Eigenmodes of optical resonators with mirrors having Gaussian reflectivity profiles

Area of Science:

• Optics and Photonics
• Laser Physics
• Resonator Design

Background:

• Optical resonators are fundamental components in lasers and optical systems.
• Characterizing resonator eigenmodes is crucial for understanding their performance.
• Mirrors with Gaussian reflectivity profiles are common in advanced optical designs.

Purpose of the Study:

• To develop a general procedure for calculating eigenmodes in optical resonators with Gaussian reflectivity mirrors.
• To provide a framework for analyzing the eigenfrequencies and mode discrimination of such resonators.

Main Methods:

• Expanding resonator eigenmodes in terms of freely propagating Hermite-Gaussian beams.
• Applying matrix techniques to the expanded eigenmode representation.
• Calculating eigenvalues to determine resonator characteristics.

Main Results:

• A general procedure for calculating all eigenmodes of optical resonators with Gaussian reflectivity mirrors.
• The eigenvalues directly yield the eigenfrequencies of the resonator.
• The method allows for the determination of mode discrimination properties.

Conclusions:

• The presented expansion method simplifies the analysis of optical resonators with Gaussian reflectivity profiles.
• This approach facilitates the design and optimization of optical resonators for specific applications.
• The eigenvalues provide critical information for predicting resonator behavior and performance.