extrema along the x and y directions in the cavity, and a is the square microcavity size. The mode ray orbits only propagate in discrete θ = tan-1(my/mx) relative to cavity sidewall normal.

2.2 Open-ray orbits oscillations in corner-cut square microcavities

In corner-cut square microcavities, 4-bounce open-ray orbits can impinge on the 45°-cut facets. The reflected ray orbits are then 90°-rotated from the initial orbits and can circulate in the same direction.

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.

Figures 1(a) and 1(b) show the ray tracing in a 45°-corner-cut square microcavity with cut size of 0.1 a. Figure 1(a) shows a wavefront-matched 4-bounce open-ray orbit of θ = 48.81° = tan-1(8/7). This ray orbit corresponds to mode (mx, my) = (7, 8). We assumed the modes in corner-cut square microcavities can be approximately represented by the (mx, my) modes. The wavefront-matched 4-bounce ray orbit can end up impinging at the cut facet with a near-normal incidence. Part of the ray refractively escapes with an out-coupling angle according to Snell’s law, and the remaining part of the ray is Fresnel reflected. Figure 1(b) shows the wavefront-matched 4-bounce open-ray orbit after the reflection at the cut facet. The reflected ray orbit preserves the same sense of circulation (clockwise) as the initial orbit, and has an incidence angle given by 90°-θ = 41.19°, which corresponds to the 90°-rotated mode (mx, my) = (8, 7). Because the corner-cut square microcavities preserve the 4-fold rotation symmetry, the pair of 90°-rotated ray orbits should give rise to degenerate modes.

The cut size can affect the ray dynamics, and thus the cavity loss or the proposed ray orbit oscillations. Figures 1(c) and 1(d) show the ray tracing in a 45°-corner-cut square microcavity with a larger cut size of 0.15 a. The wavefront-matched 4-bounce open-ray orbit of θ = 48.81° can be Fresnel reflected back and forth between parallel cut facets along the microcavity diagonal (Fig. 1(c)) before reflecting into the 90°-rotated ray orbits (Fig. 1(d)). It is conceivable that multiple Fresnel reflections between large-sized cut facets can introduce a relatively large cavity loss. Thus it is of essence to optimize the 45°-cut size in corner-cut square microcavity designs.

We remark that the angle of the corner-cut also matters. Reflections at non-45° cut facets can result in complications with reflected open-ray orbits that are not necessarily degenerate with the initial ray orbits. Here we only focused on the 45°-cut designs.

3. 2-D FDTD simulations of waveguide-coupled corner-cut square microcavities

3.1 Simulation layout

We study the waveguide-coupled corner-cut square microcavity channel add-drop filter concept using a commercial 2-D FDTD package [23

23. FullWAVE, Rsoft Inc. Research Software, http://www.rsoftinc.com.

]. Figure 2 shows the device schematic. A square microcavity of sidewall-to-sidewall distance a is laterally coupled with two parallel singlemode waveguides of width w. The microcavity and waveguide are separated with an air-gap separation of distance g. The square microcavity corners are cut at 45° from a distance c away from sidewalls. We refer to c as the cut size. The cut end face has a dimension d = c√2. In order to simulate high-index contrast silicon-based devices, we chose the device refractive index n = 3.5, while the background refractive index is 1.

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

3.2 Simulated spectra

Figures 3(a) – 3(e) show the simulated TM-polarized throughput (blue solid), drop (red dashed) and add (green dotted) spectra of parallel waveguide-coupled corner-cut square microcavities of a = 2.2 μm and c = (a) 0 μm, (b) 0.1 μm, (c) 0.2 μm, (d) 0.3 μm and (e) 0.4 μm. We chose a small microcavity size to minimize the number of multimodes. We fixed w = 0.2 μm and g = 0.2 μm. Insets show the device schematics. We labeled modes A0, B0, A1, B1, B2, B3 and B4 for the following analysis.

Figure 3(a) shows as a control the spectra of a waveguide-coupled square microcavity as discussed in Ref. [15

15. C. Y. Fong and A. W. Poon, “Mode field patterns and preferential mode coupling in planar waveguide-coupled square microcavities,” Opt. Express 11, 2897–2904, (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2897 [CrossRef] [PubMed]

]. Based on their mode-field patterns, we identify mode A0 as (6, 9) and mode B0 as (7, 8). By applying various 45° cut size (Figs. 3(b) – 3(e)), we demonstrate tuning of the resonance add-drop response characteristics (namely drop/add ratio, on/off ratio, coupling efficiency and Q). Below we outline the simulated filter performance characteristics as a function of c.

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).

3.3 Add-drop filter analysis

Figure 4(a) shows the drop/add ratio (blue) and on/off ratio (orange) of modes B0 - B4 as a function of cut size c. We define drop/add ratio as the ratio of on-resonance drop intensity to on-resonance add intensity. A large drop/add ratio suggests that the resonance is dominated by traveling wave and is desirable for add-drop applications. At c = 0 μm (square microcavity), the drop/add ratio is marginally above 0 dB, which means that the resonance is dominated by standing wave. At c = 0.2 μm - 0.3 μm, our simulations suggest that the drop/add ratio can be significantly increased to about 20 dB. This strongly suggests that traveling-wave resonances can be coupled in an optimized corner-cut square microcavity.

