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Optics Letters

Optics Letters


  • Vol. 13, Iss. 10 — Oct. 1, 1988
  • pp: 865–867

Rise–fall ambiguities and their removal from frequency-domain nonlinear-optical techniques

Rick Trebino, Charles E. Barker, and Adnah G. Kostenbauder  »View Author Affiliations

Optics Letters, Vol. 13, Issue 10, pp. 865-867 (1988)

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Most frequency-domain nonlinear-optical techniques measure only the magnitude of the Fourier transform of a temporal response and, hence, do not uniquely determine the response. We show that, for the commonly used response, h(t) = A exp(−t/τf) + B exp(−t/τs), where Aα/τf and B ≡ (1 − α)/τs, the spectral line shape can always be fitted by two different values of α. A measurement of the optical Kerr transient of carbon disulfide illustrates this ambiguity. We also demonstrate a single-scan method that is free from such ambiguities. It involves adding coherent background with a nonzero quadrature-phase component, obtained simply by proper choice of probe wavelength.

© 1988 Optical Society of America

Original Manuscript: April 21, 1988
Manuscript Accepted: June 22, 1988
Published: October 1, 1988

Rick Trebino, Charles E. Barker, and Adnah G. Kostenbauder, "Rise–fall ambiguities and their removal from frequency-domain nonlinear-optical techniques," Opt. Lett. 13, 865-867 (1988)

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  19. Ironically, the two frequency-domain methods 3,5 that do involve coherent background contain in-phase, but not quadrature, background.
  20. The existence of this ambiguity and its removal by the addition of quadrature-phase coherent background can also be seen when using Blaschke products.7 Ambiguity removal also follows from the observation that the Fourier-transform magnitude of a real decay is even, and adding iγ breaks this symmetry.
  21. In the course of this work, the fit to the data of this experiment was slightly improved, yielding the parameter values reported herein.

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