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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 8 — Mar. 10, 2010
  • pp: 1210–1218

Optimum waist of localized basis functions in truncated series employed in some optical applications

Farshid Ghasemi and Khashayar Mehrany  »View Author Affiliations

Applied Optics, Vol. 49, Issue 8, pp. 1210-1218 (2010)

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The waist parameter is a particularly important factor for functional expansion in terms of localized orthogonal basis functions. We present a systematic approach to evaluate an asymptotic trend for the optimum waist parameter in truncated orthogonal localized bases satisfying several general conditions. This asymptotic behavior is fully introduced and verified for Hermite–Gauss and Laguerre– Gauss bases. As a special case of importance, a good estimate for the optimum waist in projection of discontinuous profiles on localized basis functions is proposed. The importance and application of the proposed estimation is demonstrated via several optical applications.

© 2010 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(060.2310) Fiber optics and optical communications : Fiber optics
(130.2790) Integrated optics : Guided waves
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(130.5296) Integrated optics : Photonic crystal waveguides

ToC Category:
Integrated Optics

Original Manuscript: September 9, 2009
Revised Manuscript: January 16, 2010
Manuscript Accepted: January 23, 2010
Published: March 3, 2010

Farshid Ghasemi and Khashayar Mehrany, "Optimum waist of localized basis functions in truncated series employed in some optical applications," Appl. Opt. 49, 1210-1218 (2010)

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