Mode calculations in asymmetrically aberrated laser resonators using the Huygens-Fresnel kernel formulation

Area of Science:

• Optics and Photonics
• Laser Physics
• Computational Electromagnetics

Background:

• Calculating laser resonator modes is crucial for laser design.
• Existing methods struggle with complex, three-dimensional (3D) resonator geometries and aberrations.
• Accurate mode analysis is essential for optimizing laser performance and stability.

Purpose of the Study:

• To present a novel theoretical framework for calculating 3D resonator modes.
• To validate the framework using both stable and unstable laser resonator configurations.
• To demonstrate the method's capability in handling complex aberrations.

Main Methods:

• Utilized a kernel formulation of the Huygens-Fresnel diffraction integral for resonator round-trip analysis.
• Computed resonant modes for both stable (semi-confocal) and unstable (confocal) resonators.
• Applied the method to an asymmetrically aberrated unstable resonator.

Main Results:

• The framework accurately predicts lowest loss and higher-order modes for a stable resonator, matching analytic solutions.
• Calculated higher-order modes for an aberrated unstable resonator, with the unaberrated mode aligning with published data.
• Demonstrated the method's effectiveness for multi-mode analysis with 2D aberrations.

Conclusions:

• The 3D kernel method offers a robust approach for laser resonator mode calculation.
• This framework extends beyond previous limitations, handling complex geometries and aberrations.
• The validated method can be used for advanced laser design and analysis.