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Unstable open resonators: two-dimensional and three-dimensional losses by a waveguide analysis.
Applied Optics
|February 19, 2010
Summary
This study refines the waveguide approach for unstable resonators with hyperbolic mirrors, improving modal reflection coefficients and accurately predicting eigenmode loss for large Fresnel numbers. The validated model extends to circular mirrors and derives known equivalence relations.
Area of Science:
- Optics and Photonics
- Electromagnetism
- Resonator Physics
Background:
- Unstable open resonators with hyperbolic mirrors are crucial optical components.
- Previous waveguide approaches required refinement for accurate eigenmode loss prediction, especially at large Fresnel numbers.
Purpose of the Study:
- To refine the waveguide approach for unstable resonators with cylindrical hyperbolic mirrors.
- To improve the prediction of eigenmode loss behavior in resonators with large Fresnel numbers.
- To extend the waveguide model to circular hyperbolic mirrors and derive equivalence relations.
Main Methods:
- Refinement of modal reflection coefficients within the waveguide model.
- Self-consistent reflection of single or coupled waveguide modes from mirror edges and axial regions.
- Comparison of theoretical predictions with numerical solutions of the resonator integral equation.
Main Results:
- Improved accuracy in predicting eigenmode loss for resonators with large Fresnel numbers.
- Successful extension of the waveguide model to circular hyperbolic mirrors.
- Derivation of known equivalence relations between different resonator configurations.
Conclusions:
- The refined coupled-mode waveguide model provides a valid and accurate method for analyzing unstable resonators.
- The model's ability to predict eigenmode loss and derive equivalence relations is confirmed.
- This work enhances the understanding and design of unstable optical resonators.
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