## Discrete orthogonal Gauss–Hermite transform for optical pulse propagation analysis

JOSA B, Vol. 20, Issue 7, pp. 1508-1513 (2003)

http://dx.doi.org/10.1364/JOSAB.20.001508

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### Abstract

A discrete orthogonal Gauss–Hermite transform (DOGHT) is introduced for the analysis of optical pulse properties in the time and frequency domains. Gaussian quadrature nodes and weights are used to calculate the expansion coefficients. The discrete orthogonal properties of the DOGHT are similar to the ones satisfied by the discrete Fourier transform so the two transforms have many common characteristics. However, it is demonstrated that the DOGHT produces a more compact representation of pulses in the time and frequency domains and needs less expansion coefficients for a given accuracy. It is shown that it can be used advantageously for propagation analysis of optical signals in the linear and nonlinear regimes.

© 2003 Optical Society of America

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

(060.2430) Fiber optics and optical communications : Fibers, single-mode

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(320.5550) Ultrafast optics : Pulses

**Citation**

Pavlos Lazaridis, Guy Debarge, and Philippe Gallion, "Discrete orthogonal Gauss–Hermite transform for optical pulse propagation analysis," J. Opt. Soc. Am. B **20**, 1508-1513 (2003)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-20-7-1508

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