Abstract

Spectrum control by anisotropy in a cylindrical microcavity made of electric anisotropic medium was studied. A finite-difference time domain method for electric anisotropic medium and Volume-average Effective Permittivity approximation are applied to calculate the resonant frequencies and quality factors of Whispering-gallery modes. The resonant frequency for different whispering-gallery modes has a similar shift in direct proportion to the relative difference of two principal refractive indices. The quality factors decay exponentially due to directional emission when the difference of two principal refractive indices increases. This novel tuning characteristic of anisotropic cylindrical microcavity will play an important role in many areas, such as light source with tunable wavelength, tunable filter and sensor.

© 2009 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
    [CrossRef]
  2. M. L. M. Balistreri, D. J. W. Klunder, F. C. Blom*, A. Driessen, H. W. J. M. Hoekstra, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Visualizing the whispering gallery modes in a cylindrical optical microcavity,” Opt. Lett. 24(24), 1829 (1999).
    [CrossRef] [PubMed]
  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]
  4. R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993).
    [CrossRef]
  5. M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75(7), 3302–3307 (1994).
    [CrossRef]
  6. M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85(17), 3693–3695 (2004).
    [CrossRef]
  7. K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
    [CrossRef] [PubMed]
  8. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21(7), 453–455 (1996).
    [CrossRef] [PubMed]
  9. M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25(19), 1430–1432 (2000).
    [CrossRef] [PubMed]
  10. M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80(12), 2051–2053 (2002).
    [CrossRef]
  11. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
    [CrossRef] [PubMed]
  12. J. Yang and L. J. Guo, “Optical Sensors Based on Active Microcavities,” IEEE J. Sel. Top. Quantum Electron. 12(1), 143–147 (2006).
    [CrossRef]
  13. R. W. Boyd and J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40(31), 5742–5747 (2001).
    [CrossRef] [PubMed]
  14. S. Ricciardi, S. Popov, A. T. Friberg, and S. Sergeyev, “Thermally induced wavelength tunability of microcavity solid-state dye lasers,” Opt. Express 15(20), 12971–12978 (2007).
    [CrossRef] [PubMed]
  15. S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
    [CrossRef]
  16. F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
    [CrossRef]
  17. H. Cai, B. Liu, X. M. Zhang, A. Q. Liu, J. Tamil, T. Bourouina, and Q. X. Zhang, “A micromachined tunable coupled-cavity laser for wide tuning range and high spectral purity,” Opt. Express 16(21), 16670–16679 (2008).
    [CrossRef] [PubMed]
  18. M. C. Larson and J. S. Harris, “Broadly-Tunable Resonant-Cavity Light-Emitting Diode,” IEEE Photon. Technol. Lett. 7(11), 1267–1269 (1995).
    [CrossRef]
  19. F. Sugihwo, M. C. Larson, and J. S. Harris, “Micromachined widely tunable vertical cavity laser diodes,” J. Microelectromech. Syst. 7(1), 48–55 (1998).
    [CrossRef]
  20. M. C. Larson and J. S. Harris, “Wide and continuous wavelength tuning in a vertical-cavity surface-emitting laser using a micromachined deformable-membrane mirror,” Appl. Phys. Lett. 68(7), 891–893 (1996).
    [CrossRef]
  21. J. Schneider and S. Hudson, “The finite-difference time-domain method applied to anisotropic material,” IEEE Trans. Antenn. Propag. 41(7), 994–999 (1993).
    [CrossRef]
  22. A. Taflove, “Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures,” Wave Motion 10(6), 547–582 (1988).
    [CrossRef]
  23. A. Mohammadi, H. Nadgaran, and M. Agio, “Contour-path effective permittivities for the two-dimensional finite-difference time-domain method,” Opt. Express 13(25), 10367–10381 (2005).
    [CrossRef] [PubMed]
  24. S. Dey and R. Mittra, “A Conformal Finite-Difference Time-Domain Technique for Modeling Cylindrical Dielectric Resonators,” IEEE Trans. Microw. Theory Tech. 47(9), 1737–1739 (1999).
    [CrossRef]
  25. J. Fang and Z. Wu, “Generalized Perfectly Matched Layer for the Absorption of Propagating and Evanescent Waves in Lossless and Lossy Media,” IEEE Trans. Microw. Theory Tech. 44(12), 2216–2222 (1996).
    [CrossRef]
  26. M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5 Pt 2), 056207 (2002).
    [CrossRef] [PubMed]
  27. S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Pade approximation,” IEEE Microw. Guid. Wave Lett. 8(12), 415–417 (1998).
    [CrossRef]
  28. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Tuning of Elliptic Whispering-Gallery-Mode Microdisk Waveguide Filters,” J. Lightwave Technol. 21(9), 1987–1995 (2003).
    [CrossRef]
  29. J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385(6611), 45–47 (1997).
    [CrossRef]

