Spherical angular spectrum and the fractional order Fourier transform

Area of Science:

• Electromagnetism
• Wave propagation
• Fourier optics

Background:

• Traditional angular spectrum methods are limited for spherical sources.
• Spherical wave decomposition is crucial for understanding fields from spherical emitters.

Purpose of the Study:

• To introduce and define the spherical angular spectrum concept.
• To demonstrate its application in decomposing and propagating fields from spherical emitters.

Main Methods:

• Decomposition of field amplitude into spherical waves.
• Propagation using a spherical angular spectrum approach.
• Mathematical formulation via fractional order Fourier transform.

Main Results:

• The spherical angular spectrum allows field decomposition into converging spherical waves.
• Field propagation is achieved by directly manipulating the spherical angular spectrum.
• This propagation can be represented by a fractional order Fourier transform.

Conclusions:

• The spherical angular spectrum offers a novel perspective for analyzing fields from spherical emitters.
• It provides an alternative propagation method distinct from conventional angular spectrum techniques.
• The connection to fractional Fourier transforms opens new avenues for wave propagation analysis.