# Coupling coefficients of the Spherical dielectric microresonators with whispering gallery modes

## DOI:

https://doi.org/10.20535/RADAP.2015.62.49-61## Keywords:

microresonator, coupling coefficient, whispering gallery mode, S-matrix, filter## Abstract

**The calculation results of the Spherical dielectric microresonators coupling coefficients with whispering gallery modes are presented. Microresonator coupling coefficients as a functions of main parameters is considered. S-matrix frequency dependences of both bandstop and bandpass filters on the Spherical microresonators of infrared wavelength range are calculated.**

## References

Braginskiy V.B. and Ilchenko V.S. (1987) Properties of Optical Dielectric Microresonators, Doklady AS USSR, Vol. 293, No 6, pp.1358-1361.

Mackowsky D. W. and Mishenko M. I. (1996) Calculation of the T matrix and the scattering matrix for ensembles of spheres. *J. Opt. Soc. Am.*, Vol. 13, No. 11, pp. 2266 - 2278.

Gorodetsky M. L. and Ilchenko V. S. (1999) Optical microsphere resonators: Optimal coupling to high-Q whispering-gallery modes. *J. Opt. Soc. Amer. B*, Vol. 16, pp. 147–154.

Kippenberg T. J., Spillane S. M. and Vahala K. J. (2002) Modal coupling in traveling-wave resonators. *Optics Letters*, Vol. 27, No. 19, pp. 1669 - 1671.

Astratov V. N. (2010) Fundamentals and Applications of Microsphere Resonator Circuits. *Photonic Microresonator Research and Applications*. Springer, pp. 423-457.

Chen Z., Taflove A. and Backman V. (2006) Highly efficient optical coupling and transport phenomena in chains of dielectric microspheres. *Optics Letters*, Vol. 31, No. 3. pp. 389-391.

Kieu K. and Mansuripur M. (2007) Fiber laser using a microsphere resonator as a feedback element. *Optics Letters*, Vol. 32, No 3, pp. 244 - 246.

Thompson D.B., Keating D.A., Guler E., Ichimura K., Williams M.E. and Fuller K.A. (2010) Separation-sensitive measurements of morphology dependent resonances in coupled fluorescent microspheres. *Optics Express*, Vol. 18, No. 18, pp. 19209 -19218.

Mitsui T., Onodera T., Wakayama Y., Hayashi T., Ikeda N., Sugimoto Y., Takamasu T. and Oikawa H. (2011) Influence of micro-joints formed between spheres in coupled-resonator optical waveguide. *Optics Express*, Vol. 19, No. 22, pp. 22258-22267.

Xifre-Perez E., Domenech J.D., Fenollosa R., Munoz P., Capmany J. and Mesenguer F. (2011) All silicon waveguide spherical microcavity coupler device. *Optics Express*, Vol. 19, No. 4. pp. 3185-3192.

Ilchenko M.E. and Trubin A.A. (2004) Electrodynamics' of Dielectric Resonators, Kiev, Naukova Dumka, 265 p.

Abramowitz M. eds. and Stegun I. eds. (1964) *Handbook of mathematical functions*. National bureau of standards., 830 p.

Trubin A. A. (1991) Mutual coupling coefficients of the Spherical Dielectric Resonators in Rectangular Waveguide, Vestnik kievskogo politekhnicheskogo instituta. Radiotekhnika, No. 28, pp. 27-32.

Trubin A.A. (2007) Natural oscillations of High-Q Resonance Macrostructures in Infrared and Optical ranges on the Systems with Coupled Dielectric Resonators. *Microwave & Telecommunication Technology, CriMiCo*, pp. 473-476.

Trubin A. A. Several specified integrals of special functions, Available at:

">http://eqworld.ipmnet.ru/ru/auxiliary/aux-specfunc.htm

Trubin A. A. (1997) Scattering of electromagnetic waves on the Systems of Coupling Dielectric Resonators. Radio electronics, No 2, pp. 35-42.

## Downloads

## Published

## How to Cite

*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, 0(62), pp. 49-61. doi: 10.20535/RADAP.2015.62.49-61.

## Issue

## Section

## License

Authors who publish with this journal agree to the following terms:

- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).