Abstract

An ellipsometric method for measuring second-order cascaded phase shift is experimentally demonstrated in a KNbO3 single crystal. We analyze the polarization state composed of the two orthogonal polarizations of the transmitted fundamental wave, one of which experiences intensity-dependent depletion and phase shift while the other does not. This method does not require a well-defined beam profile or interferometric stability.

© 1998 Optical Society of America

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References

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  1. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  2. R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, and G. I. Stegeman, Opt. Lett. 19, 1949 (1994).
    [CrossRef] [PubMed]
  3. G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
    [CrossRef]
  4. P. Vidakovi?, D. J. Lovering, J. A. Levenson, J. Webjörn, and P. St. J. Russell, Opt. Lett. 22, 277 (1997).
    [CrossRef]
  5. J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  6. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Crystals (Springer-Verlag, Berlin, 1991).
    [CrossRef]
  7. H. K. Kim, J. J. Ju, and M. Cha, J. Korean Phys. Soc. 32, S468 (1998).
  8. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  9. M. Cha, Opt. Lett. 23, 250 (1998).
    [CrossRef]

1998 (2)

H. K. Kim, J. J. Ju, and M. Cha, J. Korean Phys. Soc. 32, S468 (1998).

M. Cha, Opt. Lett. 23, 250 (1998).
[CrossRef]

1997 (1)

1995 (1)

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

1994 (1)

1992 (1)

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1962 (1)

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Armstrong, J.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Assanto, G.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

Baek, Y.

Bloembergen, N.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Cha, M.

H. K. Kim, J. J. Ju, and M. Cha, J. Korean Phys. Soc. 32, S468 (1998).

M. Cha, Opt. Lett. 23, 250 (1998).
[CrossRef]

DeSalvo, R.

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

Ducuing, J.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

Hagan, D. J.

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Ju, J. J.

H. K. Kim, J. J. Ju, and M. Cha, J. Korean Phys. Soc. 32, S468 (1998).

Kim, D. Y.

Kim, H. K.

H. K. Kim, J. J. Ju, and M. Cha, J. Korean Phys. Soc. 32, S468 (1998).

Levenson, J. A.

Lovering, D. J.

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

Pershan, P.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Russell, P. St. J.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Schiek, R.

Sheik-Bahae, M.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Stegeman, G.

Stegeman, G. I.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, and G. I. Stegeman, Opt. Lett. 19, 1949 (1994).
[CrossRef] [PubMed]

Sundheimer, M. L.

Van Stryland, E. W.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Vidakovic, P.

Webjörn, J.

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

IEEE J. Quantum Electron. (2)

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. Korean Phys. Soc. (1)

H. K. Kim, J. J. Ju, and M. Cha, J. Korean Phys. Soc. 32, S468 (1998).

Opt. Lett. (4)

Phys. Rev. (1)

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Other (1)

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for measuring the second-order cascaded phase shift: P, polarizer +45 °; X, KNbO3 crystal; L, imaging lens; F, SHG-cut filter; BS, Soleil–Babinet compensator; AN, analyzer -45 °; PH, pinhole; D, detector.

Fig. 2
Fig. 2

Measured fundamental transmittance and normalized detector signal S as a function of ΓL for ΔkL=2.49. Solid curves are from theory.

Fig. 3
Fig. 3

Cascaded phase shift versus ΓL for various values of ΔkL. Solid curves are from theory.

Fig. 4
Fig. 4

Cascaded phase shift versus ΔkL for ΓL=0.88 (open squares) and ΓL=1.97 (filled circles). Curves are from theory.

Equations (5)

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

dE2dz=iωdcn2E12 expiΔkz,dE1dz=iωdcn1E2E1* exp-iΔkz,
A=Texpiϕ1,
B=½1-Texpiϕ-11.
S=B·B*A·A*=12-T1+Tcos ϕ.
Γ=ωdcn12I10c0n21/2,

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