2008

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

H. Cai, B. Liu, X. M. Zhang, A. Q. Liu, J. Tamil, T. Bourouina, and Q. X. Zhang, “A micromachined tunable coupled-cavity laser for wide tuning range and high spectral purity,” Opt. Express 16(21), 16670–16679 (2008).
[CrossRef] [PubMed]

2007

S. Ricciardi, S. Popov, A. T. Friberg, and S. Sergeyev, “Thermally induced wavelength tunability of microcavity solid-state dye lasers,” Opt. Express 15(20), 12971–12978 (2007).
[CrossRef] [PubMed]

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

2006

J. Yang and L. J. Guo, “Optical Sensors Based on Active Microcavities,” IEEE J. Sel. Top. Quantum Electron. 12(1), 143–147 (2006).
[CrossRef]

2005

2004

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85(17), 3693–3695 (2004).
[CrossRef]

2003

2002

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5 Pt 2), 056207 (2002).
[CrossRef] [PubMed]

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80(12), 2051–2053 (2002).
[CrossRef]

2001

2000

1999

1998

S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Pade approximation,” IEEE Microw. Guid. Wave Lett. 8(12), 415–417 (1998).
[CrossRef]

F. Sugihwo, M. C. Larson, and J. S. Harris, “Micromachined widely tunable vertical cavity laser diodes,” J. Microelectromech. Syst. 7(1), 48–55 (1998).
[CrossRef]

1997

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385(6611), 45–47 (1997).
[CrossRef]

1996

M. C. Larson and J. S. Harris, “Wide and continuous wavelength tuning in a vertical-cavity surface-emitting laser using a micromachined deformable-membrane mirror,” Appl. Phys. Lett. 68(7), 891–893 (1996).
[CrossRef]

J. Fang and Z. Wu, “Generalized Perfectly Matched Layer for the Absorption of Propagating and Evanescent Waves in Lossless and Lossy Media,” IEEE Trans. Microw. Theory Tech. 44(12), 2216–2222 (1996).
[CrossRef]

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21(7), 453–455 (1996).
[CrossRef] [PubMed]

1995

M. C. Larson and J. S. Harris, “Broadly-Tunable Resonant-Cavity Light-Emitting Diode,” IEEE Photon. Technol. Lett. 7(11), 1267–1269 (1995).
[CrossRef]

1994

M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75(7), 3302–3307 (1994).
[CrossRef]

1993

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993).
[CrossRef]

J. Schneider and S. Hudson, “The finite-difference time-domain method applied to anisotropic material,” IEEE Trans. Antenn. Propag. 41(7), 994–999 (1993).
[CrossRef]

1992

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]

1988

A. Taflove, “Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures,” Wave Motion 10(6), 547–582 (1988).
[CrossRef]

Agio, M.

Arnold, S.

Baba, T.

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80(12), 2051–2053 (2002).
[CrossRef]

Bae, S.-

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

Balistreri, M. L. M.

Barclay, P. E.

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85(17), 3693–3695 (2004).
[CrossRef]

Benson, T. M.

Bercha, A.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Blom*, F. C.

Bohdan, R.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Boriskina, S. V.

Borselli, M.

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85(17), 3693–3695 (2004).
[CrossRef]

Bourouina, T.

Boyd, R. W.

Cai, H.

Cai, M.

Chin, M. K.

M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75(7), 3302–3307 (1994).
[CrossRef]

Chu, D. Y.

M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75(7), 3302–3307 (1994).
[CrossRef]

Daraei, A.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Dey, S.

S. Dey and R. Mittra, “A Conformal Finite-Difference Time-Domain Technique for Modeling Cylindrical Dielectric Resonators,” IEEE Trans. Microw. Theory Tech. 47(9), 1737–1739 (1999).
[CrossRef]

S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Pade approximation,” IEEE Microw. Guid. Wave Lett. 8(12), 415–417 (1998).
[CrossRef]

Driessen, A.

Dybala, F.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Erbert, G.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Fang, J.

J. Fang and Z. Wu, “Generalized Perfectly Matched Layer for the Absorption of Propagating and Evanescent Waves in Lossless and Lossy Media,” IEEE Trans. Microw. Theory Tech. 44(12), 2216–2222 (1996).
[CrossRef]

Fox, A. M.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Friberg, A. T.

