Abstract

We present a simple optical arrangement for phase sensitive detection of degenerate four-wave mixing (DFWM) to characterize the real and imaginary parts of c (3) using an imaged 2-D phase grating. Phase sensitive coherent detection of DFWM signal is demonstrated. Phase stabilization of the interferometric arms is obtained passively with the 2-D grating. A processable polyacetylene sample is characterized at a wavelength of 1.5 µm using this technique. The observed nonlinearity is determined to be a fast (<250 fs) effect using a simple test.

© 2006 Optical Society of America

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  1. 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]
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    [CrossRef]
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  4. F. P. Strohkendl, L. R. Dalton, R. W. Hellwarth, H. W. Sarkas, and Z. H. Kafafi, "Phase-mismatched degenerate four-wave mixing: complex third-order susceptibility tensor elements of C60 at 768nm," J. Opt. Soc. Am. B 14, 92-98 (1997).
    [CrossRef]
  5. M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, "Optical heterodyning of the phase-tuned femtosecond optical Kerr gate signal for the determination of complex third-order susceptibilities," Appl. Phys. Lett. 60, 2837-2839 (1992).
    [CrossRef]
  6. H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-induced dynamic gratings (Springer-Verlag 1986), Chap. 2.
  7. A. A. Maznev, K. A. Nelson, and J. A. Rogers, "Optical heterodyne detection of laser- induced gratings," Opt. Lett. 23, 1319-1321 (1998).
    [CrossRef]
  8. G. D. Goodno, G. Dadusc, and R. J. D. Miller, "Ultrafast heterodyne-detected transient-grating spectroscopy using diffractive optics," J. Opt. Soc. Am. B 15, 1791-1794 (1998).
  9. Q.-H. Xu, Y.-Z. Ma, I. V. Stiopkin, and G. R. Fleming, "Wavelength-dependent resonant homodyne and heterodyne transient grating spectroscopy with a diffractive optics method: solvent effect on the third-order signal," J. Chem. Phys. 116, 9333-9340 (2002).
    [CrossRef]
  10. O. A. Scherman and R. H. Grubbs, "Polycyclooctatetraene (Polyacetylene) produced with a ruthenium olefin metathesis catalyst," Synth. Met. 124, 431-434 (2001).
    [CrossRef]
  11. J. C. Manifacier, J. Gasiot, J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E 9, 1002-1004 (1976).
    [CrossRef]
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    [CrossRef]
  14. J. A. Rogers, PhD Thesis, MIT (1995).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  19. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, CA, 1995).
  20. I. Z. Kozma and J. Hebling, "Comparative analysis of optical setups for excitation of dynamic gratings by ultrashort light pulses," Opt. Commun. 199, 401-415 (2001).
    [CrossRef]
  21. T. Brixner, I. V. Stiopkin, and G. R. Fleming, "Tunable two-dimensional femtosecond spectroscopy," Opt. Lett. 29, 884-886 (2004).
    [CrossRef] [PubMed]

2004 (1)

2002 (1)

Q.-H. Xu, Y.-Z. Ma, I. V. Stiopkin, and G. R. Fleming, "Wavelength-dependent resonant homodyne and heterodyne transient grating spectroscopy with a diffractive optics method: solvent effect on the third-order signal," J. Chem. Phys. 116, 9333-9340 (2002).
[CrossRef]

2001 (3)

O. A. Scherman and R. H. Grubbs, "Polycyclooctatetraene (Polyacetylene) produced with a ruthenium olefin metathesis catalyst," Synth. Met. 124, 431-434 (2001).
[CrossRef]

W. N. Herman and M. J. Roberts, "The sense of chromophore orientation in films made by alternating polyelectrolyte deposition," Adv. Mater. 13, 744-746 (2001).
[CrossRef]

I. Z. Kozma and J. Hebling, "Comparative analysis of optical setups for excitation of dynamic gratings by ultrashort light pulses," Opt. Commun. 199, 401-415 (2001).
[CrossRef]

1998 (5)

1997 (1)

1995 (1)

1992 (1)

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, "Optical heterodyning of the phase-tuned femtosecond optical Kerr gate signal for the determination of complex third-order susceptibilities," Appl. Phys. Lett. 60, 2837-2839 (1992).
[CrossRef]

1990 (1)

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]

1987 (1)

1980 (1)

1976 (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

1973 (1)

E. J. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, "Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors," IEEE J. Quantum Electron. 9, 919-933 (1973).

Bao, Z.

Brixner, T.

Canto-Said, E. J.

E. J. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, "Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors," IEEE J. Quantum Electron. 9, 919-933 (1973).

Carter, G. M.

Crimmins, T. F.

Dadusc, G.

Dalton, L. R.

Eckbreth, A. C.

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

Fleming, G. R.

