Abstract

The enhancement of quality factor for TE whispering-gallery modes is analyzed for three-dimensional microcylinder resonators based on the destructive interference between vertical leakage modes. In the microcylinder resonator, the TE whispering-gallery modes can couple with vertical propagation modes, which results in vertical radiation loss and low quality factors. However, the vertical loss can be canceled by choosing appropriate thickness of the upper cladding layer or radius of the microcylinder. A mode quality factor increase by three orders of magnitude is predicted by finite-difference time-domain simulation. Furthermore, the condition of vertical leakage cancellation is analyzed.

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  1. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-Gallery Mode Microdisk Lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
    [CrossRef]
  2. M. Arzberger, G. Bohm, M. C. Amann, and G. Abstreiter, “Continuous room-temperature operation of electrically pumped quantum-dot microcylinder lasers,” Appl. Phys. Lett. 79(12), 1766–1768 (2001).
    [CrossRef]
  3. Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 (2007).
    [CrossRef]
  4. Y. Z. Huang and Y. D. Yang, “Mode coupling and vertical radiation loss for whispering-gallery modes in 3-D microcavities,” J. Lightwave Technol. 26(11), 1411–1416 (2008).
    [CrossRef]
  5. V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
    [CrossRef]
  6. A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method, Third Edition.(Boston: Artech House, 2005).
  7. B. J. Li and P. L. Liu, “Numerical analysis of the whispering gallery modes by the finite-difference time-domain method,” IEEE J. Quantum Electron. 32(9), 1583–1587 (1996).
    [CrossRef]
  8. F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microw. Guid. Wave Lett. 7(11), 371–373 (1997).
    [CrossRef]
  9. W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation,” IEEE Microw. Wirel. Compon. Lett. 11(5), 223–225 (2001).
    [CrossRef]
  10. X. S. Luo, Y. Z. Huang, W. H. Guo, Q. Chen, M. Q. Wang, and L. J. Yu, “Investigation of mode characteristics for microdisk resonators by S-matrix and three-dimensional finite-difference time-domain technique,” J. Opt. Soc. Am. B 23(6), 1068–1073 (2006).
    [CrossRef]
  11. Q. Y. Lu, W. H. Guo, D. Byrne, and J. F. Donegan, “Compact 2D FDTD method combined with Padé approximation transform for leaky modes analysis,” J. Lightwave Technol. (to be published).
  12. B. E. Little, J. P. Laine, D. R. Lim, H. A. Haus, L. C. Kimerling, and S. T. Chu, “Pedestal antiresonant reflecting waveguides for robust coupling to microsphere resonators and for microphotonic circuits,” Opt. Lett. 25(1), 73–75 (2000).
    [CrossRef]
  13. D. Marcuse, Light Transmission Optics, Second Edition. (New York: Van Nosrand Reinhold Company, 1982).

2008 (1)

2007 (2)

Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 (2007).
[CrossRef]

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

2006 (1)

2001 (2)

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation,” IEEE Microw. Wirel. Compon. Lett. 11(5), 223–225 (2001).
[CrossRef]

M. Arzberger, G. Bohm, M. C. Amann, and G. Abstreiter, “Continuous room-temperature operation of electrically pumped quantum-dot microcylinder lasers,” Appl. Phys. Lett. 79(12), 1766–1768 (2001).
[CrossRef]

2000 (1)

1997 (1)

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microw. Guid. Wave Lett. 7(11), 371–373 (1997).
[CrossRef]

1996 (1)

B. J. Li and P. L. Liu, “Numerical analysis of the whispering gallery modes by the finite-difference time-domain method,” IEEE J. Quantum Electron. 32(9), 1583–1587 (1996).
[CrossRef]

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-Gallery Mode Microdisk Lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[CrossRef]

Abstreiter, G.

M. Arzberger, G. Bohm, M. C. Amann, and G. Abstreiter, “Continuous room-temperature operation of electrically pumped quantum-dot microcylinder lasers,” Appl. Phys. Lett. 79(12), 1766–1768 (2001).
[CrossRef]

Amann, M. C.

