How to simulate the whispering-gallery-modes of dielectric microresonators in FEMLAB/COMSOL

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 6452, Issue , 2007, Pages

  Oxborrow, Mark ^a  

^a NATIONAL PHYSICAL LABORATORY   (United Kingdom)

Author keywords

COMSOL; FEMLAB; Finite element; Microcavity; Microresonator; Simulation; WGM; Whispering gallery

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; ELECTROMAGNETIC FIELD EFFECTS; FINITE ELEMENT METHOD; MAXWELL EQUATIONS; QUANTUM OPTICS;

FEMLAB; MICROCAVITY; MICRORESONATOR; WHISPERING GALLERY;

DIELECTRIC RESONATORS;

EID: 34247346918     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.714954     Document Type: Conference Paper

References (37)

1. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, "Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics," Phys. Rev. A. 71, p. 013817, 2005.
2. M. E. Tobar, J. G. Hartnett, E. N. Ivanov, P. Blondy, and D. Cros, "Whispering gallery method of measuring complex permittivity in highly anisotropic materials: discovery of a new type of mode in anisotropic dielectric resonators," IEEE Trans. Instrum. and Meas. 50(2), pp. 522-525, 2001.
3. M. Sumetsky, "Whispering-gallery-bottle microcavities: the three-dimensional etalon," Opt. Lett. 29, pp. 8-10, 2004.
4. O. C. Zienkiewicz and R. L. Taylor, The finite element method, vol. 1: 'The Basis', Butterworth Heinemann, 5th ed., 2000.
5. B. M. A. Rahman, F. A. Fernandez, and J. B. Davies, "Review of finite element methods for microwave and optical waveguides," Proc. IEEE 79, pp. 1442-1448, 1991.
6. K. S. Kunz, The finite difference time domain method for electromagnetics, CRC Press, 1993.
7. 2 composite dielectric resonators with tuneable temperature coefficient for microwave applications," IEE Proc. Science, Measurement and Technology 47, pp. 269-273, 2000.
8. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, "Highly efficient design of specially engineered whispering-gallery-mode laser resonators," Optical and Quantum Electronics 35, pp. 545-559, 2003. see http://www.nottingham.ac.uk/ggiemr/Project/-boriskina2.htm.
9. J. Ctyroky, L. Prkna, and M. Hubalek, "Rigorous vectorial modelling of microresonators," in Proc. 2004 6th Internat. Conf. on Transparent Optical Networks, 4-8 July 2004, 2, pp. 281-286, 2004.
10. J. Krupka, D. Cros, M. Aubourg, and P. Guillon, "Study of whispering gallery modes in anisotropic single-crystal dielectric resonators," IEEE Trans. Microwave Theory Tech. 42(1), pp. 56-61, 1994.
11. J. Krupka, D. Cros, A. Luiten, and M. Tobar, "Design of very high Q sapphire resonators," Electronics Letters 32(7), pp. 670-671, 1996.
12. J. A. Monsoriu, M. V. Andrés, E. Silvestre, A. Ferrando, and B. Gimeno, "Analysis of dielectric-loaded cavities using an orthonormal-basis method," IEEE Trans. Microwave Theory Tech. 50(11), pp. 2545-2552, 2002.
13. "MAFIA." CST GmbH, Bad Nauheimer Str. 19, D-64289 Darmstadt Germany.
14. "COMSOL Multiphysics." COMSOL, Ab., Tegnérgatan 23, SE-111 40 Stockholm, Sweden. [Online]. Available: http://www.comsol.com/; the work described in this paper used version 3.2(.0.224).
15. "ANSYS Multiphysics." ANSYS, Inc., Southpointe, 275 Technology Drive, Canonsburg, PA 15317, USA.
16. D. Schmitt, B. Steffen, and T. Weiland, "2d and 3d computations of lossy eigenvalue problems," IEEE Trans. Magn. 30(5), pp. 3578-3581, 1994.
17. R. Basu, T. Schnipper, and J. Mygind, "10 GHz oscillator with ultra low phase noise," in Proc. The Jubilee 8th International Workshop 'From Andreev Reflection to the International Space Station', (Björkliden, Kiruna, Sweden, March 20-27, 2004), 2004.
18. M. Oxborrow, "Calculating WG modes with MAFIA." unpublished, 2001.
