Abstract

Radiation loss and resonant frequency shift due to sidewall surface roughness of circular and square high-contrast microcavities are estimated and compared by use of a boundary integral equations method. An effect of various harmonic components of the contour perturbation on the whispering-gallery (WG) modes in the circular microdisk and WG-like modes in the square microcavity is demonstrated. In both cases, contour deformations that are matched to the mode field pattern cause the most significant frequency detuning and Q-factor change. Favorably mode-matched deformations have been found, enabling one to manipulate the Q factors of the microcavity modes.

© 2004 Optical Society of America

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  1. M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 15, 673–681 (1999).
    [CrossRef]
  2. V. Van, P. P. Absil, J. V. Hryniewicz, and P.-T. Ho, “Propagation loss in single-mode GaAs-AlGaAs microring resonators: measurement and model,” J. Lightwave Technol. 19, 1734–1739 (2001).
    [CrossRef]
  3. W.-H. Guo, Y.-Z. Huang, Q.-Y. Lu, and L.-J. Yu, “Whispering-gallery-like modes in square resonators,” IEEE J. Quantum Electron. 39, 1106–1110 (2003).
    [CrossRef]
  4. M. Lohmeyer, “Mode expansion modeling of rectangular integrated optical resonators,” Opt. Quantum Electron. 34, 541–557 (2002).
    [CrossRef]
  5. 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]
  6. T. Ling, L. Liu, Q. Song, L. Xu, and W. Wang, “Intense directional lasing from a deformed square-shaped organic–inorganic hybrid glass microring cavity,” Opt. Lett. 28, 1784–1786 (2003).
    [CrossRef] [PubMed]
  7. A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561–563 (1993).
    [CrossRef]
  8. S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “CH4-based dry etching of high Q InP microdisks,” J. Vac. Sci. Technol. B 20, 301–305 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
  10. B.-J. Li and P.-L. Liu, “Numerical analysis of microdisk lasers with rough boundaries,” IEEE J. Quantum Electron. 35, 791–795 (1997).
  11. Y. Z. Huang, W. H. Guo, and L. J. Yu, “Analysis of mode quality factors for equilateral triangle semiconductor microlasers with rough sidewalls,” Chin. Phys. Lett. 19, 674–676 (2002).
    [CrossRef]
  12. A. I. Rahachou and I. V. Zozoulenko, “Scattering matrix approach to the resonant states and Q values of microdisk lasing cavities,” Appl. Opt. 43, 1761–1772 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
    [CrossRef]
  15. M. Fujita and T. Baba, “Proposal and finite-difference time-domain simulation of Whispering Gallery mode microgear cavity,” IEEE J. Quantum Electron. 37, 1253–1258 (2001).
    [CrossRef]
  16. M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80, 2051–2053 (2002).
    [CrossRef]
  17. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Highly efficient design of spectrally engineered whispering-gallery-mode laser resonators,” Opt. Quantum Electron. 35, 545–559 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]

2004 (2)

2003 (3)

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Highly efficient design of spectrally engineered whispering-gallery-mode laser resonators,” Opt. Quantum Electron. 35, 545–559 (2003).
[CrossRef]

W.-H. Guo, Y.-Z. Huang, Q.-Y. Lu, and L.-J. Yu, “Whispering-gallery-like modes in square resonators,” IEEE J. Quantum Electron. 39, 1106–1110 (2003).
[CrossRef]

T. Ling, L. Liu, Q. Song, L. Xu, and W. Wang, “Intense directional lasing from a deformed square-shaped organic–inorganic hybrid glass microring cavity,” Opt. Lett. 28, 1784–1786 (2003).
[CrossRef] [PubMed]

2002 (4)

M. Lohmeyer, “Mode expansion modeling of rectangular integrated optical resonators,” Opt. Quantum Electron. 34, 541–557 (2002).
[CrossRef]

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “CH4-based dry etching of high Q InP microdisks,” J. Vac. Sci. Technol. B 20, 301–305 (2002).
[CrossRef]

Y. Z. Huang, W. H. Guo, and L. J. Yu, “Analysis of mode quality factors for equilateral triangle semiconductor microlasers with rough sidewalls,” Chin. Phys. Lett. 19, 674–676 (2002).
[CrossRef]

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80, 2051–2053 (2002).
[CrossRef]

2001 (2)

V. Van, P. P. Absil, J. V. Hryniewicz, and P.-T. Ho, “Propagation loss in single-mode GaAs-AlGaAs microring resonators: measurement and model,” J. Lightwave Technol. 19, 1734–1739 (2001).
[CrossRef]

M. Fujita and T. Baba, “Proposal and finite-difference time-domain simulation of Whispering Gallery mode microgear cavity,” IEEE J. Quantum Electron. 37, 1253–1258 (2001).
[CrossRef]

1999 (3)

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]

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 15, 673–681 (1999).
[CrossRef]

J. P. Barton, “Effects of surface perturbations on the quality and the focused-beam excitation of microsphere resonance,” J. Opt. Soc. Am. A 16, 1974–1980 (1999).
[CrossRef]

1997 (2)

B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997).
[CrossRef] [PubMed]

B.-J. Li and P.-L. Liu, “Numerical analysis of microdisk lasers with rough boundaries,” IEEE J. Quantum Electron. 35, 791–795 (1997).

