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Paraxial waves in the far-field region

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By investigating the changes suffered by a paraxial beam propagating in the near-field and in the far-field regions, it has been found a set of wave equations valid for points gradually closer to the near field. A relevant expression for the validity of the far-field approximation is given from the paraxial Helmholtz equation. It is pointed out that the well-known Fresnel number associated with every transverse diffraction pattern can be interpreted as a magnitude that measures the relative standard deviation of the Fraunhofer pattern and a first-order field, thus reporting on an integral expression suitable for a general case. Finally, the Rayleigh range of the optical beam is deduced from the previously inferred Fresnel number, what has been applied for the cases of a spherical Gaussian beam and a uniform-illuminated circular aperture.

Keywords: Diffraction; wave propagation

Document Type: Original Article


Affiliations: Department of Optics, University of Valencia, E-46100 Burjassot, Spain

Publication date: October 1, 2002

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