Abstract

We describe and analyze an all-optical method to measure both the magnitude and the phase of each (complex) element of the χ(3) tensor that determines degenerate four-wave mixing in a thin isotropic film on a thick substrate. We use the method to characterize the χ(3) tensor of a 10-µm C60 film (on a CaF2 substrate) for 110-fs pulses at 768 nm. Using a fused-quartz plate as the nonlinear standard, we find the two independent Maker–Terhune elements of χ(3) to have magnitudes |c1221(-ω, ω, ω, -ω)|=(0.44±0.03)×10-12 esu and |c1122(-ω, ω, ω, -ω)|=(0.50±0.03)×10-12 esu and phase angles ϕ1221 and ϕ1122, whose magnitudes are 145°±17° and 139°±10°.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. X. Zhang, X. Ye, and K. Chen, Opt. Commun. 113, 519 (1995).
    [CrossRef]
  2. N. Tang, J. P. Partanen, R. W. Hellwarth, J. Laquindanum, L. R. Dalton, M. Q. He, and C. W. Spangler, Proc. SPIE 2285, 186 (1994).
    [CrossRef]
  3. S. M. Saltiel, B. Van Wonterghem, and P. M. Rentzepis, Opt. Lett. 14, 183 (1989).
    [CrossRef] [PubMed]
  4. M. L. Shand and R. R. Chance, J. Chem. Phys. 69, 4482 (1978).
    [CrossRef]
  5. M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, Appl. Phys. Lett. 60, 2837 (1992).
    [CrossRef]
  6. 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]
  7. P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
    [CrossRef]
  8. S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
    [CrossRef]
  9. F. P. Strohkendl, D. J. Files, and L. R. Dalton, J. Opt. Soc. Am. B 11, 742 (1994).
    [CrossRef]
  10. A. Owyoung, IEEE J. Quantum Electron. QE-9, 1064 (1973).
    [CrossRef]
  11. R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. B 11, 964 (1975).
    [CrossRef]
  12. R. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
  13. F. Kajzar, C. Taliani, R. Zamboni, S. Rossini, and R. Danieli, Synth. Met. 54, 21 (1993).
    [CrossRef]
  14. J. R. Lindle, R. G. S. Pong, F. J. Bartoli, and Z. H. Kafafi, Phys. Rev. B 48, 9447 (1993).
    [CrossRef]

1995 (1)

X. Zhang, X. Ye, and K. Chen, Opt. Commun. 113, 519 (1995).
[CrossRef]

1994 (2)

N. Tang, J. P. Partanen, R. W. Hellwarth, J. Laquindanum, L. R. Dalton, M. Q. He, and C. W. Spangler, Proc. SPIE 2285, 186 (1994).
[CrossRef]

F. P. Strohkendl, D. J. Files, and L. R. Dalton, J. Opt. Soc. Am. B 11, 742 (1994).
[CrossRef]

1993 (2)

F. Kajzar, C. Taliani, R. Zamboni, S. Rossini, and R. Danieli, Synth. Met. 54, 21 (1993).
[CrossRef]

J. R. Lindle, R. G. S. Pong, F. J. Bartoli, and Z. H. Kafafi, Phys. Rev. B 48, 9447 (1993).
[CrossRef]

1992 (1)

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, Appl. Phys. Lett. 60, 2837 (1992).
[CrossRef]

1991 (1)

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

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]

1989 (1)

1978 (1)

M. L. Shand and R. R. Chance, J. Chem. Phys. 69, 4482 (1978).
[CrossRef]

1977 (1)

R. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

1975 (1)

R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. B 11, 964 (1975).
[CrossRef]

1973 (1)

A. Owyoung, IEEE J. Quantum Electron. QE-9, 1064 (1973).
[CrossRef]

1965 (1)

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Bartoli, F. J.

J. R. Lindle, R. G. S. Pong, F. J. Bartoli, and Z. H. Kafafi, Phys. Rev. B 48, 9447 (1993).
[CrossRef]

Chance, R. R.

M. L. Shand and R. R. Chance, J. Chem. Phys. 69, 4482 (1978).
[CrossRef]

Chen, K.

X. Zhang, X. Ye, and K. Chen, Opt. Commun. 113, 519 (1995).
[CrossRef]

Cherlow, J.

R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. B 11, 964 (1975).
[CrossRef]

Dalton, L. R.

N. Tang, J. P. Partanen, R. W. Hellwarth, J. Laquindanum, L. R. Dalton, M. Q. He, and C. W. Spangler, Proc. SPIE 2285, 186 (1994).
[CrossRef]

F. P. Strohkendl, D. J. Files, and L. R. Dalton, J. Opt. Soc. Am. B 11, 742 (1994).
[CrossRef]

Danieli, R.

F. Kajzar, C. Taliani, R. Zamboni, S. Rossini, and R. Danieli, Synth. Met. 54, 21 (1993).
[CrossRef]

Eklund, P. C.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

Files, D. J.

Hagan, D. J.

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]

Hager, T.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

He, M. Q.

