Abstract

Our objective is the assessment of the accuracy of a conventional finite-difference time-domain (FDTD) code in the computation of the near- and far-field scattering characteristics of a circular dielectric cylinder. We excite the cylinder with an electric or magnetic line current and demonstrate the failure of the two-dimensional FDTD algorithm to accurately characterize the emission rate and the field patterns near high-Q whispering-gallery-mode resonances. This is proven by comparison with the exact series solutions. The computational errors in the emission rate are then studied at the resonances still detectable with FDTD, i.e., having Q-factors up to 103.

© 2008 Optical Society of America

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  1. A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
    [CrossRef]
  2. V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
    [CrossRef]
  3. A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. (to be published); available at http://www.springerlink.com/content/x74382234u02608v/.
  4. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182 (2006).
    [CrossRef]
  5. P. W. Evans and N. Holonyak Jr., “Room temperature photopump laser operation of native-oxide-defined coupled GaAs-AlAs superlattice microrings,” Appl. Phys. Lett. 69, 2391-2393 (1996).
    [CrossRef]
  6. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711-713 (1999).
    [CrossRef]
  7. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes,” Opt. Lett. 31, 921-923 (2006).
    [CrossRef] [PubMed]
  8. P.-T. Lee, T.-W. Lu, J.-H. Fan, and F.-M. Tsai, “High quality factor microcavity lasers realized by circular photonic crystal with isotropic photonic band gap effect,” Appl. Phys. Lett. 90, 151125 (2007).
    [CrossRef]
  9. S. V. Pishko, P. D. Sewell, T. M. Benson, and S. V. Boriskina, “Efficient analysis and design of low-loss WGM coupled resonator optical waveguide bends,” J. Lightwave Technol. 25, 2487-2494 (2007).
    [CrossRef]
  10. K. L. Shlager and J. B. Schneider, “A selective survey of the finite-difference time-domain literature,” IEEE Antennas Propag. Mag. 37, 39-57 (1995).
    [CrossRef]
  11. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  12. G. L. Hower, R. G. Olsen, J. D. Earls, and J. B. Schneider, “Inaccuracies in numerical calculations of scattering near natural frequencies of penetrable objects,” IEEE Trans. Antennas Propag. 41, 982-986 (1993).
    [CrossRef]
  13. K. Phan-Huy, A. Morand, D. Amans, and P. Benech, “Analytical study of the whispering-gallery modes in two-dimensional microgear cavity using coupled-mode theory,” J. Opt. Soc. Am. B 22, 1793-1804 (2005).
    [CrossRef]
  14. Y. Liu, C. D. Sarrisa, and G. V. Eleftheriades, “Triangular-mesh-based FDTD analysis of 2-D plasmonic structures supporting backward waves at optical frequencies,” J. Lightwave Technol. 25, 938-946 (2007).
    [CrossRef]
  15. E. I. Smotrova, A. I. Nosich, T. Benson, and P. Sewell, “Cold-cavity thresholds of microdisks with uniform and non-uniform gain: quasi-3D modeling with accurate 2D analysis,” IEEE J. Sel. Top. Quantum Electron. 11, 1135-1142 (2005).
    [CrossRef]
  16. D. Marcuse, Light Transmission Optics, Computer Science and Engineering Series (Van Nostrand Reinhold Electrical, 1989).
  17. S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
    [CrossRef]
  18. A. Sakai and T. Baba, “FDTD simulation of photonic devices and circuits based on circular and fan-shaped microdisks,” J. Lightwave Technol. 17, 1493-1499 (1999).
    [CrossRef]
  19. Y. Liu and C. D. Sarris, “Fast time-domain simulation of optical waveguide structures with a multilevel dynamically adaptive mesh refinement FDTD approach,” J. Lightwave Technol. 24, 3235-3248 (2006).
    [CrossRef]
  20. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
    [CrossRef]
  21. L.-P. Berenger, “Perfectly matched layer for the FDTD solution of wave-structure interaction problem,” IEEE Trans. Antennas Propag. 44, 110-118 (1996).
    [CrossRef]
  22. A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758-764 (2008).
    [CrossRef]
  23. Y.-Z. Huang, Q.-Y. Lu, W.-H. Guo, and L.-J. Yu, “Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries,” IEE Proc.: Optoelectron. 151, 202-204 (2004).
    [CrossRef]
  24. A. V. Boriskin and A. I. Nosich, “Whispering-gallery and Luneburg lens effects in a beam-fed circularly-layered dielectric cylinder,” IEEE Trans. Antennas Propag. 50, 1245-1249 (2002).
    [CrossRef]
  25. S. Rondineau, A. I. Nosich, J.-P. Daniel, M. Himdi, and S. S. Vinogradov, “MAR-based analysis of a spherical-circular printed antenna with a finite ground excited by an axially-symmetric probe,” IEEE Trans. Antennas Propag. 52, 1270-1280 (2004).
    [CrossRef]
  26. S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
    [CrossRef]
  27. A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator?—Electromagnetic behavior of an extended hemielliptic lens for a sub-mm wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
    [CrossRef]
  28. A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485-492 (2008).
    [CrossRef]