M. Arzberger, G. Bohm, M. C. Amann, and G. Abstreiter, “Continuous room-temperature operation of electrically pumped quantum-dot microcylinder lasers,” Appl. Phys. Lett. 79(12), 1766–1768 (2001).
[CrossRef]

Arzberger, M.

M. Arzberger, G. Bohm, M. C. Amann, and G. Abstreiter, “Continuous room-temperature operation of electrically pumped quantum-dot microcylinder lasers,” Appl. Phys. Lett. 79(12), 1766–1768 (2001).
[CrossRef]

Astratov, V. N.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Bohm, G.

M. Arzberger, G. Bohm, M. C. Amann, and G. Abstreiter, “Continuous room-temperature operation of electrically pumped quantum-dot microcylinder lasers,” Appl. Phys. Lett. 79(12), 1766–1768 (2001).
[CrossRef]

Byrne, D.

Q. Y. Lu, W. H. Guo, D. Byrne, and J. F. Donegan, “Compact 2D FDTD method combined with Padé approximation transform for leaky modes analysis,” J. Lightwave Technol. (to be published).

Chen, Q.

Chew, W. C.

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microw. Guid. Wave Lett. 7(11), 371–373 (1997).
[CrossRef]

Chu, S. T.

Donegan, J. F.

Q. Y. Lu, W. H. Guo, D. Byrne, and J. F. Donegan, “Compact 2D FDTD method combined with Padé approximation transform for leaky modes analysis,” J. Lightwave Technol. (to be published).

Fox, A. M.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Fry, P. W.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Guo, W. H.

X. S. Luo, Y. Z. Huang, W. H. Guo, Q. Chen, M. Q. Wang, and L. J. Yu, “Investigation of mode characteristics for microdisk resonators by S-matrix and three-dimensional finite-difference time-domain technique,” J. Opt. Soc. Am. B 23(6), 1068–1073 (2006).
[CrossRef]

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation,” IEEE Microw. Wirel. Compon. Lett. 11(5), 223–225 (2001).
[CrossRef]

Q. Y. Lu, W. H. Guo, D. Byrne, and J. F. Donegan, “Compact 2D FDTD method combined with Padé approximation transform for leaky modes analysis,” J. Lightwave Technol. (to be published).

Haus, H. A.

Hopkinson, M.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Huang, Y. Z.

Y. Z. Huang and Y. D. Yang, “Mode coupling and vertical radiation loss for whispering-gallery modes in 3-D microcavities,” J. Lightwave Technol. 26(11), 1411–1416 (2008).
[CrossRef]

Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 (2007).
[CrossRef]

X. S. Luo, Y. Z. Huang, W. H. Guo, Q. Chen, M. Q. Wang, and L. J. Yu, “Investigation of mode characteristics for microdisk resonators by S-matrix and three-dimensional finite-difference time-domain technique,” J. Opt. Soc. Am. B 23(6), 1068–1073 (2006).
[CrossRef]

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation,” IEEE Microw. Wirel. Compon. Lett. 11(5), 223–225 (2001).
[CrossRef]

Jones, B. D.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Kimerling, L. C.

Laine, J. P.

Lam, S.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-Gallery Mode Microdisk Lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[CrossRef]

Li, B. J.

B. J. Li and P. L. Liu, “Numerical analysis of the whispering gallery modes by the finite-difference time-domain method,” IEEE J. Quantum Electron. 32(9), 1583–1587 (1996).
[CrossRef]

Li, W. J.

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation,” IEEE Microw. Wirel. Compon. Lett. 11(5), 223–225 (2001).
[CrossRef]

Lim, D. R.

Little, B. E.

Liu, P. L.

B. J. Li and P. L. Liu, “Numerical analysis of the whispering gallery modes by the finite-difference time-domain method,” IEEE J. Quantum Electron. 32(9), 1583–1587 (1996).
[CrossRef]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-Gallery Mode Microdisk Lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[CrossRef]

Lu, Q. Y.