N. Tang, J. P. Partanen, R. W. Hellwarth, J. Laquindanum, L. R. Dalton, M. Q. He, and C. W. Spangler, Proc. SPIE 2285, 186 (1994).
[CrossRef]

Hellwarth, R.

R. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. B 11, 964 (1975).
[CrossRef]

Hellwarth, R. W.

N. Tang, J. P. Partanen, R. W. Hellwarth, J. Laquindanum, L. R. Dalton, M. Q. He, and C. W. Spangler, Proc. SPIE 2285, 186 (1994).
[CrossRef]

Holden, J. M.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

Kafafi, Z. H.

J. R. Lindle, R. G. S. Pong, F. J. Bartoli, and Z. H. Kafafi, Phys. Rev. B 48, 9447 (1993).
[CrossRef]

Kajzar, F.

F. Kajzar, C. Taliani, R. Zamboni, S. Rossini, and R. Danieli, Synth. Met. 54, 21 (1993).
[CrossRef]

Laquindanum, J.

N. Tang, J. P. Partanen, R. W. Hellwarth, J. Laquindanum, L. R. Dalton, M. Q. He, and C. W. Spangler, Proc. SPIE 2285, 186 (1994).
[CrossRef]

Lee, W.-T.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

Lindle, J. R.

J. R. Lindle, R. G. S. Pong, F. J. Bartoli, and Z. H. Kafafi, Phys. Rev. B 48, 9447 (1993).
[CrossRef]

Maker, P. D.

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Manickam, N.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, Appl. Phys. Lett. 60, 2837 (1992).
[CrossRef]

McRae, E.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

Ni, H. F.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

Orczyk, M. E.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, Appl. Phys. Lett. 60, 2837 (1992).
[CrossRef]

Owyoung, A.

A. Owyoung, IEEE J. Quantum Electron. QE-9, 1064 (1973).
[CrossRef]

Partanen, J. P.

N. Tang, J. P. Partanen, R. W. Hellwarth, J. Laquindanum, L. R. Dalton, M. Q. He, and C. W. Spangler, Proc. SPIE 2285, 186 (1994).
[CrossRef]

Pong, R. G. S.

J. R. Lindle, R. G. S. Pong, F. J. Bartoli, and Z. H. Kafafi, Phys. Rev. B 48, 9447 (1993).
[CrossRef]

Prasad, P. N.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, Appl. Phys. Lett. 60, 2837 (1992).
[CrossRef]

Rao, A. M.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

Ren, S. L.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

Rentzepis, P. M.

Rossini, S.

F. Kajzar, C. Taliani, R. Zamboni, S. Rossini, and R. Danieli, Synth. Met. 54, 21 (1993).
[CrossRef]

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]

Saltiel, S. M.

Samoc, M.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, Appl. Phys. Lett. 60, 2837 (1992).
[CrossRef]

Selegue, J.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

Shand, M. L.

M. L. Shand and R. R. Chance, J. Chem. Phys. 69, 4482 (1978).
[CrossRef]

Sheik-Bahae, M.

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]

Spangler, C. W.

N. Tang, J. P. Partanen, R. W. Hellwarth, J. Laquindanum, L. R. Dalton, M. Q. He, and C. W. Spangler, Proc. SPIE 2285, 186 (1994).
[CrossRef]

Strohkendl, F. P.

Swiatkiewicz, J.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, Appl. Phys. Lett. 60, 2837 (1992).
[CrossRef]

Taliani, C.

F. Kajzar, C. Taliani, R. Zamboni, S. Rossini, and R. Danieli, Synth. Met. 54, 21 (1993).
[CrossRef]

Tang, N.

N. Tang, J. P. Partanen, R. W. Hellwarth, J. Laquindanum, L. R. Dalton, M. Q. He, and C. W. Spangler, Proc. SPIE 2285, 186 (1994).
[CrossRef]

Terhune, R. W.

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Tomoaia-Cotisel, M.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, Appl. Phys. Lett. 60, 2837 (1992).
[CrossRef]

Van Stryland, E. W.

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]

Van Wonterghem, B.

Wang, K.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

Wang, Y.

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

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]

Yang, T.-T.

R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. B 11, 964 (1975).
[CrossRef]

Ye, X.

X. Zhang, X. Ye, and K. Chen, Opt. Commun. 113, 519 (1995).
[CrossRef]

Zamboni, R.

F. Kajzar, C. Taliani, R. Zamboni, S. Rossini, and R. Danieli, Synth. Met. 54, 21 (1993).
[CrossRef]

Zhang, X.

