Abstract

We present a new wave-front sensitive interferometry technique (called dispersion shearing interferometry) for the measurement of both the sign and the magnitude of n2. The interference pattern is produced by two laterally shifted second harmonics of the laser source. Only the fundamental wave passes through the nonlinear sample, which is placed before the interferometer. We demonstrate this technique on an aggregated colloidal silver solution using a YAG:Nd laser and KTiOPO4 frequency doublers.

© 1997 Optical Society of America

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  1. D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, B. Spivey, “Shearing interferometry for laser-guide-star atmospheric correction at large D/r0,” J. Opt. Soc. Am. A 11, 858–873 (1994).
    [CrossRef]
  2. J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real-time wave-front correction systems,” Appl. Opt. 14, 2622–2626 (1975).
    [CrossRef] [PubMed]
  3. T. W. Liepmann, F. A. Hopf, “Common path interferometer based on second harmonic generation,” Appl. Opt. 24, 1485–1488 (1985).
    [CrossRef] [PubMed]
  4. M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive index of glasses and crystals,” Opt. Eng. 17, 463–469 (1978).
    [CrossRef]
  5. M. J. Moran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
    [CrossRef]
  6. M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [CrossRef] [PubMed]
  7. F. A. Hopf, A. Tomito, G. Al-Jumaily, “Second-harmonic interferometers,” Opt. Lett. 5, 386–388 (1980).
    [CrossRef] [PubMed]
  8. G. V. Ostrovskaya, Kh. P. Alum, Yu. V. Kovalchuk, “Nonlinear dispersion interferometer,” Pis’ma Zh. Tehn. Fiz. 7, 1359–1364 (1981), in Russian.
  9. V. P. Drachev, “Nonlinear operating mode of dispersion interferometer,” Opt. Spektrosk. 75, 473–478 (1993), in Russian.
  10. V. P. Drachev, Yu. I. Krasnikov, P. A. Bagryansky, “Dispersion interferometer for controlled fusion devices,” Rev. Sci. Instrum. 64, 1010–1013 (1993).
    [CrossRef]
  11. B. M. Welsh, B. L. Ellerbroek, M. C. Roggemann, T. L. Pennington, “Fundamental performance comparison of a Hartmann and a shearing interferometer wave-front sensor,” Appl. Opt. 34, 4186–4195 (1995).
    [CrossRef] [PubMed]
  12. S. G. Rautian, V. P. Safonov, P. A. Chubakov, V. M. Shalaev, M. I. Stockman, “Giant parametrical light scattering on the silver clusters,” Pis’ma Zh. Eksp. Teor. Fiz. 47, 200–203 (1988), in Russian.
  13. Yu. E. Danilova, V. P. Drachev, S. V. Perminov, V. P. Safonov, “The nonlinearity of refractive index and absorption coefficient of fractal clasters in colloidal solutions,” Izv. RAN Ser. Fiz. 60, 18–22 (1996), in Russian.
  14. R. E. Bridges, G. L. Fisher, R. W. Boyd, “Z-scan measurements technique for non-Gaussian beams and arbitrary sample thicknesses,” Opt. Lett. 20, 1821–1823 (1995).
    [CrossRef]

1996

Yu. E. Danilova, V. P. Drachev, S. V. Perminov, V. P. Safonov, “The nonlinearity of refractive index and absorption coefficient of fractal clasters in colloidal solutions,” Izv. RAN Ser. Fiz. 60, 18–22 (1996), in Russian.

1995

1994

1993

V. P. Drachev, “Nonlinear operating mode of dispersion interferometer,” Opt. Spektrosk. 75, 473–478 (1993), in Russian.

V. P. Drachev, Yu. I. Krasnikov, P. A. Bagryansky, “Dispersion interferometer for controlled fusion devices,” Rev. Sci. Instrum. 64, 1010–1013 (1993).
[CrossRef]

1989

1988

S. G. Rautian, V. P. Safonov, P. A. Chubakov, V. M. Shalaev, M. I. Stockman, “Giant parametrical light scattering on the silver clusters,” Pis’ma Zh. Eksp. Teor. Fiz. 47, 200–203 (1988), in Russian.

1985

1981

G. V. Ostrovskaya, Kh. P. Alum, Yu. V. Kovalchuk, “Nonlinear dispersion interferometer,” Pis’ma Zh. Tehn. Fiz. 7, 1359–1364 (1981), in Russian.

1980

1978

M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive index of glasses and crystals,” Opt. Eng. 17, 463–469 (1978).
[CrossRef]

1975

M. J. Moran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[CrossRef]

J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real-time wave-front correction systems,” Appl. Opt. 14, 2622–2626 (1975).
[CrossRef] [PubMed]

Al-Jumaily, G.