1996 (1)

1993 (1)

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561–563 (1993).
[CrossRef]

Absil, P. P.

Baba, T.

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80, 2051–2053 (2002).
[CrossRef]

M. Fujita and T. Baba, “Proposal and finite-difference time-domain simulation of Whispering Gallery mode microgear cavity,” IEEE J. Quantum Electron. 37, 1253–1258 (2001).
[CrossRef]

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 15, 673–681 (1999).
[CrossRef]

Barton, J. P.

Benson, T. M.

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Highly efficient design of spectrally engineered whispering-gallery-mode laser resonators,” Opt. Quantum Electron. 35, 545–559 (2003).
[CrossRef]

Boriskina, S. V.

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Highly efficient design of spectrally engineered whispering-gallery-mode laser resonators,” Opt. Quantum Electron. 35, 545–559 (2003).
[CrossRef]

Choi, S. J.

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “CH4-based dry etching of high Q InP microdisks,” J. Vac. Sci. Technol. B 20, 301–305 (2002).
[CrossRef]

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “CH4-based dry etching of high Q InP microdisks,” J. Vac. Sci. Technol. B 20, 301–305 (2002).
[CrossRef]

Chu, S. T.

Dapkus, P. D.

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “CH4-based dry etching of high Q InP microdisks,” J. Vac. Sci. Technol. B 20, 301–305 (2002).
[CrossRef]

Djordjev, K.

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “CH4-based dry etching of high Q InP microdisks,” J. Vac. Sci. Technol. B 20, 301–305 (2002).
[CrossRef]

Fan, S.

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]

Fujita, M.

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80, 2051–2053 (2002).
[CrossRef]

M. Fujita and T. Baba, “Proposal and finite-difference time-domain simulation of Whispering Gallery mode microgear cavity,” IEEE J. Quantum Electron. 37, 1253–1258 (2001).
[CrossRef]

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 15, 673–681 (1999).
[CrossRef]

Glass, J. L.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561–563 (1993).
[CrossRef]

Guo, W. H.

Y. Z. Huang, W. H. Guo, and L. J. Yu, “Analysis of mode quality factors for equilateral triangle semiconductor microlasers with rough sidewalls,” Chin. Phys. Lett. 19, 674–676 (2002).
[CrossRef]

Guo, W.-H.

W.-H. Guo, Y.-Z. Huang, Q.-Y. Lu, and L.-J. Yu, “Whispering-gallery-like modes in square resonators,” IEEE J. Quantum Electron. 39, 1106–1110 (2003).
[CrossRef]

Haus, H. A.

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]

Ho, P.-T.

Hryniewicz, J. V.

Huang, Y. Z.

Y. Z. Huang, W. H. Guo, and L. J. Yu, “Analysis of mode quality factors for equilateral triangle semiconductor microlasers with rough sidewalls,” Chin. Phys. Lett. 19, 674–676 (2002).
[CrossRef]

Huang, Y.-Z.

W.-H. Guo, Y.-Z. Huang, Q.-Y. Lu, and L.-J. Yu, “Whispering-gallery-like modes in square resonators,” IEEE J. Quantum Electron. 39, 1106–1110 (2003).
[CrossRef]

Joannopoulos, J. D.

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]

Khan, M. J.

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]

Laine, J. P.

Levi, A. F. J.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561–563 (1993).
[CrossRef]

Li, B.-J.

B.-J. Li and P.-L. Liu, “Numerical analysis of microdisk lasers with rough boundaries,” IEEE J. Quantum Electron. 35, 791–795 (1997).

Ling, T.

Little, B.

Little, B. E.

Liu, L.

Liu, P.-L.

B.-J. Li and P.-L. Liu, “Numerical analysis of microdisk lasers with rough boundaries,” IEEE J. Quantum Electron. 35, 791–795 (1997).

Logan, R. A.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561–563 (1993).
[CrossRef]

Lohmeyer, M.

M. Lohmeyer, “Mode expansion modeling of rectangular integrated optical resonators,” Opt. Quantum Electron. 34, 541–557 (2002).
[CrossRef]

Lu, Q.-Y.

W.-H. Guo, Y.-Z. Huang, Q.-Y. Lu, and L.-J. Yu, “Whispering-gallery-like modes in square resonators,” IEEE J. Quantum Electron. 39, 1106–1110 (2003).
[CrossRef]

Manolatou, C.

