Propagation law for the generating function of Hermite-Gaussian-type modes in first-order optical systems
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
- M. Abramowitz and I. A. Stegun, eds., Pocketbook of Mathematical Functions (Deutsch, Frankfurt am Main, Germany, 1984).
- R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley and Los Angeles, CA, USA, 1966).
- S. A. Collins Jr., “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970). [CrossRef]
- 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]
- A. Wünsche, “General Hermite and Laguerre two-dimensional polynomials,” J. Phys. A: Math Gen. 33, 1603–1629 (2000). [CrossRef]
- 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]
- J. A. Arnaud, “Mode coupling in first-order optics,” J. Opt. Soc. Am. 61, 751–758 (1971). [CrossRef]
- T. Alieva and M. J. Bastiaans, “Mode mapping in paraxial lossless optics,” submitted to Opt. Lett. (2005).
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