Fujita, M.

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80(12), 2051–2053 (2002).
[CrossRef]

Gorodetsky, M. L.

Guimaraes, P. S. S.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Guo, L. J.

J. Yang and L. J. Guo, “Optical Sensors Based on Active Microcavities,” IEEE J. Sel. Top. Quantum Electron. 12(1), 143–147 (2006).
[CrossRef]

Harris, J. S.

F. Sugihwo, M. C. Larson, and J. S. Harris, “Micromachined widely tunable vertical cavity laser diodes,” J. Microelectromech. Syst. 7(1), 48–55 (1998).
[CrossRef]

M. C. Larson and J. S. Harris, “Wide and continuous wavelength tuning in a vertical-cavity surface-emitting laser using a micromachined deformable-membrane mirror,” Appl. Phys. Lett. 68(7), 891–893 (1996).
[CrossRef]

M. C. Larson and J. S. Harris, “Broadly-Tunable Resonant-Cavity Light-Emitting Diode,” IEEE Photon. Technol. Lett. 7(11), 1267–1269 (1995).
[CrossRef]

Heebner, J. E.

Hentschel, M.

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5 Pt 2), 056207 (2002).
[CrossRef] [PubMed]

Ho, S. T.

M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75(7), 3302–3307 (1994).
[CrossRef]

Ho, Y.-L. D.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Hoekstra, H. W. J. M.

Holler, S.

Hong, Y.-K.

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

Hopkinson, M.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Hudson, S.

J. Schneider and S. Hudson, “The finite-difference time-domain method applied to anisotropic material,” IEEE Trans. Antenn. Propag. 41(7), 994–999 (1993).
[CrossRef]

Ilchenko, V. S.

Jang, H.-J.

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

Khoshsima, M.

Klehr, A.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Klunder, D. J. W.

Ko, H.-S.

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

Korterik, J. P.

Kuipers, L.

Lam, S.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Larson, M. C.

F. Sugihwo, M. C. Larson, and J. S. Harris, “Micromachined widely tunable vertical cavity laser diodes,” J. Microelectromech. Syst. 7(1), 48–55 (1998).
[CrossRef]

M. C. Larson and J. S. Harris, “Wide and continuous wavelength tuning in a vertical-cavity surface-emitting laser using a micromachined deformable-membrane mirror,” Appl. Phys. Lett. 68(7), 891–893 (1996).
[CrossRef]

M. C. Larson and J. S. Harris, “Broadly-Tunable Resonant-Cavity Light-Emitting Diode,” IEEE Photon. Technol. Lett. 7(11), 1267–1269 (1995).
[CrossRef]

Lee, Y.-H.

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

Levi, A. F. J.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993).
[CrossRef]

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]

Liu, A. Q.

Liu, B.

Logan, R. A.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993).
[CrossRef]

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]

McCall, S. L.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993).
[CrossRef]

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]

Mittra, R.

S. Dey and R. Mittra, “A Conformal Finite-Difference Time-Domain Technique for Modeling Cylindrical Dielectric Resonators,” IEEE Trans. Microw. Theory Tech. 47(9), 1737–1739 (1999).
[CrossRef]

S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Pade approximation,” IEEE Microw. Guid. Wave Lett. 8(12), 415–417 (1998).
[CrossRef]

Mohammadi, A.

Mohideen, U.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993).
[CrossRef]

Mrozowicz, M.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Nadgaran, H.

Nöckel, J. U.

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385(6611), 45–47 (1997).
[CrossRef]

Nosich, A. I.

Painter, O.

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85(17), 3693–3695 (2004).
[CrossRef]

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25(19), 1430–1432 (2000).
[CrossRef] [PubMed]

Pearton, S. J.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993).
[CrossRef]

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]

Piechal, B.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Popov, S.

Rarity, J. G.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Ressel, P.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Ricciardi, S.

Richter, K.

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5 Pt 2), 056207 (2002).
[CrossRef] [PubMed]

Sanvitto, D.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Savchenkov, A. A.

Schneider, J.

J. Schneider and S. Hudson, “The finite-difference time-domain method applied to anisotropic material,” IEEE Trans. Antenn. Propag. 41(7), 994–999 (1993).
[CrossRef]

Sercel, P. C.

Sergeyev, S.

Sewell, P.

Skolnick, M. S.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Slusher, R. E.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993).
[CrossRef]

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]

Son, J.-K.