X. Zhang, X. Ye, and K. Chen, Opt. Commun. 113, 519 (1995).
[CrossRef]

Appl. Phys. Lett. (2)

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, Appl. Phys. Lett. 60, 2837 (1992).
[CrossRef]

S. L. Ren, Y. Wang, A. M. Rao, E. McRae, J. M. Holden, T. Hager, K. Wang, W.-T. Lee, H. F. Ni, J. Selegue, and P. C. Eklund, Appl. Phys. Lett. 59, 2678 (1991).
[CrossRef]

IEEE J. Quantum Electron. (2)

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]

A. Owyoung, IEEE J. Quantum Electron. QE-9, 1064 (1973).
[CrossRef]

J. Chem. Phys. (1)

M. L. Shand and R. R. Chance, J. Chem. Phys. 69, 4482 (1978).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

X. Zhang, X. Ye, and K. Chen, Opt. Commun. 113, 519 (1995).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Phys. Rev. B (2)

R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. B 11, 964 (1975).
[CrossRef]

J. R. Lindle, R. G. S. Pong, F. J. Bartoli, and Z. H. Kafafi, Phys. Rev. B 48, 9447 (1993).
[CrossRef]

Proc. SPIE (1)

N. Tang, J. P. Partanen, R. W. Hellwarth, J. Laquindanum, L. R. Dalton, M. Q. He, and C. W. Spangler, Proc. SPIE 2285, 186 (1994).
[CrossRef]

Prog. Quantum Electron. (1)

R. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Synth. Met. (1)

F. Kajzar, C. Taliani, R. Zamboni, S. Rossini, and R. Danieli, Synth. Met. 54, 21 (1993).
[CrossRef]

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 (2)

Fig. 1
Fig. 1

Beam geometry for degenerate forward-four-wave mixing. Three beams, labeled 1, 2, and 3, copropagate nearly collinearly along the z axis. The angle of intersection in air between beams 1 and 2, and 2 and 3, is denoted by θ. The sample normal is parallel to the z axis. The three incident beams intersect inside the sample and generate, because of third-order nonlinear optical interaction, nine signal beams that are labeled 4–12 in a plane, which we call the observation plane, parallel to the sample. Beam 4 is the phase-matched signal beam; beams 5–12 are non-phase-matched.

Fig. 2
Fig. 2

Degenerate four-wave mixing signals for all-parallel beam polarizations versus beam delay. The signals in beams 4, 5, and 6 emerging from the thin-film sample (C60 film on a CaF2 substrate) and the signals in beam 4 from the pure CaF2 substrate and the fused-silica standard are shown. Beam 3 was delayed for signals in beams 4 and 6. Beam 2 was delayed for signals in beam 5. All data sets are fit to Gaussians to guide the eye. Note that for the thin-film sample the signal in phase-matched beam 4 is smaller than in non-phase-matched beams 5 and 6. This demonstrates destructive interference between thin-film and substrate signals. Note also that the thin-film signals in beams 5 and 6 are equal, as expected for the parallel polarization configuration.

Tables (2)

Tables Icon

Table 1 Powers S4, S5, and S6 Generated in Beams 4, 5, and 6 of Fig. 1 for Various Polarizations of the Input Beams 1, 2, and 3a

Tables Icon

Table 2 Results for the Amplitudes and the Phases of the Third-Order Nonlinear Susceptibility Tensor χf(-ω, ω, ω, -ω) of C60 Obtained by Use of the Data of Table 1 in Eqs. (12)–(16) for the Optical Fields Generated in Beams 4, 5, and 6 in Fig. 1a

Equations (22)

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

Pf(3)=3χf(-ω, ω, ω, -ω)EωfEωfEωf*,
Eωα=jEjα exp(ikjα·r),
E5αz=i12πωnαcχαE1αE2αE3α* exp(iΔk5αz),
k5α=k1α+k2α-k3α-Δk5αzˆ,
θ=tan-12aba2+a22ac/ω.
(k5α)2=10a2+(b5α)2=(k1α)2=2a2+bα2=nα2ω2/c2.
Δk5α=b5α-bα=4a2c/(nαω)θ2ω/(nαc).
E4αz=i12πωnαcχαE1αE3αE2α*,
E6fz=i12πωnfcχfE2fE3fE1f*,
Pα(3)=3c1221αEω*Eω·Eω+6c1122αEωEω·Eω*,
tαβ=2nαnα+nβ.
E5L=i12πωlf[c1221fE3*E2·E1+c1122f(E1E2·E3*+E2E1·E3*)]taf3tfstsa/cnf.
E6L=i12πωlf[c1221fE1*E2·E3+c1122f(E2E3·E1*+E3E2·E1*)]taf3tfstsa/cnf.
E4Lfs=i12πω{[c1221fE2*E1·E3+c1122f(E1E3·E2*
+E3E1·E2*)]lftaf3tfstsa/cnf
+χsE1E3E2*lstaf3tfs3tsa/cns}.
E4Ls=i12πωχsE1E3E2*lstas3tsa/cns,
E4Lq=i12πω[c1221qE2*E1·E3+c1122q(E1E3·E2*+E3E1·E2*)]lqtaq3tqa/cnq.
S4(f, s)=Sp(f)+ξ2S4(s)+2ξSp(f)S4(s) cos(ϕijkl),
c1221q=1.24×10-15esu
c1122q/c1221q=1.091±0.013.
c1111q=(3.95±0.05)×10-15esu

Metrics