## Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions

JOSA A, Vol. 28, Issue 6, pp. 1003-1006 (2011)

http://dx.doi.org/10.1364/JOSAA.28.001003

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### Abstract

The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.

© 2011 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(260.2110) Physical optics : Electromagnetic optics

(350.5500) Other areas of optics : Propagation

(350.7420) Other areas of optics : Waves

(070.7345) Fourier optics and signal processing : Wave propagation

**ToC Category:**

Fourier Optics and Signal Processing

**History**

Original Manuscript: February 7, 2011

Revised Manuscript: March 28, 2011

Manuscript Accepted: March 28, 2011

Published: May 9, 2011

**Citation**

R. Mahillo-Isla, M. J. Gonźalez-Morales, and C. Dehesa-Martínez, "Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions," J. Opt. Soc. Am. A **28**, 1003-1006 (2011)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-6-1003

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