Diffraction of apertured Gaussian beams: solution by expansion in Chebyshev polynomials

Area of Science:

• Optics and Photonics
• Computational Physics
• Mathematical Physics

Background:

• Diffraction integrals are crucial for understanding light propagation.
• Accurate and efficient computation of diffraction is essential for optical system design.
• Existing methods may lack efficiency for complex optical system optimization.

Purpose of the Study:

• To derive a differential equation for the diffraction integral.
• To obtain an analytic solution using Chebyshev polynomial expansion.
• To enable efficient numerical computation for optical system optimization.

Main Methods:

• Derivation of a differential equation governing the diffraction integral.
• Solution of the differential equation via Chebyshev polynomial series expansion.
• Numerical implementation for computational efficiency.

Main Results:

• An analytic expression for the diffraction integral is obtained.
• The series solution allows for fast numerical computation.
• The method is validated for its efficiency in diffraction analysis.

Conclusions:

• The Chebyshev polynomial expansion provides an efficient analytic solution for the diffraction integral.
• This approach is suitable for optimizing optical systems where diffraction is significant.
• The derived method enhances computational speed for diffraction-related optical design.