Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition.

Area of Science:

• Optics and Photonics
• Computational Electromagnetics
• Wave Propagation

Background:

• Analyzing three-dimensional (3D) diffraction fields on curved surfaces is computationally challenging.
• Existing methods may struggle with the complexities of non-planar geometries.

Purpose of the Study:

• To introduce a novel local signal decomposition method for analyzing 3D diffraction fields on curved surfaces.
• To represent the 3D field as a sum of Gaussian beams for simplified propagation analysis.

Main Methods:

• Decomposition of the field on a 2D curved surface into shifted and modulated Gaussian elementary signals.
• Representation of the 3D diffraction field as a sum of Gaussian beams.
• Propagation of Gaussian beams using an approximate expression derived from the Rayleigh-Sommerfeld diffraction model.
• Treating Gaussian window functions on smooth curved surfaces as if on planar patches.

Main Results:

• The proposed method decomposes the field into a sum of Gaussian beams.
• Gaussian beams are propagated using an approximate Rayleigh-Sommerfeld model.
• Simulation results demonstrate accurate 3D field solutions for surfaces meeting the smoothness assumption.

Conclusions:

• The local signal decomposition method provides an accurate approach for analyzing 3D diffraction fields on curved surfaces.
• The Gaussian beam representation simplifies the modeling of wave propagation in complex geometries.