2008 (2)

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758-764 (2008).
[CrossRef]

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485-492 (2008).
[CrossRef]

2007 (3)

2006 (5)

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes,” Opt. Lett. 31, 921-923 (2006).
[CrossRef] [PubMed]

Y. Liu and C. D. Sarris, “Fast time-domain simulation of optical waveguide structures with a multilevel dynamically adaptive mesh refinement FDTD approach,” J. Lightwave Technol. 24, 3235-3248 (2006).
[CrossRef]

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182 (2006).
[CrossRef]

2005 (2)

K. Phan-Huy, A. Morand, D. Amans, and P. Benech, “Analytical study of the whispering-gallery modes in two-dimensional microgear cavity using coupled-mode theory,” J. Opt. Soc. Am. B 22, 1793-1804 (2005).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. Benson, and P. Sewell, “Cold-cavity thresholds of microdisks with uniform and non-uniform gain: quasi-3D modeling with accurate 2D analysis,” IEEE J. Sel. Top. Quantum Electron. 11, 1135-1142 (2005).
[CrossRef]

2004 (4)

Y.-Z. Huang, Q.-Y. Lu, W.-H. Guo, and L.-J. Yu, “Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries,” IEE Proc.: Optoelectron. 151, 202-204 (2004).
[CrossRef]

S. Rondineau, A. I. Nosich, J.-P. Daniel, M. Himdi, and S. S. Vinogradov, “MAR-based analysis of a spherical-circular printed antenna with a finite ground excited by an axially-symmetric probe,” IEEE Trans. Antennas Propag. 52, 1270-1280 (2004).
[CrossRef]

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator?—Electromagnetic behavior of an extended hemielliptic lens for a sub-mm wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

2002 (1)

A. V. Boriskin and A. I. Nosich, “Whispering-gallery and Luneburg lens effects in a beam-fed circularly-layered dielectric cylinder,” IEEE Trans. Antennas Propag. 50, 1245-1249 (2002).
[CrossRef]

1999 (2)

1997 (1)

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

1996 (2)

L.-P. Berenger, “Perfectly matched layer for the FDTD solution of wave-structure interaction problem,” IEEE Trans. Antennas Propag. 44, 110-118 (1996).
[CrossRef]

P. W. Evans and N. Holonyak Jr., “Room temperature photopump laser operation of native-oxide-defined coupled GaAs-AlAs superlattice microrings,” Appl. Phys. Lett. 69, 2391-2393 (1996).
[CrossRef]

1995 (1)

K. L. Shlager and J. B. Schneider, “A selective survey of the finite-difference time-domain literature,” IEEE Antennas Propag. Mag. 37, 39-57 (1995).
[CrossRef]

1993 (1)

G. L. Hower, R. G. Olsen, J. D. Earls, and J. B. Schneider, “Inaccuracies in numerical calculations of scattering near natural frequencies of penetrable objects,” IEEE Trans. Antennas Propag. 41, 982-986 (1993).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Altintas, A.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator?—Electromagnetic behavior of an extended hemielliptic lens for a sub-mm wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

Amans, D.

