Optical resonators in the unstable region.

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.
• 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.