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Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

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Optical resonators in the unstable region.

¹TRG Inc., Route 110, Melville, New York 11746, USA.

|January 9, 2010

Summary

This study derives oscillation frequencies and modal losses for spherical mirror resonators using geometrical optics. This approximation is valuable for unstable, high-loss configurations with large Fresnel numbers.

Area of Science:

Optics and Photonics
Resonator Physics

Background:

Spherical mirror resonators are fundamental optical components.
Understanding their oscillation frequencies and modal losses is crucial for designing stable and efficient laser systems.
High-loss and unstable configurations present unique analytical challenges.

Purpose of the Study:

To derive the spectrum of characteristic oscillation frequencies and modal losses for spherical mirror optical resonators.
To validate the applicability of a geometrical optics approximation for these resonators.
To provide a method for analyzing unstable or high-loss resonator configurations.

Main Methods:

The analysis employs an approximation equivalent to geometrical optics.
Scalar integral equations, specifically those developed by Fox and Li, form the basis of the derivation.

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The method is applied to spherical mirror optical resonators.

Main Results:

A spectrum of characteristic oscillation frequencies and modal losses was successfully derived.
The geometrical optics approximation was shown to be significant for unstable or high-loss configurations with large Fresnel numbers.
The derived results align with established findings for dominant mode losses in the geometrical optics limit.

Conclusions:

The geometrical optics approximation provides a valid and useful framework for analyzing spherical mirror optical resonators, particularly in complex configurations.
This approach offers insights into the behavior of unstable and high-loss resonators.
The derived spectrum of frequencies and losses can inform the design and optimization of optical systems.