Compact FDTD formulation for structures with spherical invariance

IEEE Transactions on Antennas and Propagation

Volumn 59, Issue 3, 2011, Pages 987-993

  Mock, Adam ^a  

^a CENTRAL MICHIGAN UNIVERSITY   (United States)

Author keywords

Electromagnetic analysis; finite difference time domain (FDTD) methods; microresonators; Q factor; spheres

Indexed keywords

ASSOCIATED LEGENDRE FUNCTIONS; COMPUTATIONAL GRIDS; DIELECTRIC MICROSPHERES; DIFFERENT MODES; EFFICIENT ANALYSIS; ELECTRIC AND MAGNETIC FIELDS; ELECTROMAGNETIC ANALYSIS; FINITE-DIFFERENCE TIME-DOMAIN (FDTD) METHODS; FINITE-DIFFERENCE TIME-DOMAIN ALGORITHMS; LONGITUDINAL FIELDS; MATERIAL PROPERTY; MAXWELL'S EQUATIONS; MICRO RESONATORS; Q-FACTORS; QUALITY FACTORS; RESONANCE FREQUENCIES; THREE-DIMENSIONAL VECTORS;

ELECTRIC FIELDS; ELECTROMAGNETISM; FINITE DIFFERENCE TIME DOMAIN METHOD; MAGNETIC FIELDS; MAXWELL EQUATIONS; Q FACTOR MEASUREMENT; RESONANCE; RESONATORS; SPHERES;

MAGNETIC DOMAINS;

EID: 79952156021     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2010.2103040     Document Type: Article

References (30)

1. K. S. Yee, "Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media," IEEE Trans. Antennas Propag., vol. AP-14, pp. 302-307, 1966.
2. A. Taflove and S. C. Hagness, Computational Electrodynamics. MA: Artech House, 2000.
3. R. E. Collin, Field Theory of Guided Waves. New York:Wiley, 1990.
4. S. Xiao, R. Vahldieck, and H. Jin, "Full-wave analysis of guided wave structures using a novel 2-D FDTD," IEEE Microwave Guided Wave Lett., vol. 2, pp. 165-167, May 1992.
5. S. Xiao and R. Vahldieck, "An efficient 2-D FDTD algorithm using real variables [guided wavestructure analysis]," IEEE Microw. Guided Wave Lett., vol. 3, pp. 127-129, 1993. (Pubitemid 23685909)
6. A. Asi and L. Shafai, "Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD," IEEE Electron. Lett., vol. 28, no. 15, pp. 1451-1452, 1992. (Pubitemid 23566806)
7. A. Mock and J. D. O'Brien, "Dependence of silicon-on-insulator waveguide loss on lower oxide cladding thickness," presented at the Integrated Photonics Nanophotonics Res. Applicat. Topical Meeting (IWG4), Boston, MA, Jul. 2008.
8. M. Qiu, "Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method," Microwave Opt Technol Lett, vol. 30, no. 5, pp. 327-330, Sep. 5, 2001. (Pubitemid 32814242)
9. D. B. Davidson and R. W. Ziolkowski, "Body-of-revolution finite-difference time-domain modeling of space-time focusing by a three-dimensional lens," J. Opt. Soc. Am., vol. 11, no. 4, pp. 1471-1490, Apr. 1, 1994.
10. Y. Chen and R. Mittra, "A highly efficient finite-difference time domain algorithm for analyzing axisymmetric waveguides," Microwave Opt. Technol. Lett., vol. 15, no. 4, pp. 201-203, Jul. 1997. (Pubitemid 127640696)
11. J. A. Stratton, Electromagnetic Theory. New York: McGraw Hill, 1941.
12. M. Cai, G. Hunziker, and K. Vahala, "Fiber-optic add-drop device based on a silica microsphere-whispering gallery mode system," IEEE Photon. Technol. Lett., vol. 11, pp. 686-687, 1999.
13. H. C. Tapalian, J.-P. Laine, and P. A. Lane, "Thermooptical switches using coated microsphere resonators," IEEE Photon. Technol. Lett., vol. 14, no. 8, pp. 1118-1120, Aug. 2002.
14. Y. O. Yilmaz, A. Demir, A.Kurt, and A. Serpengüzel, "Optical channel dropping with a silicon microsphere," IEEE Photon. Technol. Lett., vol. 17, no. 8, pp. 1662-1664, Aug. 2005. (Pubitemid 41174995)
15. A. Serpengüzel, K. Adnan, and U. K. Ayaz, "Microsphere photonics," in Proc. SPIE, 2007, vol. 6593.
16. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimonov, S. Stout, and E. Herz, "Demonstration of a spaser-based nanolaser," Nature, vol. 460, pp. 1110-1113, 2009.
17. V. V. Datsyuk, "Gain effects on microsphere resonant emission structures," J. Opt. Soc. Am. B, vol. 19, no. 1, pp. 142-147, 1997.
18. V. Lefèvre-Seguin and S. Haroche, "Towards cavity-QED experiments with silica microspheres," Mater. Sci. Eng., vol. B48, pp. 53-58, 1997.
19. M. Pelton and Y. Yamamoto, "Ultralow threshold laser using a single quantum dot and a microsphere cavity," Phys. Rev., vol. 59, no. 3, pp. 2418-2421, Mar. 1999. (Pubitemid 40648392)
20. A. Soriano, E. A. Navarro, D. L. Pual, J. A. Portí, J. A. Morente, and I. J. Craddock, "Finite difference time domain simulation of the earth-ionosphere resonant cavity: Schumann resonances," IEEE Trans. Antennas Propag., vol. 53, no. 4, pp. 1535-1541, Apr. 2005. (Pubitemid 40679275)
21. J. D. Jackson, Classical Electrodynamics, 3rd ed. Hoboken, NJ: Wiley, 1999.
22. M. Born and E. Wolf, Principles of Optics. New York: Cambridge Univ. Press, 2003.
23. M. Okoniewski, M. Mrozowski, and M. A. Stuchly, "Simple treatment of multi-term dispersion in FDTD," IEEE Microw. Guided Wave Lett., vol. 7, pp. 121-123, 1997. (Pubitemid 127571640)
24. 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. Guided Wave Lett., vol. 8, no. 12, pp. 415-417, Dec. 1998. (Pubitemid 128445531)
25. M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, "Highorder FDTD and auxiliary differential equation formulation of optical pulse propagation in 2D Kerr and Raman nonlinear dispersive media," IEEE J. Quantum Electron., vol. 40, pp. 175-182, 2004.
26. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York: Dover, 1970.
27. J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys., vol. 114, no. 2, pp. 185-200, 1994. (Pubitemid 124012822)
28. F. L. Teixeira and W. C. Chew, "Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates," IEEE Microw. Guided Wave Lett., vol. 7, no. 11, pp. 371-373, Nov. 1997. (Pubitemid 127580623)
29. A. Mock and J. D. O'Brien, "Direct extraction of large quality factors and resonant frequencies from Padé interpolated resonance spectra," Opt. Quant. Elect., vol. 40, no. 14, pp. 1187-1192, 2009.
30. C. C. Lam, P. T. Leung, and K. Young, "Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering," J. Opt. Soc. Am. B, vol. 9, no. 9, pp. 1585-1592, 1992.