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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 23 — Nov. 12, 2007
  • pp: 15387–15401

The von Neumann picture: a new representation for ultrashort laser pulses

Susanne Fechner, Frank Dimler, Tobias Brixner, Gustav Gerber, and David J. Tannor  »View Author Affiliations


Optics Express, Vol. 15, Issue 23, pp. 15387-15401 (2007)
http://dx.doi.org/10.1364/OE.15.015387


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Abstract

In recent years, the use of joint time-frequency representations to characterize and interpret shaped femtosecond laser pulses has proven to be very useful. However, the number of points in a joint time-frequency representation is daunting as compared with those in either the frequency or time representation. In this article we introduce the use of the von Neumann representation, in which a femtosecond pulse is represented on a discrete lattice of evenly spaced time-frequency points using a non-orthogonal Gaussian basis. We show that the information content in the von Neumann representation using a lattice of N points in time and √N points in frequency is exactly the same as in a frequency (or time) array of N points. Explicit formulas are given for the forward and reverse transformation between an N-point frequency signal and the von Neumann representation. We provide numerical examples of the forward and reverse transformation between the two representations for a variety of different pulse shapes; in all cases the original pulse is reconstructed with excellent precision. The von Neumann representation has the interpretational advantages of the Husimi representation but requires a bare minimum number of points and is stably and conveniently inverted; moreover, it avoids the periodic boundary conditions of the Fourier representation.

© 2007 Optical Society of America

OCIS Codes
(320.5550) Ultrafast optics : Pulses
(070.7425) Fourier optics and signal processing : Quasi-probability distribution functions

ToC Category:
Ultrafast Optics

History
Original Manuscript: August 7, 2007
Revised Manuscript: September 12, 2007
Manuscript Accepted: September 14, 2007
Published: November 5, 2007

Citation
Susanne Fechner, Frank Dimler, Tobias Brixner, Gustav Gerber, and David J. Tannor, "The von Neumann picture: a new representation for ultrashort laser pulses," Opt. Express 15, 15387-15401 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-23-15387


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