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Unstable optical resonators.

¹Polytechnic Institute of Brooklyn, Brooklyn, New York, USA.

|January 6, 2010

Summary

A new ray optics technique calculates losses in unstable optical resonators caused by finite mirror sizes. This method, based on ray modes, offers results equivalent to existing geometrical approaches and expands applicability to complex resonator designs.

Area of Science:

Optics and Photonics
Laser Physics

Background:

Unstable optical resonators are known for high losses due to finite mirror sizes.
Existing geometrical methods for loss calculation in unstable resonators are effective but ad hoc.
Siegman's geometrical method provides a way to calculate these losses for laser applications.

Purpose of the Study:

To present a novel technique for calculating optical resonator losses based on ray optics.
To demonstrate the equivalence of this new method to existing geometrical approaches.
To extend the applicability of loss calculation to re-entrant and inhomogeneous resonators.

Main Methods:

Development of a ray optics technique using ray modes in an equivalent beam waveguide.
Calculation of fractional loss per resonator pass using eigenvalues of the transfer matrix.

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Comparison of results with Siegman's geometrical method for unstable resonators.

Main Results:

The presented ray optics technique yields results equivalent to Siegman's geometrical method.
The fractional loss per resonator pass is determined by 1-|lambda(2)|, where lambda(2) is an eigenvalue of the transfer matrix.
The derived formulas are applicable to re-entrant resonators and those with inhomogeneous media.

Conclusions:

The ray optics approach provides a valid and independently established method for calculating losses in unstable optical resonators.
This technique offers broader applicability than existing methods, including for complex resonator configurations.
The eigenvalue of the transfer matrix directly relates to the resonator's fractional loss per pass.