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]

McCall, S. L.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561–563 (1993).
[CrossRef]

Nosich, A. I.

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Highly efficient design of spectrally engineered whispering-gallery-mode laser resonators,” Opt. Quantum Electron. 35, 545–559 (2003).
[CrossRef]

Pearton, S. J.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561–563 (1993).
[CrossRef]

Rahachou, A. I.

Sakai, A.

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 15, 673–681 (1999).
[CrossRef]

Sewell, P.

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Highly efficient design of spectrally engineered whispering-gallery-mode laser resonators,” Opt. Quantum Electron. 35, 545–559 (2003).
[CrossRef]

Slusher, R. E.

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561–563 (1993).
[CrossRef]

Song, Q.

Van, V.

Villeneuve, P. R.

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]

Wang, W.

Xu, L.

Yu, L. J.

Y. Z. Huang, W. H. Guo, and L. J. Yu, “Analysis of mode quality factors for equilateral triangle semiconductor microlasers with rough sidewalls,” Chin. Phys. Lett. 19, 674–676 (2002).
[CrossRef]

Yu, L.-J.

W.-H. Guo, Y.-Z. Huang, Q.-Y. Lu, and L.-J. Yu, “Whispering-gallery-like modes in square resonators,” IEEE J. Quantum Electron. 39, 1106–1110 (2003).
[CrossRef]

Zozoulenko, I. V.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561–563 (1993).
[CrossRef]

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80, 2051–2053 (2002).
[CrossRef]

Chin. Phys. Lett. (1)

Y. Z. Huang, W. H. Guo, and L. J. Yu, “Analysis of mode quality factors for equilateral triangle semiconductor microlasers with rough sidewalls,” Chin. Phys. Lett. 19, 674–676 (2002).
[CrossRef]

IEEE J. Quantum Electron. (4)

M. Fujita and T. Baba, “Proposal and finite-difference time-domain simulation of Whispering Gallery mode microgear cavity,” IEEE J. Quantum Electron. 37, 1253–1258 (2001).
[CrossRef]

W.-H. Guo, Y.-Z. Huang, Q.-Y. Lu, and L.-J. Yu, “Whispering-gallery-like modes in square resonators,” IEEE J. Quantum Electron. 39, 1106–1110 (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]

B.-J. Li and P.-L. Liu, “Numerical analysis of microdisk lasers with rough boundaries,” IEEE J. Quantum Electron. 35, 791–795 (1997).

IEEE J. Sel. Top. Quantum Electron. (1)

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 15, 673–681 (1999).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

J. Vac. Sci. Technol. B (1)

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “CH4-based dry etching of high Q InP microdisks,” J. Vac. Sci. Technol. B 20, 301–305 (2002).
[CrossRef]

Opt. Lett. (3)

Opt. Quantum Electron. (2)

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Highly efficient design of spectrally engineered whispering-gallery-mode laser resonators,” Opt. Quantum Electron. 35, 545–559 (2003).
[CrossRef]

M. Lohmeyer, “Mode expansion modeling of rectangular integrated optical resonators,” Opt. Quantum Electron. 34, 541–557 (2002).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Field intensity distributions for (a) the WG5,1 mode of the circular microcavity (λ=1.572 µm) and (b) the WG-like mode of the square microcavity (λ=1.503 µm). The cavities have a diameter (side length) of 1.6 µm and permittivity =6.9169+i10-4.

Fig. 2
Fig. 2

(a) Circular microcavity resonant wavelength detuning and (b) normalized loss-limited Q factor as a function of the contour perturbation harmonic number ν. Radial depth of the perturbation is δ=8 nm. Regions of the mode-matched perturbations and mismatched surface roughness can be observed. The inset shows two favorably mode-matched contour deformations (ν=5 and ν=10).

Fig. 3
Fig. 3

(a) Square microcavity resonant wavelength detuning and (b) normalized loss-limited Q factor as a function of the contour perturbation harmonic number ν. Radial depth of the perturbation is δ=8 nm. Two types of the favorably mode-matched deformation (ν=4 and ν=12) are shown in the inset.

Fig. 4
Fig. 4

(a) Resonant wavelength shift and (b) normalized Q-factor change versus the perturbation amplitude δ for the two types of the favorably matched deformation of the square microcavity (ν=4 and ν=12).

Fig. 5
Fig. 5

Intensity patterns of the WG-like modes in the deformed square microcavities. The radial depth of each perturbation corresponds to the points of the maxima of the mode Q factor in Fig. 4(b) (δν=4=28 nm, δν=12=48 nm).

Fig. 6
Fig. 6

(a) Resonant wavelength detuning and (b) Q-factor degradation of the WG5,1 mode of the circular microdisk and WG-like mode of the square microcavity as a function of the depth of the mismatched contour perturbation with the period Λ=0.033 (ν=30).

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