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.

We define on/off ratio as the ratio of on-resonance drop intensity to on-resonance throughput intensity. A large on/off ratio means a large input coupling and a correspondingly large output coupling to the drop port. At c = 0 μm, the on/off ratio is only about -10 dB. At c = 0.2 μm, our simulations suggest a significant improvement of about 20 dB in on-off ratio.

Figure 4(b) shows the coupling efficiency (green) and Q (red) of modes B0 - B4 as a function of cut size c. We define coupling efficiency as the ratio of an estimated on-resonance dip at the throughput to estimated off-resonance throughput intensity. At c = 0.2 μm, coupling efficiency of mode B can be optimized to about 95 % (as compared with only about 50 % coupling efficiency at mode B0), whereas Q can be optimized to about 500 (as compared with Q ≈ 200 at mode B0).

As the cut size increases to 0.4 μm, mode B4 and other modes are much suppressed (Fig. 3(e)). We attribute this to the potentially increased cavity loss due to the refractive escape at the relatively large-sized cut, as discussed using ray optics in Section 2. It is worth mentioning that as the cut size becomes sufficiently large, we will obtain an octagonal microcavity, whose resonances and add-drop responses have been recently demonstrated on silicon nitride substrates [21

21. C. Li, N. Ma, and A. W. Poon, “Waveguide-coupled octagonal microdisk channel add-drop filters,” Opt. Lett. 29, 471–473 (2004). [CrossRef] [PubMed]

].

It is evident that modes A0 and A1 do not display similar improvement in filter responses (Figs. 3(a) and 3(b)). Modes A0 and A1 have drop/add ratio near 0 dB and are only differed by a spectral shift, suggesting that the improvement due to corner-cut is mode sensitive.

3.4 Mode-field patterns and Fourier transform analysis

In order to gain further insights to the coupled modes in corner-cut square microcavities, we simulate and analyze the steady-state mode-field patterns of modes A1, B1 and B2. Figure 5(a) shows the FDTD simulated steady-state electric field pattern of mode A1 at an arbitrary time. By counting the number of field extrema in the microcavity in the x and y directions, we can identify mode A1 as (mx, my) = (6, 9) [15

15. C. Y. Fong and A. W. Poon, “Mode field patterns and preferential mode coupling in planar waveguide-coupled square microcavities,” Opt. Express 11, 2897–2904, (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2897 [CrossRef] [PubMed]

, 18

18. 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.

]. We also simulated the mode-field pattern time evolution and observed that mode A1 essentially evolve as a standing wave. We remark that mode A1 standing-wave field pattern highly resembles that of mode A0 [15

15. C. Y. Fong and A. W. Poon, “Mode field patterns and preferential mode coupling in planar waveguide-coupled square microcavities,” Opt. Express 11, 2897–2904, (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2897 [CrossRef] [PubMed]

].

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

Figures 7(a) and 7(b) show the FT of mode B1 field patterns at t = t0 (Fig. 6(a)) and t ≈ t0 + T/4 (Fig. 6(c)). We emphasized on one quadrant of the k-space. As expected, the FT pattern peaks near (a) (7, 8) mode and (b) (8, 7) mode, with similar FT peak counts and widths. The spectral red-shifts from the integer mode numbers are denoted by white arrows.

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.

Figure 8(a) shows the FDTD simulated steady-state electric-field pattern of mode B2 at an arbitrary time t = t0. Interestingly, the pattern reveals a vortex-like traveling wave with essentially zero field amplitude at the cavity center. This traveling-wave resonance allows an efficient energy transfer to the drop port (Fig. 3(c)). Figures 8(b) – 8(e) show the detailed mode-field evolution from t ≈ t0 + T/8 to t ≈ t0 + T/2. Here we only show one-quarter of the microcavity in order to focus on the wavefront propagation. The dashed line indicates the wavefront traveling in near the 45° direction (denoted by the arrow) in a clockwise manner. It is worth mentioning that similar vortex-like mode-field pattern, yet a standing wave, has also been observed in planar waveguide-coupled square microcavities [15

15. C. Y. Fong and A. W. Poon, “Mode field patterns and preferential mode coupling in planar waveguide-coupled square microcavities,” Opt. Express 11, 2897–2904, (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2897 [CrossRef] [PubMed]

].

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

3.5 Waveguide-width tuning

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).

We further optimize the add-drop filter response by fine-tuning the waveguide width w. Figures 10 show the 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. We fixed c = 0.2 μm, a = 2.2 μm and g = 0.2 μm. It is evident that w = 0.15 μm exhibits desirable nearly singlemode add-drop filter responses. Our simulations of w tuning suggest an optimum coupling efficiency exceeding 99 %, a drop/add ratio of about 23 dB, and an on/off ratio of about 24 dB. We remark that the w = 0.15 μm slab waveguide (with index n = 3.5) has a mode propagation angle near 45°, and thus possibly favorable for phase matching with 4-bounce modes [15

15. C. Y. Fong and A. W. Poon, “Mode field patterns and preferential mode coupling in planar waveguide-coupled square microcavities,” Opt. Express 11, 2897–2904, (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2897 [CrossRef] [PubMed]

].