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

Song, Y.-H.

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

Srinivasan, K.

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85(17), 3693–3695 (2004).
[CrossRef]

Stone, A. D.

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385(6611), 45–47 (1997).
[CrossRef]

Sugihwo, F.

F. Sugihwo, M. C. Larson, and J. S. Harris, “Micromachined widely tunable vertical cavity laser diodes,” J. Microelectromech. Syst. 7(1), 48–55 (1998).
[CrossRef]

Sumpf, B.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Sung, G.-Y.

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

Taflove, A.

A. Taflove, “Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures,” Wave Motion 10(6), 547–582 (1988).
[CrossRef]

Tahraoui, A.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Tamil, J.

Teraoka, I.

Timpson, J. A.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Trzeciakowski, W.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Vahala, K. J.

van Hulst, N. F.

Vinck, H.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Vollmer, F.

Wenzel, H.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Whittaker, D. M.

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

Wu, Z.

J. Fang and Z. Wu, “Generalized Perfectly Matched Layer for the Absorption of Propagating and Evanescent Waves in Lossless and Lossy Media,” IEEE Trans. Microw. Theory Tech. 44(12), 2216–2222 (1996).
[CrossRef]

Yang, G.-M.

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

Yang, J.

J. Yang and L. J. Guo, “Optical Sensors Based on Active Microcavities,” IEEE J. Sel. Top. Quantum Electron. 12(1), 143–147 (2006).
[CrossRef]

Yang, S.-S.

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

Zhang, Q. X.

Zhang, X. M.

Appl. Opt.

Appl. Phys. Lett.

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80(12), 2051–2053 (2002).
[CrossRef]

D. M. Whittaker, P. S. S. Guimaraes, D. Sanvitto, H. Vinck, S. Lam, A. Daraei, J. A. Timpson, A. M. Fox, M. S. Skolnick, Y.-L. D. Ho, J. G. Rarity, M. Hopkinson, and A. Tahraoui, “High Q modes in elliptical microcavity pillars,” Appl. Phys. Lett. 90(16), 161105 (2007).
[CrossRef]

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]

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993).
[CrossRef]

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85(17), 3693–3695 (2004).
[CrossRef]

M. C. Larson and J. S. Harris, “Wide and continuous wavelength tuning in a vertical-cavity surface-emitting laser using a micromachined deformable-membrane mirror,” Appl. Phys. Lett. 68(7), 891–893 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. Yang and L. J. Guo, “Optical Sensors Based on Active Microcavities,” IEEE J. Sel. Top. Quantum Electron. 12(1), 143–147 (2006).
[CrossRef]

IEEE Microw. Guid. Wave Lett.

S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Pade approximation,” IEEE Microw. Guid. Wave Lett. 8(12), 415–417 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

M. C. Larson and J. S. Harris, “Broadly-Tunable Resonant-Cavity Light-Emitting Diode,” IEEE Photon. Technol. Lett. 7(11), 1267–1269 (1995).
[CrossRef]

S.-S. Yang, J.-K. Son, Y.-K. Hong, Y.-H. Song, H.-J. Jang, S.- Bae, Y.-H. Lee, G.-M. Yang, H.-S. Ko, and G.-Y. Sung, “Wavelength Tuning of Vertical-Cavity Surface-Emitting Lasers by an Internal Device Heater,” IEEE Photon. Technol. Lett. 20(20), 1679–1681 (2008).
[CrossRef]

IEEE Trans. Antenn. Propag.

J. Schneider and S. Hudson, “The finite-difference time-domain method applied to anisotropic material,” IEEE Trans. Antenn. Propag. 41(7), 994–999 (1993).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

S. Dey and R. Mittra, “A Conformal Finite-Difference Time-Domain Technique for Modeling Cylindrical Dielectric Resonators,” IEEE Trans. Microw. Theory Tech. 47(9), 1737–1739 (1999).
[CrossRef]

J. Fang and Z. Wu, “Generalized Perfectly Matched Layer for the Absorption of Propagating and Evanescent Waves in Lossless and Lossy Media,” IEEE Trans. Microw. Theory Tech. 44(12), 2216–2222 (1996).
[CrossRef]

J. Appl. Phys.

M. K. Chin, D. Y. Chu, and S. T. Ho, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. 75(7), 3302–3307 (1994).
[CrossRef]

J. Lightwave Technol.

J. Microelectromech. Syst.

F. Sugihwo, M. C. Larson, and J. S. Harris, “Micromachined widely tunable vertical cavity laser diodes,” J. Microelectromech. Syst. 7(1), 48–55 (1998).
[CrossRef]

Nature

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385(6611), 45–47 (1997).
[CrossRef]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5 Pt 2), 056207 (2002).
[CrossRef] [PubMed]

Semicond. Sci. Technol.