T. Brixner, I. V. Stiopkin, and G. R. Fleming, "Tunable two-dimensional femtosecond spectroscopy," Opt. Lett. 29, 884-886 (2004).
[CrossRef] [PubMed]

Q.-H. Xu, Y.-Z. Ma, I. V. Stiopkin, and G. R. Fleming, "Wavelength-dependent resonant homodyne and heterodyne transient grating spectroscopy with a diffractive optics method: solvent effect on the third-order signal," J. Chem. Phys. 116, 9333-9340 (2002).
[CrossRef]

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

Goodno, G. D.

Grubbs, R. H.

O. A. Scherman and R. H. Grubbs, "Polycyclooctatetraene (Polyacetylene) produced with a ruthenium olefin metathesis catalyst," Synth. Met. 124, 431-434 (2001).
[CrossRef]

Hagan, D. J.

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]

E. J. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, "Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors," IEEE J. Quantum Electron. 9, 919-933 (1973).

Hall, R. J.

Hebling, J.

I. Z. Kozma and J. Hebling, "Comparative analysis of optical setups for excitation of dynamic gratings by ultrashort light pulses," Opt. Commun. 199, 401-415 (2001).
[CrossRef]

Hellwarth, R. W.

Herman, W. N.

W. N. Herman and M. J. Roberts, "The sense of chromophore orientation in films made by alternating polyelectrolyte deposition," Adv. Mater. 13, 744-746 (2001).
[CrossRef]

Hsieh, B.

Kafafi, Z. H.

Kato, T.

Kozma, I. Z.

I. Z. Kozma and J. Hebling, "Comparative analysis of optical setups for excitation of dynamic gratings by ultrashort light pulses," Opt. Commun. 199, 401-415 (2001).
[CrossRef]

Luther-Davies, B.

Ma, Y.-Z.

Q.-H. Xu, Y.-Z. Ma, I. V. Stiopkin, and G. R. Fleming, "Wavelength-dependent resonant homodyne and heterodyne transient grating spectroscopy with a diffractive optics method: solvent effect on the third-order signal," J. Chem. Phys. 116, 9333-9340 (2002).
[CrossRef]

Manickam, N.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, "Optical heterodyning of the phase-tuned femtosecond optical Kerr gate signal for the determination of complex third-order susceptibilities," Appl. Phys. Lett. 60, 2837-2839 (1992).
[CrossRef]

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

Maznev, A. A.

Milam, D.

Miller, R. J. D.

Nelson, K. A.

Nishimura, M.

Orczyk, M. E.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, "Optical heterodyning of the phase-tuned femtosecond optical Kerr gate signal for the determination of complex third-order susceptibilities," Appl. Phys. Lett. 60, 2837-2839 (1992).
[CrossRef]

Prasad, P. N.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, "Optical heterodyning of the phase-tuned femtosecond optical Kerr gate signal for the determination of complex third-order susceptibilities," Appl. Phys. Lett. 60, 2837-2839 (1992).
[CrossRef]

Roberts, M. J.

W. N. Herman and M. J. Roberts, "The sense of chromophore orientation in films made by alternating polyelectrolyte deposition," Adv. Mater. 13, 744-746 (2001).
[CrossRef]

Rogers, J. A.

Said, A. A.

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]

Samoc, A.

Samoc, M.

M. Samoc, A. Samoc, B. Luther-Davies, Z. Bao, L. Yu, B. Hsieh, and U. Scherf, "Femtosecond Z-scan and degenerate four-wave mixing measurements of real and imaginary parts of the third-order nonlinearity of soluble conjugated polymers," J. Opt. Soc. Am. B 15, 817-825 (1998).
[CrossRef]

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, "Optical heterodyning of the phase-tuned femtosecond optical Kerr gate signal for the determination of complex third-order susceptibilities," Appl. Phys. Lett. 60, 2837-2839 (1992).
[CrossRef]

Sarkas, H. W.

Sasaoka, E.

Scherf, U.

Scherman, O. A.

O. A. Scherman and R. H. Grubbs, "Polycyclooctatetraene (Polyacetylene) produced with a ruthenium olefin metathesis catalyst," Synth. Met. 124, 431-434 (2001).
[CrossRef]

Sheik-Bahae, M.

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]

Shirley, J. A.

Stiopkin, I. V.

T. Brixner, I. V. Stiopkin, and G. R. Fleming, "Tunable two-dimensional femtosecond spectroscopy," Opt. Lett. 29, 884-886 (2004).
[CrossRef] [PubMed]

Q.-H. Xu, Y.-Z. Ma, I. V. Stiopkin, and G. R. Fleming, "Wavelength-dependent resonant homodyne and heterodyne transient grating spectroscopy with a diffractive optics method: solvent effect on the third-order signal," J. Chem. Phys. 116, 9333-9340 (2002).
[CrossRef]

Strohkendl, F. P.

Suetsugu, Y.

