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Stability of planar ring lasers with mirror misalignment.

H R Bilger, G E Stedman

|May 22, 2010

Summary

Beam steering in symmetric ring resonators diverges when mirror curvature constraints are met. This research identifies critical mirror misalignments and conditions where beam steering effects vanish, offering practical insights for optical resonator design.

Area of Science:

Optics and Photonics
Laser Physics
Optical Engineering

Background:

Active optical cavities with symmetric mirror arrangements are crucial in various laser systems.
Understanding beam steering dynamics under mirror misalignment is essential for resonator stability and performance.
Previous studies focused on stability criteria, but critical divergence conditions and vanishing steering effects require further investigation.

Purpose of the Study:

To analyze the conditions under which beam steering in a symmetric ring resonator diverges.
To identify specific mirror misalignment parameters that are most sensitive.
To explore resonator configurations where beam steering effects can be eliminated.

Main Methods:

Mathematical analysis of beam propagation in a symmetric ring resonator with N mirrors.

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Derivation of constraints on mirror radii of curvature (R(i)) leading to divergence.

Comparison of divergence conditions with standard ray stability criteria (|K(N)({R(i)})| <= 2).

Identification of critical radii and sensitive misalignment parameters.

Main Results:

Beam steering diverges when mirror radii satisfy K(N)({R(i)}) = 2.
Approximately half of the critical radii for stability also lead to divergence.
Specific misalignment parameters are identified as most sensitive to beam steering.
For resonators with K(N) = -2, certain beam steering effects vanish, notably in the N=2 confocal resonator.

Conclusions:

The study provides precise conditions for beam steering divergence in symmetric ring resonators.
The findings highlight the importance of specific mirror curvature constraints and misalignment parameters.
The identification of configurations with vanishing beam steering effects, such as the N=2 confocal resonator, has practical implications for optical system design and stability.