Three-dimensional finite element computation of laser cavity eigenmodes [corrected]

Area of Science:

• Optics and Photonics
• Computational Physics
• Laser Engineering

Background:

• Accurate computation of laser resonator eigenmodes is crucial for laser design and performance optimization.
• Traditional methods like the Gaussian mode approximation have limitations, particularly in complex optical systems.
• Finite element analysis (FEA) offers a powerful numerical tool for solving complex wave equations.

Purpose of the Study:

• To present a new finite element analysis (FEA) method for calculating laser resonator eigenmodes.
• To transform the scalar wave equation into a solvable three-dimensional eigenvalue problem.
• To verify the accuracy of the FEA method against established algorithms and demonstrate its utility in realistic laser scenarios.

Main Methods:

• The scalar wave equation (∇² + k²)E(x, y, z) = 0 is utilized.
• Separation of the propagation factor exp(-ikz) from the phasor amplitude E(x, y, z) is performed.
• A two-wave ansatz represents the beam within standing wave resonators.
• The method is validated using the Gaussian mode algorithm for cavities with parabolic optical elements.

Main Results:

• The FEA method was successfully verified against the Gaussian mode algorithm for parabolic optical elements.
• The method accurately models the beam within standing wave resonators using a two-wave ansatz.
• Significant deviations between Gaussian approximation and numerical solutions were observed for a diode-pumped solid-state laser with thermal lensing.

Conclusions:

• The presented FEA method provides a robust and accurate approach for computing laser resonator eigenmodes.
• This technique overcomes limitations of the Gaussian approximation, especially in lasers with intracavity thermal lensing.
• The FEA method offers a valuable tool for the precise design and analysis of advanced laser systems.