Baba, T.

Benech, P.

Benson, T.

E. I. Smotrova, A. I. Nosich, T. Benson, and P. Sewell, “Cold-cavity thresholds of microdisks with uniform and non-uniform gain: quasi-3D modeling with accurate 2D analysis,” IEEE J. Sel. Top. Quantum Electron. 11, 1135-1142 (2005).
[CrossRef]

Benson, T. M.

S. V. Pishko, P. D. Sewell, T. M. Benson, and S. V. Boriskina, “Efficient analysis and design of low-loss WGM coupled resonator optical waveguide bends,” J. Lightwave Technol. 25, 2487-2494 (2007).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes,” Opt. Lett. 31, 921-923 (2006).
[CrossRef] [PubMed]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182 (2006).
[CrossRef]

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator?—Electromagnetic behavior of an extended hemielliptic lens for a sub-mm wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. (to be published); available at http://www.springerlink.com/content/x74382234u02608v/.

Berenger, L.-P.

L.-P. Berenger, “Perfectly matched layer for the FDTD solution of wave-structure interaction problem,” IEEE Trans. Antennas Propag. 44, 110-118 (1996).
[CrossRef]

Boriskin, A. V.

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485-492 (2008).
[CrossRef]

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758-764 (2008).
[CrossRef]

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator?—Electromagnetic behavior of an extended hemielliptic lens for a sub-mm wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

A. V. Boriskin and A. I. Nosich, “Whispering-gallery and Luneburg lens effects in a beam-fed circularly-layered dielectric cylinder,” IEEE Trans. Antennas Propag. 50, 1245-1249 (2002).
[CrossRef]

Boriskina, S. V.

S. V. Pishko, P. D. Sewell, T. M. Benson, and S. V. Boriskina, “Efficient analysis and design of low-loss WGM coupled resonator optical waveguide bends,” J. Lightwave Technol. 25, 2487-2494 (2007).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182 (2006).
[CrossRef]

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator?—Electromagnetic behavior of an extended hemielliptic lens for a sub-mm wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. (to be published); available at http://www.springerlink.com/content/x74382234u02608v/.

Daniel, J.-P.

S. Rondineau, A. I. Nosich, J.-P. Daniel, M. Himdi, and S. S. Vinogradov, “MAR-based analysis of a spherical-circular printed antenna with a finite ground excited by an axially-symmetric probe,” IEEE Trans. Antennas Propag. 52, 1270-1280 (2004).
[CrossRef]

Earls, J. D.

G. L. Hower, R. G. Olsen, J. D. Earls, and J. B. Schneider, “Inaccuracies in numerical calculations of scattering near natural frequencies of penetrable objects,” IEEE Trans. Antennas Propag. 41, 982-986 (1993).
[CrossRef]

Eleftheriades, G. V.

Evans, P. W.

P. W. Evans and N. Holonyak Jr., “Room temperature photopump laser operation of native-oxide-defined coupled GaAs-AlAs superlattice microrings,” Appl. Phys. Lett. 69, 2391-2393 (1996).
[CrossRef]

Fan, J.-H.

P.-T. Lee, T.-W. Lu, J.-H. Fan, and F.-M. Tsai, “High quality factor microcavity lasers realized by circular photonic crystal with isotropic photonic band gap effect,” Appl. Phys. Lett. 90, 151125 (2007).
[CrossRef]

Godi, G.

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485-492 (2008).
[CrossRef]

Guo, W.-H.

Y.-Z. Huang, Q.-Y. Lu, W.-H. Guo, and L.-J. Yu, “Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries,” IEE Proc.: Optoelectron. 151, 202-204 (2004).
[CrossRef]

Hagness, S. C.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Himdi, M.

