Compact formulation of the beam shape coefficients for elliptical Gaussian beam based on localized approximation

Area of Science:

• Optics and Photonics
• Electromagnetics
• Computational Physics

Background:

• Generalized Lorenz-Mie theory (GLMT) is crucial for light scattering analysis.
• Evaluating beam shape coefficients (BSCs) in GLMT typically involves complex infinite series summations.
• Existing methods for BSC calculation can be computationally intensive and suffer from slow convergence.

Purpose of the Study:

• To develop a more efficient and convenient method for calculating BSCs in GLMT.
• To present a compact expression for BSCs of an elliptical Gaussian beam using localized approximation (LA).
• To validate the proposed formulation against existing methods.

Main Methods:

• Application of localized approximation (LA) to derive BSCs for an elliptical Gaussian beam.
• Development of a compact mathematical expression for the BSCs.
• Comparative analysis of the new formulation with integral LA methods.

Main Results:

• A compact and efficient expression for BSCs of an elliptical Gaussian beam based on LA was derived.
• The presented formulation simplifies numerical computations compared to traditional infinite series methods.
• The new method demonstrates reliability, stability, and superior efficiency.

Conclusions:

• The compact expression for BSCs using LA provides a significant advancement for numerical calculations in GLMT.
• This formulation offers a more practical and efficient approach for analyzing elliptical Gaussian beams.
• The validated method enhances the applicability and computational feasibility of GLMT.