OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 1 — Jan. 1, 2007
  • pp: 77–83

Quantum analysis of the z-scan technique

Kahraman G. Köprülü and Prem Kumar  »View Author Affiliations

JOSA B, Vol. 24, Issue 1, pp. 77-83 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (126 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A Gaussian-wave theory is developed for the classical and quantum analysis of the z-scan method that is often used to measure third-order nonlinearities. The theory allows us to compute the transmittance in the z scan and the associated regimes of amplitude squeezing. The classical limits of our theory are in perfect agreement with the previous theoretical results. We show that amplitude squeezing of 1.2 dB can be obtained using the z scan with a careful selection of the signal power and the aperture size.

© 2006 Optical Society of America

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(270.6570) Quantum optics : Squeezed states

ToC Category:
Nonlinear Optics

Original Manuscript: July 24, 2006
Manuscript Accepted: September 22, 2006

Kahraman G. Köprülü and Prem Kumar, "Quantum analysis of the z-scan technique," J. Opt. Soc. Am. B 24, 77-83 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Levandovsky, M. Vasilyev, and P. Kumar, "Perturbation theory of quantum solitons: continuum evolution and optimum squeezing by spectral filtering," Opt. Lett. 24, 43-45 (1999). [CrossRef]
  2. F. Konig, S. Spalter, I. L. Shumay, A. Sizmann, T. Fauster, and G. Leuchs, "Fibre-optic photon-number squeezing in the normal group-velocity dispersion regime," J. Mod. Opt. 45, 2425-2431 (1998). [CrossRef]
  3. S. Spalter, M. Burk, U. Strossner, A. Sizmann, and G. Leuchs, "Propagation of quantum properties of sub-picosecond solitons in a fiber," Opt. Express 2, 77-83 (1998). [CrossRef]
  4. S. Spalter, M. Burk, U. Strossner, M. Bohm, A. Sizmann, and G. Leuchs, "Photon number squeezing of spectrally filtered sub-picosecond optical solitons," Europhys. Lett. 38, 335-340 (1997). [CrossRef]
  5. A. Mecozzi and P. Kumar, "Sub-Poissonian light by spatial soliton filtering," Quantum Semiclassic. Opt. 10, L21-L26 (1998). [CrossRef]
  6. M. Sheik-Bahae, A. A. Said, and E. W. Stryland, "High-sensitivity, single-beam n2 measurements," Opt. Lett. 14, 955-957 (1989). [CrossRef] [PubMed]
  7. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990). [CrossRef]
  8. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  9. K. G. Köprülü and O. Aytür, "Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states," Phys. Rev. A 60, 4122-4134 (1999). [CrossRef]
  10. K. G. Köprülü and O. Aytür, "Analysis of amplitude-squeezed light generation with Gaussian-beam degenerate optical parametric amplifiers," J. Opt. Soc. Am. B 18, 846-854 (2001). [CrossRef]
  11. D. Weaire, B. S. Wherrett, D. A. B. Miller, and S. D. Smith, "Effect of low-power nonlinear refraction on laser beam propagation in InSb," Opt. Lett. 4, 331-333 (1979). [CrossRef] [PubMed]
  12. One must keep in mind that the assumption of a purely dispersive nonlinearity is usually valid when working far away from resonances in any medium. Of course, the Kramers-Kronig relation must be satisfied. In such a case, the linearization approximation is usually valid, and quantum fluctuations can be treated in a similar way as classical fluctuations, provided the contribution of the vacuum noise from all relevant modes is accounted for.
  13. S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, "Squeezing of quantum solitons," Phys. Rev. Lett. 58, 1841-1844 (1987). [CrossRef] [PubMed]
  14. H. A. Haus and Y. Lai, "Quantum theory of soliton squeezing: a linearized approach," J. Opt. Soc. Am. B 7, 386-392 (1990). [CrossRef]
  15. L. Boivin, F. X. Kärtner, and H. A. Haus, "Analytical solution to the quantum field theory of self-phase modulation with a finite response time," Phys. Rev. Lett. 73, 240-243 (1994). [CrossRef] [PubMed]
  16. J. H. Shapiro and L. Boivin, "Raman-noise limit on squeezing in continuous-wave four-wave mixing," Opt. Lett. 20, 925-927 (1995). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited