Calculation of the Resonant Frequencies for a Whispering Gallery Mode Optical Resonator
Abstract
A method of calculation of resonant frequencies and thus free spectral range of high-Q dielectric disk resonators with whispering gallery modes is proposed. The method is based on application to the dispersion equation derived for a dielectric cylinder with unlimited length, dimensional quantization, due to the requirement of phase balance for the standing waves in the resonator. The simplified expressions suitable for calculation of optical microcavities used in the devices of radio photons are obtained.
About the Authors
G. A. Zaretskaya
Saint Petersburg Electrotechnical University "LETI"
Russian Federation
Master’s Degree of techniques and technology in electronics and micro electronics, post-graduate student of the department of Physical Electronics and Technology
Russian Federation
Master’s Degree of techniques and technology in electronics and micro electronics, post-graduate student of the department of Physical Electronics and Technology
A. V. Drozdovskii
Saint Petersburg Electrotechnical University "LETI"
Russian Federation
Ph. D. in physics and mathematics, assistant of the department of Physical Electronics and Technology
Russian Federation
Ph. D. in physics and mathematics, assistant of the department of Physical Electronics and Technology
B. A. Kalinikos
Saint Petersburg Electrotechnical University "LETI"
Russian Federation
D. Sc. in physics and mathematics, Professor, the Chief of the Department of Physical Electronics and Technology
Russian Federation
D. Sc. in physics and mathematics, Professor, the Chief of the Department of Physical Electronics and Technology
References
1. Capmany J., Novak D. Microwave Photonics Combines Two Worlds. Nature Photon. 2007, vol. 1, no. 1, pp. 319-330.
2. Yao J. Microwave Photonics. J. Lightwave Technol. 2009, vol. 27, no. 3, pp. 314-335.
3. Marpaung D., Roeloffzen Ch., Heideman R., Leinse A., Sales S., Capmany J. Integrated Microwave Photonics. Lasers & Photon. Rev. 2013, vol. 7, no. 4, pp. 506-538.
4. Ilchenko M. E. Dielektricheskie rezonatory [The dielectric resonators]. Radio i svyaz', 1989, 328 p. (In Russian)
5. Gorodetsky M. L. Opticheskie mikrorezonatory s gigantskoi dobrotnost'yu [Optical microcavities with a giant Q]. Moskow, Fizmatlit, 2011, 416 p. (In Russian)
6. Savchenkov A. A., Matsko A. B., Ilchenko V. S., Maleki L. Optical Resonators with Ten Million Finesse. Optics Express. 2007, vol. 15, no. 11, pp. 6768-6773.
7. Ayazi A., Hsu R. C. J., Houshmand B., Steier W. H., Jalali B. All-Dielectric Photonic-Assisted Wireless Receiver Optics express. 2008, vol. 16, no. 3, pp. 1742-1747.
8. Matsko A. B., Maleki L., Savchenkov A. A., Ilchenko V. S. Whispering Gallery Mode based Optoelectronic Microwave Oscillator. Journal of Modern Optics. 2003, vol. 50, no. 15-17, pp. 2523-2542.
9. Merrer P. H., Saleh K., Llopis O., Berneschi S., Cosi F., Conti G. N. Characterization Technique of Optical Whispering Gallery Mode Resonators in the Microwave Frequency Domain for Optoelectronic Oscillators. Appl. Opt. 2012, vol. 51, no. 20, pp. 4742-4748.
10. Ilchenko V. S., Volikov P. S., Velichansky V. L., Treussart F., Lefevre-Seguin V., Raimond J. M., Haroche S. Strain-tunable High-Q Optical Microsphere Resonator. Optics communications. 1998, vol. 145, no. 1, pp. 86-90.
11. Vernooy D. W., Ilchenko V. S., Mabuchi H., Streed E. W., Kimble H. J. High-Q Measurements of Fused-Silica Microspheres in the Near Infrared. Optics Letters. 1998, vol. 23, no. 4, pp. 247-249.
12. Vassiliev V. V., Velichansky V. L., Ilchenko V. S., Gorodetsky M. L., Hollberg L., Yarovitsky A. V. NarrowLine-Width Diode Laser with a High-Q Microsphere Resonator. Optics Communications. 1998, vol, 158, no. 1, pp. 305-312.
13. Armani D. K., Kippenberg T. J., Spillane S. M. Vahala K. J. Ultra-high-Q Toroid Microcavity on a Chip. Nature. 2003, vol. 421, no. 6926, pp. 925-928.
14. Lee H., Tong Chen, Jiang L., Ki Youl Yang, Seokmin J., Painter O., Vahala K. J. Chemically Etched Ultrahigh-Q Wedge-Resonator on a Silicon Chip. Nature Photonics. 2012, vol. 6, no. 6, pp. 369-373.
15. Pollinger M., O'Shea D., Warken F., Rauschenbeutel A. Ultrahigh-Q Tunable Whispering-Gallery-Mode Microresonator. Physical Review Letters. 2009, vol. 103, no. 5, pp. 053901.
16. Kippenberg T. J., Spillane S. M., Armani D. K., Vahala K. J. Fabrication and Coupling to Planar High-Q Silica Disk Microcavities. Applied Physics Letters. 2003, vol. 83, no. 4, pp. 797-799.
17. Knox R. M. Dielectric Waveguide Microwave Integrated Circuits - an Overview. IEEE Trans. on Microwave Theory Techniques. 1976, vol. MTT-24, no. 11, pp. 806-814. (In Russian)
18. Tsibizov K. N., Borisov S. A., Bezborodov Yu. M. Metody rascheta rezonansnykh chastot dielektricheskikh rezonatorov. Zarubezh. Radioelektron. 1981, no.11, pp. 21-34. (In Russian)
19. Braginsky V. B., Gorodetsky M. L., Ilchenko V. S. Quality-Factor and Nonlinear Properties of Optical Whispering-Gallery Modes. Physics Letters A. 1989, vol. 137, no. 7-8, pp. 393-397.
Review
For citations:
Zaretskaya G.A., Drozdovskii A.V., Kalinikos B.A. Calculation of the Resonant Frequencies for a Whispering Gallery Mode Optical Resonator. Journal of the Russian Universities. Radioelectronics. 2017;(1):56-62. (In Russ.)
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