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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 4 — Feb. 21, 2005
  • pp: 1107–1112

Propagation law for the generating function of Hermite-Gaussian-type modes in first-order optical systems

Martin J. Bastiaans and Tatiana Alieva  »View Author Affiliations


Optics Express, Vol. 13, Issue 4, pp. 1107-1112 (2005)
http://dx.doi.org/10.1364/OPEX.13.001107


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Abstract

Based on the common Hermite-Gaussian modes, a general class of orthonormal sets of Hermite-Gaussian-type modes is introduced. Such modes can most easily be defined by means of their generating function. It is shown that these modes remain in their class of orthonormal Hermite-Gaussian-type modes, when they propagate through first-order optical systems. A propagation law for the generating function is formulated.

© 2005 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.4690) Fourier optics and signal processing : Morphological transformations
(080.2730) Geometric optics : Matrix methods in paraxial optics
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(140.3300) Lasers and laser optics : Laser beam shaping
(350.5500) Other areas of optics : Propagation

ToC Category:
Research Papers

History
Original Manuscript: November 30, 2004
Revised Manuscript: November 26, 2004
Published: February 21, 2005

Citation
Martin Bastiaans and Tatiana Alieva, "Propagation law for the generating function of Hermite-Gaussian-type modes in first-order optical systems," Opt. Express 13, 1107-1112 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-4-1107


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References

  1. M. Abramowitz and I. A. Stegun, eds., Pocketbook of Mathematical Functions (Deutsch, Frankfurt am Main, Germany, 1984).
  2. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley and Los Angeles, CA, USA, 1966).
  3. S. A. Collins Jr., “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970). [CrossRef]
  4. M. J. Bastiaans and T. Alieva, “Generating function for Hermite-Gaussian modes propagating through first-order optical systems,” J. Phys. A: Math. Gen 38, L73–L78 (2005). [CrossRef]
  5. A. Wünsche, “General Hermite and Laguerre two-dimensional polynomials,” J. Phys. A: Math Gen. 33, 1603–1629 (2000). [CrossRef]
  6. M.W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P.Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993). [CrossRef]
  7. J. A. Arnaud, “Mode coupling in first-order optics,” J. Opt. Soc. Am. 61, 751–758 (1971). [CrossRef]
  8. T. Alieva and M. J. Bastiaans, “Mode mapping in paraxial lossless optics,” submitted to Opt. Lett. (2005).

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