S. Rondineau, A. I. Nosich, J.-P. Daniel, M. Himdi, and S. S. Vinogradov, “MAR-based analysis of a spherical-circular printed antenna with a finite ground excited by an axially-symmetric probe,” IEEE Trans. Antennas Propag. 52, 1270-1280 (2004).
[CrossRef]

Ho, S. T.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

Holonyak, N.

P. W. Evans and N. Holonyak Jr., “Room temperature photopump laser operation of native-oxide-defined coupled GaAs-AlAs superlattice microrings,” Appl. Phys. Lett. 69, 2391-2393 (1996).
[CrossRef]

Hower, G. L.

G. L. Hower, R. G. Olsen, J. D. Earls, and J. B. Schneider, “Inaccuracies in numerical calculations of scattering near natural frequencies of penetrable objects,” IEEE Trans. Antennas Propag. 41, 982-986 (1993).
[CrossRef]

Huang, Y.-Z.

Y.-Z. Huang, Q.-Y. Lu, W.-H. Guo, and L.-J. Yu, “Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries,” IEE Proc.: Optoelectron. 151, 202-204 (2004).
[CrossRef]

Ilchenko, V. S.

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

Kim, C.-M.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Kurdoglyan, M. S.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Lee, P.-T.

P.-T. Lee, T.-W. Lu, J.-H. Fan, and F.-M. Tsai, “High quality factor microcavity lasers realized by circular photonic crystal with isotropic photonic band gap effect,” Appl. Phys. Lett. 90, 151125 (2007).
[CrossRef]

Lee, R. K.

Lee, S.-Y.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Liu, Y.

Lu, Q.-Y.

Y.-Z. Huang, Q.-Y. Lu, W.-H. Guo, and L.-J. Yu, “Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries,” IEE Proc.: Optoelectron. 151, 202-204 (2004).
[CrossRef]

Lu, T.-W.

P.-T. Lee, T.-W. Lu, J.-H. Fan, and F.-M. Tsai, “High quality factor microcavity lasers realized by circular photonic crystal with isotropic photonic band gap effect,” Appl. Phys. Lett. 90, 151125 (2007).
[CrossRef]

Marcuse, D.

D. Marcuse, Light Transmission Optics, Computer Science and Engineering Series (Van Nostrand Reinhold Electrical, 1989).

Matsko, A. B.

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

Morand, A.

Nosich, A. I.

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758-764 (2008).
[CrossRef]

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485-492 (2008).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes,” Opt. Lett. 31, 921-923 (2006).
[CrossRef] [PubMed]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. Benson, and P. Sewell, “Cold-cavity thresholds of microdisks with uniform and non-uniform gain: quasi-3D modeling with accurate 2D analysis,” IEEE J. Sel. Top. Quantum Electron. 11, 1135-1142 (2005).
[CrossRef]

S. Rondineau, A. I. Nosich, J.-P. Daniel, M. Himdi, and S. S. Vinogradov, “MAR-based analysis of a spherical-circular printed antenna with a finite ground excited by an axially-symmetric probe,” IEEE Trans. Antennas Propag. 52, 1270-1280 (2004).
[CrossRef]

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator?—Electromagnetic behavior of an extended hemielliptic lens for a sub-mm wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

A. V. Boriskin and A. I. Nosich, “Whispering-gallery and Luneburg lens effects in a beam-fed circularly-layered dielectric cylinder,” IEEE Trans. Antennas Propag. 50, 1245-1249 (2002).
[CrossRef]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. (to be published); available at http://www.springerlink.com/content/x74382234u02608v/.

Olsen, R. G.

G. L. Hower, R. G. Olsen, J. D. Earls, and J. B. Schneider, “Inaccuracies in numerical calculations of scattering near natural frequencies of penetrable objects,” IEEE Trans. Antennas Propag. 41, 982-986 (1993).
[CrossRef]

Phan-Huy, K.

Pishko, S. V.

Rafizadeh, D.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

Rim, S.

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Rolland, A.

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758-764 (2008).
[CrossRef]

Rondineau, S.