19. T. J. A. Kippenberg, Nonlinear Optics in Ultra-high-Q Whispering-Gallery Optical Microcavities. PhD thesis, Caltech, 2004. particularly Appendix B; http://www.mpq.mpg.de/-~tkippenb/TJKippenbergThesis. pdf.
20. K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, "Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots," Opt. Express 14, pp. 1094-1105, 2006.
21. J.-F. Lee, G. M. Wilkins, and R. Mittra, "Finite-element analysis of axisymmetric cavity resonator using a hybrid edge element technique," IEEE Trans. Microwave Theory Tech. 41(11), pp. 1981-1987, 1993.
22. A. Auborg and P. Guillon, "A mixed finite element formulation for microwave device problems, application to MIS structure," J. Electromagn. Wave Appl. 5, pp. 371-386, 1991.
23. R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villava, G. J. Dick, D. G. Santiago, and R. T. Wang, "Azimuthally-dependent finite element solution to the cylindrical resonator," tech. rep., Univ. Texas, El Paso and JPL, Caltech, 1994. http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/ 32335/1/94-0066.pdf or http://hdl.handle.net/2014/32335.
24. D. G. Santiago, R. T. Wang, G. J. Dick, R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, and G. J. Villalva, "Experimental test and application of a 2-D finite element calculation for whispering gallery sapphire resonators," in IEEE 48th International Frequency Control Symposium, 1994, pp. 482-485, (Boston, MA, USA), 1994. http://trs-new.jpl.nasa.gov/ dspace/bitstream/2014/33066/1/94-1000.pdf or http://hdl.handle.net/2014/33066.
25. M. Oxborrow, "Ex-house 2d finite-element simulation of the whispering-gallery modes of arbitrarily shaped axisymmetric electromagnetic resonators," 2006. preprint arXiv:quant-ph/0607156; contains "Configuration of COMSOL Multiphysics for simulating axisymmetric dielectric resonators: explicit weak-form expressions" as an appendix.
26. M. Oxborrow, "Traceable 2d finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators," 2006. preprint arXiv:quant-ph/0611099; submitted to IEEE Transactions on Microwave Theory and Techniques.
27. U. S. Inan and A. S. Inan, Electromagnetic Waves, Prentice Hall, 2000. particularly subsection 5.3.2 (pp. 391-400).
28. B. I. Bleaney and B. Bleaney, Electricity and magnetism, Oxford University Press, 3rd ed., 1976.
29. P.-Y. Bourgeois, F. Lardet-Vieudrin, Y. Kersale, N. Bazin, M. Chaubet, and V. Giordano, "Ultra-low drift microwave cryogenic oscillator," Electronics letters 40, p. 605, 2004.
30. H. Rokhsari, T. Kippenberg, T. Carmon, and K. J. Vahala, "Radiation-pressure-driven micro-mechanical oscillator," Opt. Express 13, pp. 5293-5301, 2005.
31. S.A. Schelkunoff, "Some equivalence theorems of electromagnetic and their application to radiation problems," Bell Syst. Tech. J. 15, pp. 92+, 1936.
32. C. A. Balanis, Antenna Theory, Wiley, 1997. particularly chapter 12.
33. S. Ramo, J. R. Whinnery, and T. van Duzer, Fields and Waves in Communications Electronics, John Wiley & Sons, 2nd ed., 1984.
34. S. A. Schelkunoff, "On diffraction and radiation of electromagnetic waves," Physical Review 56(4), pp. 308 LP - 316, 1939.
35. C. A. Flory and R. C. Taber, "High performance distributed bragg reflector microwave resonator," IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 44(2), pp. 486-495, 1997. specifically, the mode corresponding to figures 1, 2 and 7, and the last three paragraphs of section IV, therein.
36. C. A. Flory and R. C. Taber, "Microwave oscillators incorporating cryogenic sapphire dielectric resonators," in IEEE International Frequency Control Symposium 1993, pp. 763-773, 1993.
37. P. Wolf, M. E. Tobar, S. Bize, A. Clairon, A. Luiten, and G. Santarelli, "Whispering gallery resonators and tests of Lorentz invariance," General Relativity and Gravitation 36(10), pp. 2351-2372, 2004. preprint version: arXiv:gr-qc/0401017 v1.