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Spherical angular spectrum and the fractional order Fourier transform.

Pierre Pellat-Finet¹, Pierre-Emmanuel Durand, Eric Fogret

¹Groupe d'Optique Théorique et Appliquée, Université de Bretagne Sud, Lorient, France. pierre-pellat-finet@univ-ubs.fr

|November 14, 2006

Summary

This study introduces a spherical angular spectrum for analyzing fields from spherical emitters. This new method decomposes fields into spherical waves and propagates them using a fractional Fourier transform.

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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.