S. Rondineau, A. I. Nosich, J.-P. Daniel, M. Himdi, and S. S. Vinogradov, “MAR-based analysis of a spherical-circular printed antenna with a finite ground excited by an axially-symmetric probe,” IEEE Trans. Antennas Propag. 52, 1270-1280 (2004).
[CrossRef]

Sakai, A.

Sarris, C. D.

Sarrisa, C. D.

Sauleau, R.

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758-764 (2008).
[CrossRef]

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485-492 (2008).
[CrossRef]

Scherer, A.

Schneider, J. B.

K. L. Shlager and J. B. Schneider, “A selective survey of the finite-difference time-domain literature,” IEEE Antennas Propag. Mag. 37, 39-57 (1995).
[CrossRef]

G. L. Hower, R. G. Olsen, J. D. Earls, and J. B. Schneider, “Inaccuracies in numerical calculations of scattering near natural frequencies of penetrable objects,” IEEE Trans. Antennas Propag. 41, 982-986 (1993).
[CrossRef]

Sewell, P.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes,” Opt. Lett. 31, 921-923 (2006).
[CrossRef] [PubMed]

E. I. Smotrova, A. I. Nosich, T. Benson, and P. Sewell, “Cold-cavity thresholds of microdisks with uniform and non-uniform gain: quasi-3D modeling with accurate 2D analysis,” IEEE J. Sel. Top. Quantum Electron. 11, 1135-1142 (2005).
[CrossRef]

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator?—Electromagnetic behavior of an extended hemielliptic lens for a sub-mm wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. (to be published); available at http://www.springerlink.com/content/x74382234u02608v/.

Sewell, P. D.

Shlager, K. L.

K. L. Shlager and J. B. Schneider, “A selective survey of the finite-difference time-domain literature,” IEEE Antennas Propag. Mag. 37, 39-57 (1995).
[CrossRef]

Smotrova, E. I.

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes,” Opt. Lett. 31, 921-923 (2006).
[CrossRef] [PubMed]

E. I. Smotrova, A. I. Nosich, T. Benson, and P. Sewell, “Cold-cavity thresholds of microdisks with uniform and non-uniform gain: quasi-3D modeling with accurate 2D analysis,” IEEE J. Sel. Top. Quantum Electron. 11, 1135-1142 (2005).
[CrossRef]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. (to be published); available at http://www.springerlink.com/content/x74382234u02608v/.

Taflove, A.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Tsai, F.-M.

P.-T. Lee, T.-W. Lu, J.-H. Fan, and F.-M. Tsai, “High quality factor microcavity lasers realized by circular photonic crystal with isotropic photonic band gap effect,” Appl. Phys. Lett. 90, 151125 (2007).
[CrossRef]

Vinogradov, S. S.

S. Rondineau, A. I. Nosich, J.-P. Daniel, M. Himdi, and S. S. Vinogradov, “MAR-based analysis of a spherical-circular printed antenna with a finite ground excited by an axially-symmetric probe,” IEEE Trans. Antennas Propag. 52, 1270-1280 (2004).
[CrossRef]

Xu, Y.

Yariv, A.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Yu, L.-J.

Y.-Z. Huang, Q.-Y. Lu, W.-H. Guo, and L.-J. Yu, “Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries,” IEE Proc.: Optoelectron. 151, 202-204 (2004).
[CrossRef]

Appl. Phys. Lett. (2)

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[CrossRef]

P.-T. Lee, T.-W. Lu, J.-H. Fan, and F.-M. Tsai, “High quality factor microcavity lasers realized by circular photonic crystal with isotropic photonic band gap effect,” Appl. Phys. Lett. 90, 151125 (2007).
[CrossRef]

IEE Proc.: Optoelectron. (1)

Y.-Z. Huang, Q.-Y. Lu, W.-H. Guo, and L.-J. Yu, “Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries,” IEE Proc.: Optoelectron. 151, 202-204 (2004).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

K. L. Shlager and J. B. Schneider, “A selective survey of the finite-difference time-domain literature,” IEEE Antennas Propag. Mag. 37, 39-57 (1995).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (4)