Alum, Kh. P.

G. V. Ostrovskaya, Kh. P. Alum, Yu. V. Kovalchuk, “Nonlinear dispersion interferometer,” Pis’ma Zh. Tehn. Fiz. 7, 1359–1364 (1981), in Russian.

Arnold, R.

Bagryansky, P. A.

V. P. Drachev, Yu. I. Krasnikov, P. A. Bagryansky, “Dispersion interferometer for controlled fusion devices,” Rev. Sci. Instrum. 64, 1010–1013 (1993).
[CrossRef]

Barrett, T.

Boyd, R. W.

Bridges, R. E.

Carman, R. L.

M. J. Moran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[CrossRef]

Chubakov, P. A.

S. G. Rautian, V. P. Safonov, P. A. Chubakov, V. M. Shalaev, M. I. Stockman, “Giant parametrical light scattering on the silver clusters,” Pis’ma Zh. Eksp. Teor. Fiz. 47, 200–203 (1988), in Russian.

Cuellar, L.

Danilova, Yu. E.

Yu. E. Danilova, V. P. Drachev, S. V. Perminov, V. P. Safonov, “The nonlinearity of refractive index and absorption coefficient of fractal clasters in colloidal solutions,” Izv. RAN Ser. Fiz. 60, 18–22 (1996), in Russian.

Drachev, V. P.

Yu. E. Danilova, V. P. Drachev, S. V. Perminov, V. P. Safonov, “The nonlinearity of refractive index and absorption coefficient of fractal clasters in colloidal solutions,” Izv. RAN Ser. Fiz. 60, 18–22 (1996), in Russian.

V. P. Drachev, Yu. I. Krasnikov, P. A. Bagryansky, “Dispersion interferometer for controlled fusion devices,” Rev. Sci. Instrum. 64, 1010–1013 (1993).
[CrossRef]

V. P. Drachev, “Nonlinear operating mode of dispersion interferometer,” Opt. Spektrosk. 75, 473–478 (1993), in Russian.

Ellerbroek, B. L.

Fisher, G. L.

Hopf, F. A.

Johnson, P.

Kovalchuk, Yu. V.

G. V. Ostrovskaya, Kh. P. Alum, Yu. V. Kovalchuk, “Nonlinear dispersion interferometer,” Pis’ma Zh. Tehn. Fiz. 7, 1359–1364 (1981), in Russian.

Krasnikov, Yu. I.

V. P. Drachev, Yu. I. Krasnikov, P. A. Bagryansky, “Dispersion interferometer for controlled fusion devices,” Rev. Sci. Instrum. 64, 1010–1013 (1993).
[CrossRef]

Lefebvre, M.

Liepmann, T. W.

Milam, D.

M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive index of glasses and crystals,” Opt. Eng. 17, 463–469 (1978).
[CrossRef]

Moran, M. J.

M. J. Moran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[CrossRef]

Ostrovskaya, G. V.

G. V. Ostrovskaya, Kh. P. Alum, Yu. V. Kovalchuk, “Nonlinear dispersion interferometer,” Pis’ma Zh. Tehn. Fiz. 7, 1359–1364 (1981), in Russian.

Pennington, T. L.

Perminov, S. V.

Yu. E. Danilova, V. P. Drachev, S. V. Perminov, V. P. Safonov, “The nonlinearity of refractive index and absorption coefficient of fractal clasters in colloidal solutions,” Izv. RAN Ser. Fiz. 60, 18–22 (1996), in Russian.

Rautian, S. G.

S. G. Rautian, V. P. Safonov, P. A. Chubakov, V. M. Shalaev, M. I. Stockman, “Giant parametrical light scattering on the silver clusters,” Pis’ma Zh. Eksp. Teor. Fiz. 47, 200–203 (1988), in Russian.

Rego, A.

Roggemann, M. C.

Safonov, V. P.

Yu. E. Danilova, V. P. Drachev, S. V. Perminov, V. P. Safonov, “The nonlinearity of refractive index and absorption coefficient of fractal clasters in colloidal solutions,” Izv. RAN Ser. Fiz. 60, 18–22 (1996), in Russian.

S. G. Rautian, V. P. Safonov, P. A. Chubakov, V. M. Shalaev, M. I. Stockman, “Giant parametrical light scattering on the silver clusters,” Pis’ma Zh. Eksp. Teor. Fiz. 47, 200–203 (1988), in Russian.

Said, A. A.

Sandler, D. G.

Shalaev, V. M.

S. G. Rautian, V. P. Safonov, P. A. Chubakov, V. M. Shalaev, M. I. Stockman, “Giant parametrical light scattering on the silver clusters,” Pis’ma Zh. Eksp. Teor. Fiz. 47, 200–203 (1988), in Russian.

