### Abstract

In this paper, airy functions to represent Bessel functions of large index order are applied. The eigenvalue wave equation is then reduced to a polynomial equation. The complex roots of such a polynomial are the sought whispering gallery modes (WGM) resonant frequencies which in effect, provide the Q-factors and determine the WGM field profiles. Particular emphasis has been given to deriving the spectral and spatial distribution of WGMs, along the Q-factors of the resonators. These properties are essential to characterise circular semiconductor lasers, which use WGMs as modal emission.

Original language | English |
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Publication status | Published - 2003 |

Event | Numerical Simulation of Semiconductor Optoelectronic Devices, 2003. NUSOD 2003. Proceedings of the IEEE/LEOS 3rd International Conference on - Duration: 1 Jan 2003 → … |

### Conference

Conference | Numerical Simulation of Semiconductor Optoelectronic Devices, 2003. NUSOD 2003. Proceedings of the IEEE/LEOS 3rd International Conference on |
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Period | 1/01/03 → … |

### Keywords

- Q-factors
- whispering gallery mode resonators
- laser cavity resonators
- ring lasers
- resonant frequencies
- wave equations
- circular semiconductor lasers
- Bessel functions
- Q-factor
- airy functions
- polynomial equation
- eigenvalues and eigenfunctions
- polynomials
- eigenvalue wave equation

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## Cite this

Cinosi, N., Sarma, J., Mencarelli, D., & Causa, F. (2003).

*Analysis of whispering gallery mode resonators by using airy functions*. Paper presented at Numerical Simulation of Semiconductor Optoelectronic Devices, 2003. NUSOD 2003. Proceedings of the IEEE/LEOS 3rd International Conference on, .