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: basics,” IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. Benson, and P. Sewell, “Cold-cavity thresholds of microdisks with uniform and non-uniform gain: quasi-3D modeling with accurate 2D analysis,” IEEE J. Sel. Top. Quantum Electron. 11, 1135-1142 (2005).
[CrossRef]

IEEE Trans. Antennas Propag. (7)

A. V. Boriskin and A. I. Nosich, “Whispering-gallery and Luneburg lens effects in a beam-fed circularly-layered dielectric cylinder,” IEEE Trans. Antennas Propag. 50, 1245-1249 (2002).
[CrossRef]

S. Rondineau, A. I. Nosich, J.-P. Daniel, M. Himdi, and S. S. Vinogradov, “MAR-based analysis of a spherical-circular printed antenna with a finite ground excited by an axially-symmetric probe,” IEEE Trans. Antennas Propag. 52, 1270-1280 (2004).
[CrossRef]

G. L. Hower, R. G. Olsen, J. D. Earls, and J. B. Schneider, “Inaccuracies in numerical calculations of scattering near natural frequencies of penetrable objects,” IEEE Trans. Antennas Propag. 41, 982-986 (1993).
[CrossRef]

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

L.-P. Berenger, “Perfectly matched layer for the FDTD solution of wave-structure interaction problem,” IEEE Trans. Antennas Propag. 44, 110-118 (1996).
[CrossRef]

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758-764 (2008).
[CrossRef]

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485-492 (2008).
[CrossRef]

J. Lightwave Technol. (5)

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

Microwave Opt. Technol. Lett. (1)

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator?—Electromagnetic behavior of an extended hemielliptic lens for a sub-mm wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

S.-Y. Lee, M. S. Kurdoglyan, S. Rim, and C.-M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Other (3)

D. Marcuse, Light Transmission Optics, Computer Science and Engineering Series (Van Nostrand Reinhold Electrical, 1989).

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. (to be published); available at http://www.springerlink.com/content/x74382234u02608v/.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

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Figures (6)

Fig. 1
Fig. 1

Normalized total emission rate of the line source illuminating quartz ( ε = 2.0 ) circular resonator computed by the FDTD method and Series (thick solid curves): (a) E-polarization and (b) H-polarization. The family of four FDTD curves is computed with different meshes. The values of M for each FDTD curve are represented by the monotonic lines of corresponding types.

Fig. 2
Fig. 2

Normalized near-field maps of quartz circular resonators excited by the E-polarized line source: (a) Series ( k a = 6.543 ) and (b) FDTD ( k a = 6.600 ) . The corresponding WGM - E 10.1 resonance is indicated by the triangle in Fig. 1a.

Fig. 3
Fig. 3

Same as in Fig. 1 but for a silicon resonator ( ε = 3.42 ) .

Fig. 4
Fig. 4

Normalized near-field maps of the silicon circular resonators excited by a line H-polarized current: (a) Series ( k a = 4.625 ) and (b) FDTD ( k a = 4.645 ) . The corresponding WGM - H 8.2 resonance is indicated by the triangle in Fig. 3b.

Fig. 5
Fig. 5

Normalized frequency shift extracted from comparison between FTDT and Series solutions for the WGM-related spikes in the normalized emission rate observed in Fig. 1 for the quartz resonator versus the resonances Q-factor. The family of four curves is for different mesh sizes.

Fig. 6
Fig. 6

Computation errors of the FDTD algorithm for the normalized emission rate extracted from comparison between FTDT and Series solutions presented in Fig. 1 for the quartz resonator versus the resonances Q-factor. The family of four curves is for different mesh sizes.

Tables (1)

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Table 1 Q-Factors of the ( m , 2 ) WGMs in a Silicon Circular Resonator

Equations (2)

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J m ( k a ε ) H m ( k a ) ε H m ( k a ) J m ( k a ε ) = 0 ,
P 0 = 2 Z 0 k ( E - pol. ) , P 0 = 2 Z 0 k ( H - pol. ) ,

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