Q. Y. Lu, W. H. Guo, D. Byrne, and J. F. Donegan, “Compact 2D FDTD method combined with Padé approximation transform for leaky modes analysis,” J. Lightwave Technol. (to be published).

Luo, X. S.

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-Gallery Mode Microdisk Lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[CrossRef]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-Gallery Mode Microdisk Lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[CrossRef]

Sanvitto, D.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Skolnick, M. S.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-Gallery Mode Microdisk Lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[CrossRef]

Tahraoui, A.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Teixeira, F. L.

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microw. Guid. Wave Lett. 7(11), 371–373 (1997).
[CrossRef]

Wang, M. Q.

Whittaker, D. M.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Yang, S.

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

Yang, Y. D.

Y. Z. Huang and Y. D. Yang, “Mode coupling and vertical radiation loss for whispering-gallery modes in 3-D microcavities,” J. Lightwave Technol. 26(11), 1411–1416 (2008).
[CrossRef]

Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 (2007).
[CrossRef]

Yu, L. J.

Appl. Phys. Lett. (3)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-Gallery Mode Microdisk Lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992).
[CrossRef]

M. Arzberger, G. Bohm, M. C. Amann, and G. Abstreiter, “Continuous room-temperature operation of electrically pumped quantum-dot microcylinder lasers,” Appl. Phys. Lett. 79(12), 1766–1768 (2001).
[CrossRef]

V. N. Astratov, S. Yang, S. Lam, B. D. Jones, D. Sanvitto, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, “Whispering gallery resonances in semiconductor micropillars,” Appl. Phys. Lett. 91(7), 071115 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

B. J. Li and P. L. Liu, “Numerical analysis of the whispering gallery modes by the finite-difference time-domain method,” IEEE J. Quantum Electron. 32(9), 1583–1587 (1996).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (1)

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microw. Guid. Wave Lett. 7(11), 371–373 (1997).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation,” IEEE Microw. Wirel. Compon. Lett. 11(5), 223–225 (2001).
[CrossRef]

J. Lightwave Technol. (2)

Q. Y. Lu, W. H. Guo, D. Byrne, and J. F. Donegan, “Compact 2D FDTD method combined with Padé approximation transform for leaky modes analysis,” J. Lightwave Technol. (to be published).

Y. Z. Huang and Y. D. Yang, “Mode coupling and vertical radiation loss for whispering-gallery modes in 3-D microcavities,” J. Lightwave Technol. 26(11), 1411–1416 (2008).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Phys. Rev. A (1)

Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 (2007).
[CrossRef]

Other (2)

A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method, Third Edition.(Boston: Artech House, 2005).

D. Marcuse, Light Transmission Optics, Second Edition. (New York: Van Nosrand Reinhold Company, 1982).

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Figures (6)

Fig. 1
Fig. 1

Cross section of a microcylinder and the FDTD simulation region.

Fig. 2
Fig. 2

Mode Q factor of TE9,1 mode versus the thickness of upper cladding layer in the microcylinder with R = 1 obtained by FDTD simulation. The dashed line is the mode Q factor for the microcylinder resonator with an infinite upper cladding layer.

Fig. 3
Fig. 3

Field distributions of Ez for TE9,1 mode at the upper cladding layer thickness d 2 of (a) 1.42μm and (b) 1.50μm, and Hz at d 2 of (c) 1.42μm and (d) 1.50μm.

Fig. 4
Fig. 4

The schematic diagram of the destructive interference for the vertical radiation waves.

Fig. 5
Fig. 5

The mode Q factors of TE v ,1 modes with the wavelengths near 1.55 μm versus the radius of microcylinder resonator obtained by FDTD simulation.. The squares and circles are for the resonator with d 2 = 1.5μm and an infinite upper cladding layer.

Fig. 6
Fig. 6

The mode Q factor of TE11,2 mode versus the thickness of upper cladding layer in the microcylinder with R = 1.5μm obtained by the FDTD simulation. The dashed line is the mode Q factor for the microcylinder resonator with an infinite upper cladding layer.

Equations (1)

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Φ = θ 1 + 2 β 2 d 2 + β 1 d 1 + θ 2

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