Abstract

Based on Fresnel–Kirchhoff diffraction theory, a diffraction model of nonlinear optical media interacting with a Gaussian beam has been set up that can interpret the Z-scan phenomenon in a new way. This theory not only is consistent with the conventional Z-scan theory for a small nonlinear phase shift but also can be used for larger nonlinear phase shifts. Numerical computations indicate that the shape of the Z-scan curve is greatly affected by the value of the nonlinear phase shift. The symmetric dispersionlike Z-scan curve is valid only for small nonlinear phase shifts (|Δϕ0| <π), but, with increasingly larger nonlinear phase shifts, the valley of the transmittance is severely suppressed and the peak is greatly enhanced. The power output through the aperture will oscillate with increasing nonlinear phase shift caused by the input laser power. The aperture transmittance will attenuate and saturate with increasing Kerr constant.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High sensitivity single beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [CrossRef] [PubMed]
  2. M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. 17, 258–260 (1992).
    [CrossRef] [PubMed]
  3. J. Castillo, V. P. Kozich, and A. O. Marcano, “Thermal lensing resulting from one- and two-photon absorption studied with a two-color time-resolved Z scan,” Opt. Lett. 19, 171–173 (1994).
    [CrossRef] [PubMed]
  4. D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” Appl. Opt. 38, 5168–5180 (1999).
    [CrossRef]
  5. P. B. Chapple, J. Staromlynska, and R. G. McDuff, “Z-scan studies in the thin- and thick-sample limits,” J. Opt. Soc. Am. B 11, 975–982 (1994).
    [CrossRef]
  6. C. Liu, H. Zeng, Y. Segawa, and M. Kira, “Optical limiting performance of a novel σ–π alternating polymer,” Opt. Commun. 162, 53–56 (1999).
    [CrossRef]
  7. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlin-earities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
  8. C. H. Kwak, Y. L. Lee, and S. G. Kim, “Analysis of asym-metric Z-scan measurement for large optical nonlinearities in an amorphous As2S3 thin film,” J. Opt. Soc. Am. B 16, 600–604 (1999).
    [CrossRef]
  9. R. E. Samad and N. D. Vieira, Jr., “Analytical description of Z-scan on-axis intensity based on the Huygens–Fresnel principle,” J. Opt. Soc. Am. B 15, 2742–2747 (1998).
    [CrossRef]
  10. K. Zhao and X. Zhong, Optics, 6th ed. (Beijing U. Press, Beijing, 1998), pp. 186–190.

1999 (3)

1998 (1)

1994 (2)

1992 (1)

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlin-earities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

1989 (1)

Castillo, J.

Chapple, P. B.

DeSalvo, R.

Hagan, D. J.

Kim, S. G.

Kira, M.

C. Liu, H. Zeng, Y. Segawa, and M. Kira, “Optical limiting performance of a novel σ–π alternating polymer,” Opt. Commun. 162, 53–56 (1999).
[CrossRef]

Kovsh, D. I.

Kozich, V. P.

Kwak, C. H.

Lee, Y. L.

Liu, C.

C. Liu, H. Zeng, Y. Segawa, and M. Kira, “Optical limiting performance of a novel σ–π alternating polymer,” Opt. Commun. 162, 53–56 (1999).
[CrossRef]

Marcano, A. O.

McDuff, R. G.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlin-earities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High sensitivity single beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Samad, R. E.

Segawa, Y.

C. Liu, H. Zeng, Y. Segawa, and M. Kira, “Optical limiting performance of a novel σ–π alternating polymer,” Opt. Commun. 162, 53–56 (1999).
[CrossRef]

Sheik-Bahae, M.

Staromlynska, J.

Van Stryland, E. W.

Vieira Jr., N. D.

Wang, J.

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlin-earities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Yang, S.

Zeng, H.

C. Liu, H. Zeng, Y. Segawa, and M. Kira, “Optical limiting performance of a novel σ–π alternating polymer,” Opt. Commun. 162, 53–56 (1999).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlin-earities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

C. Liu, H. Zeng, Y. Segawa, and M. Kira, “Optical limiting performance of a novel σ–π alternating polymer,” Opt. Commun. 162, 53–56 (1999).
[CrossRef]

Opt. Lett. (3)

Other (1)

K. Zhao and X. Zhong, Optics, 6th ed. (Beijing U. Press, Beijing, 1998), pp. 186–190.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Comparison of the new Z-scan theory with the conventional theory for a small nonlinear phase shift, Δϕ0=-π/2.

Fig. 2
Fig. 2

Theoretical plots of closed-aperture Z-scan transmittance for purely nonlinear refraction for several nonlinear phase shifts.

Fig. 3
Fig. 3

Theoretical plot of the output power through the aperture versus the input laser power or the corresponding Δϕ0. The sample is fixed at focus; a=2 mm and Z2=1 m.

Fig. 4
Fig. 4

Theoretical plot of the aperture transmittance versus Kerr constant or Δϕ0. The sample is fixed at focus; a=2 mm and Z2=1 m.

Tables (2)

Tables Icon

Table 1 Influence of the Aperture Size (a ) on the Z-Scan Curve

Tables Icon

Table 2 Influence of the Distance between the Sample and the Aperture (Z2) on the Z-Scan Curve a

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

T(z, Δϕ0)1+4Δϕ0x(x2+9)(x2+1),
E(r, z)=E(0, 0) ω0ω(z)exp[-α(z-Z1)/2]exp-r2ω2(z)×exp-ikr22R(z)-iϕ(z),
Δn=γI,
Δn(r, z)=2γPπω2(z)exp[-α(z-Z1)]exp-2r2ω2(z).
Δϕ(r, Z1)=2πλZ1Z1+dΔn(r, z)dz.
Δϕ(r, Z1)Δϕ0exp-2r2ω12,
Δϕ0=4γP[1-exp(-αd)]λαω12.
U˜(r, Z1)=exp[-iΔϕ(r, Z1)].
V˜(r, Z1)=E(0, 0) ω0ω1exp(-αd/2)×exp-r2ω12exp-ikr22R1.
E˜(ρ)=-iλF(θ0, θ)V˜(r)U˜(r) exp(ikD)D rdrdφ.
I(ρ, Z1, Z2)=P2πλ2ω12exp(-αd)×02π05ω(Z1)1D+Z2D2×exp-r2ω12expi2πλ D-kr22R1-Δϕ0exp-2r2ω12rdrdφ2.
PA(Z1, Z2, a, Δϕ0)=2π0aI(ρ, Z1, Z2)ρdρ.

Metrics