F. Dybała, A. Bercha, B. Piechal, W. Trzeciakowski, R. Bohdan, M. Mrozowicz, A. Klehr, P. Ressel, H. Wenzel, B. Sumpf, and G. Erbert, “Pressure and temperature tuning of an external cavity InGaAsP laser diode,” Semicond. Sci. Technol. 23(12), 125012 (2008).
[CrossRef]

Wave Motion

A. Taflove, “Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures,” Wave Motion 10(6), 547–582 (1988).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Sketch of cylindrical cavity. The structure of anisotropic microcavity to be studied is a cylindrical dielectric rod with dielectric constant ε 1 and radius R = 1μm in background medium with dielectric constant ε 2 = 1. The direction along the rod is parallel to one of the three principal axes and is set to be axis z, and the two orthogonal directions lying within the cross section are parallel to the other two principal axes and are set to be axis x and axis y to form a right-handed set with axis z. The rod is assumed infinite in the z direction. Both source point S and detection point D locate at axis y (to avoid exciting degenerate mode which will be discussed in another paper) and have a distance 15R/16 away from the cavity centre.

Fig. 2
Fig. 2

Influence of medium electric anisotropy on the cavity resonant frequencies. The red real curve, green dashed curve and blue dotted curve is the spectrum of cylindrical microcavities with relative difference of two principal refractive indices (nx - ny )/nx equal to 0, 0.01 and 0.02, respectively. Other parameters are the same as that in Fig. 1.

Fig. 3
Fig. 3

The relationship between the resonant frequencies of WGMs and relative difference of two principal refractive indices (nx - ny )/nx . The red circles, green asterisks and blue squares refer to numerical results for WGM8,1, WGM9,1, and WGM10,1, respectively. The red real line, green dashed line and blue dotted line are the corresponding fitting lines.

Fig. 4
Fig. 4

The relationship between the Q factors of WGMs and relative difference of two principal refractive indices (nx - ny )/nx . The red circles, green asterisks and blue squares refer to numerical results for WGM8,1, WGM9,1, and WGM10,1, respectively. The red real curve, green dashed curve and blue dotted curve are the corresponding fitting curves.

Tables (3)

Tables Icon

Table 1 Comparison of analytical solution and numerical solution for isotropic cylindrical microcavity with refractive index n 2 = 3.2 and radius R = 1μm.

Tables Icon

Table 2 Linear fit parameters of the three fitting lines for WGM8,1, WGM9,1, and WGM10,1, respectively, in Fig. 3 a .

Tables Icon

Table 3 Parameters of the three fitting curves for WGM8,1, WGM9,1, and WGM10,1, respectively, in Fig. 4 a .

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

ε = [ ε x 0 0 0 ε y 0 0 0 ε z ] .
E x n + 1 ( i + 1 2 , j ) = E x n ( i + 1 2 , j ) + Δ t ε 0 ε x [ H z n + 1 / 2 ( i + 1 2 , j + 1 2 ) H z n + 1 / 2 ( i + 1 2 , j 1 2 ) ] / Δ y E y n + 1 ( i , j + 1 2 ) = E y n ( i , j + 1 2 ) Δ t ε 0 ε y [ H z n + 1 / 2 ( i + 1 2 , j + 1 2 ) H z n + 1 / 2 ( i 1 2 , j + 1 2 ) ] / Δ x H z n + 1/2 ( i + 1 2 , j + 1 2 ) = H z n-1/2 ( i + 1 2 , j + 1 2 ) Δ t μ o { [ E y n ( i + 1 , j + 1 2 ) E y n ( i , j + 1 2 ) ] / Δ x [ E x n ( i + 1 2 , j + 1 ) E x n ( i + 1 2 , j ) ] / Δ y } } ,
ε e f f = V ( i , j , k ) * ε 1 + [ 1 V ( i , j , k ) ] * ε 2 ,
J m ( k n 1 R ) H m ( 2 ) ' ( k n 2 R ) = η J m ' ( k n 1 R ) H m ( 2 ) ( k n 2 R ) ,
f m , l = c Re ( k m , l ) / ( 2 π ) ,
Q m , l = Re ( k m , l ) / [ 2 Im ( k m , l ) ] .

Metrics