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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 15 — Jul. 20, 2009
  • pp: 13178–13186

An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane

Harald G. L. Schwefel and Christopher G. Poulton  »View Author Affiliations

Optics Express, Vol. 17, Issue 15, pp. 13178-13186 (2009)

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We present a numerically improved multipole formulation for the calculation of resonances of multiple disks located at arbitrary positions in a 2-d plane, and suitable for the accurate computation of the resonances of large numbers of disks and of high-wavenumber eigenstates. Using a simple reformulation of the field expansions and boundary conditions, we are able to transform the multipole formalism into a linear eigenvalue problem, for which fast and accurate methods are available. Observing that the motion of the eigenvalues in the complex plane is analytic with respect to a two parameter family, we present a numerical algorithm to compute a range of multiple-disk resonances and field distributions using only two diagonalizations. This method can be applied to photonic molecules, photonic crystals, photonic crystal fibers, and random lasers.

© 2009 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(230.5750) Optical devices : Resonators
(140.3945) Lasers and laser optics : Microcavities
(230.4555) Optical devices : Coupled resonators

ToC Category:
Optical Devices

Original Manuscript: April 29, 2009
Revised Manuscript: June 30, 2009
Manuscript Accepted: June 30, 2009
Published: July 17, 2009

Harald G. Schwefel and Christopher G. Poulton, "An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane," Opt. Express 17, 13178-13186 (2009)

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  1. B. Little, S. Chu, H. Haus, J. Foresi, and J. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997). [CrossRef]
  2. T. Carmon, T. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. Vahala, "Feedback control of ultra-high-Q microcavities: application to micro-Raman lasers and microparametric oscillators," Opt. Express 13, 3558-3566 (2005). [CrossRef] [PubMed]
  3. S. Preu, H. G. L. Schwefel, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, "Coupled whispering gallery mode resonators in the Terahertz frequency range," Opt. Express 16, 7336-7343 (2008). [CrossRef] [PubMed]
  4. D. S. Wiersma and A. Lagendijk, "Light diffusion with gain and random lasers," Phys. Rev. E 54, 4256-4265 (1996). [CrossRef]
  5. H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, "Spatial Confinement of Laser Light in Active Random Media," Phys. Rev. Lett. 84, 5584-5587 (2000). [CrossRef] [PubMed]
  6. H. E. T¨ureci, L. Ge, S. Rotter, and A. D. Stone, "Strong interactions in multimode random lasers," Science 320, 643-646 (2008). [CrossRef] [PubMed]
  7. E. B. Becker, G. F. Carey, and J. T. Oden, Finite Elements (Pentice-Hall, Englewood Cliffs, N.J., 1981).
  8. Q1. J. B. Davies, "Finite element analysis of waveguides and cavities - a review." IEEE T. Magn. 29, 1578 (1993). [CrossRef]
  9. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the Flow of Light (Princeton University Press, Pinceton, 2008).
  10. M. Fujii, C. Koos, C. Poulton, J. Leuthold, and W. Freude, "Nonlinear FDTD analysis and experimental verification of four-wave mixing in InGaAsP-InP racetrack microresonators," IEEE Photon. Technol. Lett. 18, 361-363 (2006). [CrossRef]
  11. J. Wiersig, "Boundary element method for resonances in dielectric microcavities," J. Opt. Soc. Am. A 5, 53-60 (2003). physics/0206018.
  12. 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]
  13. A. B. Movchan, N. V. Movchan, and C. G. Poulton, Asymptotics of dilute and densely packed composites (Imperial College Press, London, 2002). [CrossRef]
  14. H. E. T¨ureci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, "Modes of wave-chaotic dielectric resonators," Prog. Opt. 47, 75-137 (2005). physics/0308016. [CrossRef]
  15. W. T. Perrins, D. R. McKenzie, and R. C. McPhedran, "Transport Properties of Regular Arrays of Cylinders," P. Roy. Soc. Lond. A Mat. 369, 207-225 (1979). URL http://www.jstor.org/stable/2398611. [CrossRef]
  16. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. C. McPhedran, "Multipole method for microstructured optical fibers. II. Implementation and results," J. Opt. Soc. B 19, 2331- 2340 (2002). URL http://josab.osa.org/abstract.cfm?URI=josab-19-10-2331. [CrossRef]
  17. A. Spence and C. Poulton, "Photonic band structure calculations using nonlinear eigenvalue techniques," J. Comput. Phys. 204, 65-81 (2005). [CrossRef]
  18. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide, 3rd ed. (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999).
  19. Q2. H. E. Tureci and H. G. L. Schwefel, "An efficient Fredholm method for the calculation of highly excited states of billiards," J. Phys. A 40, 13,869-13,882 (2007). [CrossRef]

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