She, C. Y.

M. J. Moran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[CrossRef]

Sheik-Bahae, M.

Smith, G.

Smith, W. L.

M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive index of glasses and crystals,” Opt. Eng. 17, 463–469 (1978).
[CrossRef]

Spivey, B.

Stockman, M. I.

S. G. Rautian, V. P. Safonov, P. A. Chubakov, V. M. Shalaev, M. I. Stockman, “Giant parametrical light scattering on the silver clusters,” Pis’ma Zh. Eksp. Teor. Fiz. 47, 200–203 (1988), in Russian.

Taylor, G.

Tomito, A.

Van Stryland, E. W.

Weber, M. J.

M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive index of glasses and crystals,” Opt. Eng. 17, 463–469 (1978).
[CrossRef]

Welsh, B. M.

Wyant, J. C.

Appl. Opt.

IEEE J. Quantum Electron.

M. J. Moran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[CrossRef]

Izv. RAN Ser. Fiz.

Yu. E. Danilova, V. P. Drachev, S. V. Perminov, V. P. Safonov, “The nonlinearity of refractive index and absorption coefficient of fractal clasters in colloidal solutions,” Izv. RAN Ser. Fiz. 60, 18–22 (1996), in Russian.

J. Opt. Soc. Am. A

Opt. Eng.

M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive index of glasses and crystals,” Opt. Eng. 17, 463–469 (1978).
[CrossRef]

Opt. Lett.

Opt. Spektrosk.

V. P. Drachev, “Nonlinear operating mode of dispersion interferometer,” Opt. Spektrosk. 75, 473–478 (1993), in Russian.

Pis’ma Zh. Eksp. Teor. Fiz.

S. G. Rautian, V. P. Safonov, P. A. Chubakov, V. M. Shalaev, M. I. Stockman, “Giant parametrical light scattering on the silver clusters,” Pis’ma Zh. Eksp. Teor. Fiz. 47, 200–203 (1988), in Russian.

Pis’ma Zh. Tehn. Fiz.

G. V. Ostrovskaya, Kh. P. Alum, Yu. V. Kovalchuk, “Nonlinear dispersion interferometer,” Pis’ma Zh. Tehn. Fiz. 7, 1359–1364 (1981), in Russian.

Rev. Sci. Instrum.

V. P. Drachev, Yu. I. Krasnikov, P. A. Bagryansky, “Dispersion interferometer for controlled fusion devices,” Rev. Sci. Instrum. 64, 1010–1013 (1993).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Scheme of DSI: 1, the studied nonlinear medium; 2 and 5, frequency doublers; 3, a quartz wedge with a compensator; 4, two identical prisms; 6, a filter; 7, a polarizer; 8, a photodiode array. Beam overlap is shown in the right-hand part of the figure, as well as the photodiode array position.

Fig. 2
Fig. 2

Experimental relative phase profile of two sheared beams without a nonlinear sample. The shear Δx = 0.7 mm. Curves 1, 2, and 3 correspond to different parameters of the beams: 1, w0 = 0.015 cm, z0 = 6.7 cm, and the waist and the photodetector are spaced at z = 65 cm; 2, w0 = 0.05 cm, z0 = 74 cm, and z = 100 cm; 3, w0 = 0.2 cm, z0 = 1200 cm, and z = 100 cm.

Fig. 3
Fig. 3

Experimental profiles obtained 1, without passing through the nonlinear medium and 2, after passing through it. The incident beam parameters w0 = 0.2 cm and the waist and photodiode array are spaced at z = 100 cm, Δx = 0.5 mm. The solid curve gives the best fit assuming that n2 < 0. The dotted curve is the calculated profile F(x) for the opposite sign of n2.

Equations (5)

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

I ( x , θ 0 ) = I 1 ( x - x 1 ) + I 2 ( x - x 2 ) + 2 ( I 1 I 2 ) 1 / 2 × cos [ θ 0 + Φ 1 ( x - x 1 ) - Φ 2 ( x - x 2 ) ] ,
A ω ( x , y , z ) = A 0 w 0 w ( z ) exp [ - x 2 + y 2 w 2 ( z ) ] exp [ i π ( x 2 + y 2 ) λ R ] ,
F ( x ) Φ ( x - x 1 , y ) - Φ ( x - x 2 , y ) = 2 π λ R [ ( x - x 1 ) 2 + y 2 - ( x - x 2 ) 2 - y 2 ] = - 4 π λ R Δ x ( x - x 1 + x 2 2 ) .
Φ NL ( x ) = [ 2 π l γ I ( x ) ] / λ .
F NL ( x ) [ ( 4 π l γ / λ ) ] [ I ( x - x 1 , y ) - I ( x - x 2 , y ) ] .

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