4. Conclusion

In summary, we examined the recently proposed planar waveguide-coupled corner-cut square microcavity channel add-drop filters, using ray tracing and FDTD method. Ray tracing reveals that 4-bounce open-ray orbits that are 90°-rotated can oscillate between each other upon reflections at the 45°-cut facets. These corner-reflected ray orbits can travel in the same sense of circulation, and thus potentially give rise to traveling-wave resonances that are desirable for add-drop applications.

Lastly, our simulations suggest that the add-drop filter responses can be optimized by fine-tuning the coupled-waveguide width. By properly tailoring the square microcavity shape, in particular the microcavity corners, we believe that square microcavities with optimum corner-cut designs are promising building blocks for high-index contrast integrated photonic circuits.

Acknowledgments

The work described in this paper was substantially supported by grants from the Research Grants Council and from the University Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKUST6166/02E & HIA01/02.EG05). C. Y. Fong’s studentship was partially supported by a grant from the Institute of Integrated Microsystems of The Hong Kong University of Science and Technology (Project No. I2MS01/02.EG07).

References and links

1.

D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997). [CrossRef] [PubMed]

2.

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]

3.

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]

4.

Y. Yanagase, S. Suzuki, Y. Kokubun, and S.T. Chu, “Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter,” J. Lightwave Technol. 20, 1525–1529 (2002). [CrossRef]

5.

T. Barwicz, M. A. Popovic, P. T. Rakich, M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, “Microring-resonator-based add-drop filters in SiN: fabrication and analysis,” Opt. Express 12, 1437–1442, (2004). [CrossRef] [PubMed]

6.

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.

7.

S. Blair and Y. Chen, “Resonant-Enhanced Evanescent-Wave Fluorescence Biosensing with Cylindrical Optical Cavities,” Appl. Opt. 40, 570–582, (2001). [CrossRef]

8.

R. W. Boyd and J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40, 5742–5747, (2001). [CrossRef]

9.

E. Krioukov, D.J. W. Klunder, A. Driessen, J. Greve, and C. Otto, “Sensor based on an integrated optical microcavity,” Opt. Lett. 27, 512–514, (2002). [CrossRef]

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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]

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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]

12.

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]

13.

A. W. Poon, F. Courvoisier, and R. K. Chang, “Multimode resonances in square-shaped optical microcavities,” Opt. Lett. 26, 632–634 (2001). [CrossRef]

14.

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]

15.

C. Y. Fong and A. W. Poon, “Mode field patterns and preferential mode coupling in planar waveguide-coupled square microcavities,” Opt. Express 11, 2897–2904, (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2897 [CrossRef] [PubMed]

16.

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]

17.

H. T. Lee and A. W. Poon, “Fano resonances in prism-coupled square micropillars,” Opt. Lett. 29, 5–7, (2004). [CrossRef] [PubMed]

18.

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.

19.

G. D. Chern, A. W. Poon, R. K. Chang, T. Ben-Messaoud, O. Alloschery, E. Toussaere, J. Zyss, and S.-Y. Kuo, “Direct evidence of open ray orbits in a square two-dimensional resonator of dye-doped polymers,” Opt. Lett. 29, 1674–1676 (2004). [CrossRef] [PubMed]

20.

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.

21.

C. Li, N. Ma, and A. W. Poon, “Waveguide-coupled octagonal microdisk channel add-drop filters,” Opt. Lett. 29, 471–473 (2004). [CrossRef] [PubMed]

22.

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

23.

FullWAVE, Rsoft Inc. Research Software, http://www.rsoftinc.com.

OCIS Codes
(230.5750) Optical devices : Resonators
(260.5740) Physical optics : Resonance

ToC Category:
Research Papers

History
Original Manuscript: August 26, 2004
Revised Manuscript: September 20, 2004
Published: October 4, 2004

Citation
Chung Yan Fong and Andrew Poon, "Planar corner-cut square microcavities: ray optics and FDTD analysis," Opt. Express 12, 4864-4874 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-20-4864


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References

  1. D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho and R. C. Tiberio, �??Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,�?? Opt. Lett. 22, 1244-1246 (1997). [CrossRef] [PubMed]
  2. 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]
  3. 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]
  4. Y. Yanagase, S. Suzuki, Y. Kokubun and S.T. Chu, "Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter," J. Lightwave Technol. 20, 1525-1529 (2002). [CrossRef]
  5. T. Barwicz, M. A. Popovic, P. T. Rakich, M. R. Watts, H. A. Haus, E. P. Ippen, H. I. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437-1442, (2004). [CrossRef] [PubMed]
  6. 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.
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