Swiatkiewicz, J.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, "Optical heterodyning of the phase-tuned femtosecond optical Kerr gate signal for the determination of complex third-order susceptibilities," Appl. Phys. Lett. 60, 2837-2839 (1992).
[CrossRef]

Takagi, N.

Tomoaia-Cotisel, M.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, "Optical heterodyning of the phase-tuned femtosecond optical Kerr gate signal for the determination of complex third-order susceptibilities," Appl. Phys. Lett. 60, 2837-2839 (1992).
[CrossRef]

Van Stryland, E. W.

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]

E. J. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, "Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors," IEEE J. Quantum Electron. 9, 919-933 (1973).

Wei, T.-H.

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]

Xu, Q.-H.

Q.-H. Xu, Y.-Z. Ma, I. V. Stiopkin, and G. R. Fleming, "Wavelength-dependent resonant homodyne and heterodyne transient grating spectroscopy with a diffractive optics method: solvent effect on the third-order signal," J. Chem. Phys. 116, 9333-9340 (2002).
[CrossRef]

Young, J.

E. J. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, "Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors," IEEE J. Quantum Electron. 9, 919-933 (1973).

Yu, L.

Adv. Mater. (1)

W. N. Herman and M. J. Roberts, "The sense of chromophore orientation in films made by alternating polyelectrolyte deposition," Adv. Mater. 13, 744-746 (2001).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, N. Manickam, M. Tomoaia-Cotisel, and P. N. Prasad, "Optical heterodyning of the phase-tuned femtosecond optical Kerr gate signal for the determination of complex third-order susceptibilities," Appl. Phys. Lett. 60, 2837-2839 (1992).
[CrossRef]

IEEE J. Quantum Electron. (2)

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]

E. J. Canto-Said, D. J. Hagan, J. Young, and E. W. Van Stryland, "Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors," IEEE J. Quantum Electron. 9, 919-933 (1973).

J. Chem. Phys. (1)

Q.-H. Xu, Y.-Z. Ma, I. V. Stiopkin, and G. R. Fleming, "Wavelength-dependent resonant homodyne and heterodyne transient grating spectroscopy with a diffractive optics method: solvent effect on the third-order signal," J. Chem. Phys. 116, 9333-9340 (2002).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. E (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E 9, 1002-1004 (1976).
[CrossRef]

Opt. Commun. (1)

I. Z. Kozma and J. Hebling, "Comparative analysis of optical setups for excitation of dynamic gratings by ultrashort light pulses," Opt. Commun. 199, 401-415 (2001).
[CrossRef]

Opt. Lett. (5)

Synth. Met. (1)

O. A. Scherman and R. H. Grubbs, "Polycyclooctatetraene (Polyacetylene) produced with a ruthenium olefin metathesis catalyst," Synth. Met. 124, 431-434 (2001).
[CrossRef]

Other (3)

J. A. Rogers, PhD Thesis, MIT (1995).

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-induced dynamic gratings (Springer-Verlag 1986), Chap. 2.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, CA, 1995).

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Figures (5)

Fig. 1.
Fig. 1.

Ring opening metathesis polymerization method used to synthesize the polyacetylene polymer.

Fig. 2.
Fig. 2.

Optical microscope image of the 2-D phase grating fabricated on a quartz plate.

Fig. 3.
Fig. 3.

Experimental setup for DFWM measurement using an imaged 2-D phase grating.

Fig. 4.
Fig. 4.

Cubic dependence of the DFWM signals of polyacetylene and fused silica to the input intensity. Slopes of the linear fits are 2.97 and 3.00 for polyacetylene and fused silica, respectively.

Fig. 5.
Fig. 5.

Interferograms of the coherent detected DFWM signals of polyacetylene and fused silica.

Equations (11)

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I 4 χ ( 3 ) 2 L 2 n 4 I 1 I 2 I 3 = m I 1 I 2 I 3 ,
χ sam ( 3 ) = χ ref ( 3 ) ( m sam m ref ) 1 2 L ref L sam ( n sam n ref ) 2 .
I = I DFWM + I ref + 2 I DFWM I ref cos ( θ + Δ θ ) .
Δ θ = 2 π d λ [ n cs ( 1 cos β 1 cos β 0 ) n a ( cos ( α β ) cos β cos ( α 0 β 0 ) cos β 0 ) ] ,
n = n 0 + n 2 I ,
n 2 = 3 Re χ ( 3 ) 4 ε 0 cn 0 2 .
n 2 [ m 2 W ] = π 3 ε 0 cn 0 2 10 8 Re χ ( 3 ) [ esu ] .
α = α 0 + α 2 I ,
α 2 = 3 ω Im χ ( 3 ) 2 ε 0 c 2 n 0 2 .
α 2 [ m W ] = 2 π ω 3 ε 0 c 2 n 0 2 10 8 Im χ ( 3 ) [ esu ] .
I = m I 1 I 2 I 3 + I ref + 2 m I 1 I 2 I 3 I ref cos ( θ + Δ θ ) ,

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