Abstract

By taking advantage of axial symmetry of the planar whispering gallery microresonators, the three-dimensional (3D) problem of the resonator is reduced to a two-dimensional (2D) one; thus, only the cross section of the resonator needs to be analyzed. Then, the proposed formulation, which works based on a combination of the finite-elements method (FEM) and Fourier expansion of the fields, can be applied to the 2D problem. First, the axial field variation is expressed in terms of a Fourier series. Then, a FEM method is applied to the radial field variation. This formulation yields an eigenvalue problem with sparse matrices and can be solved using a well-known numerical technique. This method takes into account both the radiation loss and the dielectric loss; hence, it works efficiently either for high number or low number modes. Efficiency of the method was investigated by comparison of the results with those of commercial software.

© 2014 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Fully vectorial modeling of cylindrical microresonators with aperiodic Fourier modal method

Ying Li, Haitao Liu, Hongwei Jia, Fang Bo, Guoquan Zhang, and Jingjun Xu
J. Opt. Soc. Am. A 31(11) 2459-2466 (2014)

Three-dimensional analysis of cylindrical microresonators based on the aperiodic Fourier modal method

Andrea Armaroli, Alain Morand, Pierre Benech, Gaetano Bellanca, and Stefano Trillo
J. Opt. Soc. Am. A 25(3) 667-675 (2008)

Method for predicting whispering gallery mode spectra of spherical microresonators

Jonathan M. M. Hall, V. Shahraam Afshar, Matthew R. Henderson, Alexandre François, Tess Reynolds, Nicolas Riesen, and Tanya M. Monro
Opt. Express 23(8) 9924-9937 (2015)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (11)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (5)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (17)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription