Rays and ray envelopes within stable optical resonators containing focusing media

Area of Science:

• Geometric Optics
• Resonator Analysis
• Wave Propagation

Background:

• Previously, ray envelopes in empty resonators were identified with spot size variations.
• Existing geometric optical approaches were limited to simpler resonator configurations.

Purpose of the Study:

• To extend geometric optical methods to analyze ray envelopes in general resonators.
• To investigate the behavior of ray envelopes in resonators with arbitrary lenses and inhomogeneous focusing media.
• To correlate envelope characteristics with resonator stability limits.

Main Methods:

• Development of an invariant quadratic form for ray segments.
• Derivation of a differential equation for ray segments and their envelopes.
• Formulation and solution of a maximum-minimum problem for the envelope function.

Main Results:

• The envelope function in convergent media exhibits periodic modulation.
• The modulation period is solely dependent on the convergent medium's properties.
• The location and ratio of envelope maxima/minima depend on both the medium and associated optics.

Conclusions:

• The study provides a generalized geometric optical framework for analyzing ray envelopes in complex resonators.
• Periodic modulation of the envelope in convergent media is a key finding.
• Envelope characteristics are directly correlated with resonator stability limits, offering predictive capabilities.