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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 7 — Jul. 1, 2013
  • pp: 1381–1386

Propagation equation of Hermite–Gauss beams through a complex optical system with apertures and its application to focal shift

Sun Peng, Guo Jin, and Wang Tingfeng  »View Author Affiliations


JOSA A, Vol. 30, Issue 7, pp. 1381-1386 (2013)
http://dx.doi.org/10.1364/JOSAA.30.001381


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Abstract

Based on the generalized Huygens–Fresnel diffraction integral (Collins’ formula), the propagation equation of Hermite–Gauss beams through a complex optical system with a limiting aperture is derived. The elements of the optical system may be all those characterized by an ABCD ray-transfer matrix, as well as any kind of apertures represented by complex transmittance functions. To obtain the analytical expression, we expand the aperture transmittance function into a finite sum of complex Gaussian functions. Thus the limiting aperture is expressed as a superposition of a series of Gaussian-shaped limiting apertures. The advantage of this treatment is that we can treat almost all kinds of apertures in theory. As application, we define the width of the beam and the focal plane using an encircled-energy criterion and calculate the intensity distribution of Hermite–Gauss beams at the actual focus of an aperture lens.

© 2013 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: May 2, 2013
Revised Manuscript: May 29, 2013
Manuscript Accepted: May 31, 2013
Published: June 20, 2013

Citation
Sun Peng, Guo Jin, and Wang Tingfeng, "Propagation equation of Hermite–Gauss beams through a complex optical system with apertures and its application to focal shift," J. Opt. Soc. Am. A 30, 1381-1386 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-7-1381

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