Comparison of laser mode calculations.

Area of Science:

• Optics and Photonics
• Computational Physics

Background:

• Solving the laser mode problem is crucial for understanding laser behavior.
• Existing methods include numerical and kernel expansion procedures.

Purpose of the Study:

• To demonstrate the essential equivalence of numerical and kernel expansion methods for solving the laser mode problem.
• To identify the most efficient and versatile computational procedure for laser resonator analysis.

Main Methods:

• Equating integral equations to matrix equations.
• Analyzing the Fox and Li iterative method as a matrix diagonalization technique.
• Employing Gaussian-Hermite function kernel expansion.
• Utilizing Gaussian quadrature for numerical integration.
• Applying the ALLMAT computer program for matrix diagonalization.

Main Results:

• Numerical and kernel expansion methods are fundamentally the same, converting integral equations to matrix equations.
• The Fox and Li method is a matrix diagonalization technique.
• The optimal procedure involves Gaussian quadrature integration and ALLMAT for matrix diagonalization.

Conclusions:

• The combined Gaussian quadrature and ALLMAT diagonalization method is computationally simple and efficient.
• This optimal procedure can determine multiple laser modes simultaneously.
• The method is applicable to various resonator configurations, including unstable, tilted, and selectively coated reflectors.