Abstract

We have investigated theoretically and experimentally the nonlinear propagation of intense elliptically polarized light pulses along a fourfold axis of the cubic crystal BaF2. Third-order nonlinear optical processes generate a cross-polarized wave, an effect that presents significant possibilities for application in femtosecond pulse contrast enhancement. The experimental setup consists of an input linear polarized light that passes through a cubic crystal sandwiched between two crossed quarter-wave plates. The exit orthogonal polarization-state production amount is measured at the output of an analyzer. When the light impinging on the sample is elliptically polarized with a quarter-wave plate at 22.5 deg, the achieved efficiency reaches 15%. It is more than twice that of a conventional polarization filter based on nonlinear ellipse rotation in an isotropic medium. This device is compared with previously reported polarization filtering [J. Opt. Soc. Am. B 21, 1659 (2004) ], in which a linearly polarized light produced a perpendicular field component. The theoretical model describes in detail the obtained dependencies and allows the different nonlinear processes that contribute to the generation of a cross-polarized wave to be distinguished. Possible applications are discussed.

© 2005 Optical Society of America

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  1. G. P. Agrawal, Nonlinear Fiber Optics (U. of Rochester, 2001).
  2. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  3. M. E. Orczyk, M. Samoc, J. Swiatkiewicz, and P. N. Prasad, "Dynamics of third-order nonlinearity of canthaxanthin carotenoid by the optically heterodyned phase-tuned femtosecond optical Kerr gate," J. Chem. Phys. 98, 2524-2533 (1983).
    [CrossRef]
  4. M. Lefkir and G. Rivoire, "Influence of transverse effects on measurement of third-order nonlinear susceptibility by self-induced polarization state changes," J. Opt. Soc. Am. B 14, 2856-2864 (1997).
    [CrossRef]
  5. D. Homoelle, A. L. Gaeta, V. Yanovsky, and G. Mourou, "Pulse contrast enhancement of high-energy pulses by use of a gas-filled hollow waveguide," Opt. Lett. 27, 1646-1648 (2002).
    [CrossRef]
  6. A. Jullien, F. Auge-Rochereau, G. Cheriaux, J. P. Chambaret, P. d'Oliveira, T. Auguste, and F. Falcoz, "High-efficiency, simple setup for pulse cleaning at the millijoule level by nonlinear induced birefringence," Opt. Lett. 29, 2184-2186 (2004).
    [CrossRef] [PubMed]
  7. M. P. Kalashnikov, E. Risse, H. Schönnagel, A. Husakou, J. Herrmann, and W. Sandner, "Characterization of a nonlinear filter for the front-end of a high contrast double-CPA Ti:sapphire laser," Opt. Express 12, 5088-5097 (2004).
    [CrossRef] [PubMed]
  8. K. Sala and M. C. Richardson, "A passive nonresonant technique for pulse contrast enhancement and gain isolation," J. Appl. Phys. 49, 2268-2276 (1978).
    [CrossRef]
  9. K. Sala, M. Richardson, and N. Isenor, "Passive mode locking of lasers with the optical Kerr effect modulator," IEEE J. Quantum Electron. QE-13, 915-924 (1977).
    [CrossRef]
  10. R. H. Stolen, I. Botineau, and A. Ashkin, "Intensity discrimination of optical pulses with birefringent fibers," Opt. Lett. 7, 512-514 (1982).
    [CrossRef] [PubMed]
  11. B. Nikolaus, D. Grischkowsky, and A. C. Balant, "Optical pulse reshaping based on the nonlinear birefringence of single-mode optical fibers," Opt. Lett. 8, 189-191 (1983).
    [CrossRef] [PubMed]
  12. H. G. Winful, "Self-induced polarization changes in birefringent optical fibers," Appl. Phys. Lett. 47, 213-215 (1985).
    [CrossRef]
  13. M. Horowitz and Y. Silberberg, "Nonlinear filtering by use of intensity-dependent polarization rotation in birefringent fibers," Opt. Lett. 22, 1760-1763 (1997).
    [CrossRef]
  14. K. Otsuka, J. Yumoto, and J. J. Song, "Optical bistability based on self-induced polarization-state change in anisotropic Kerr-like media," Opt. Lett. 10, 508-510 (1985).
    [CrossRef] [PubMed]
  15. J. L. Tapie and G. Mourou, "Shaping of clean, femtosecond pulses at 1.053 µm for chirped-pulse amplification," Opt. Lett. 17, 136-138 (1992).
    [CrossRef]
  16. N. Minkovski, S. M. Saltiel, G. I. Petrov, O. Albert, and J. Etchepare, "Polarization rotation induced by cascaded third-order processes," Opt. Lett. 27, 2025-2027 (2002).
    [CrossRef]
  17. N. Minkovski, G. I. Petrov, S. M. Saltiel, O. Albert, and J. Etchepare, "Nonlinear polarization rotation and orthogonal polarization generation experienced in a single-beam configuration," J. Opt. Soc. Am. B 21, 1659-1665 (2004).
    [CrossRef]
  18. W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors," J. Opt. Soc. Am. B 12, 401-415 (1995).
    [CrossRef]
  19. M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors," IEEE J. Quantum Electron. 30, 256-267 (1994).
    [CrossRef]
  20. D. C. Hutchings, J. S. Aitchison, and J. M. Arnold, "Nonlinear refractive coupling and vector solitons in anisotropic cubic media," J. Opt. Soc. Am. B 14, 869-879 (1997).
    [CrossRef]
  21. A. Jullien, O. Albert, F. Burgy, G. Hamoniaux, J.-P. Rousseau, J.-P. Chambaret, F. Augé-Rochereau, G. Chériaux, J. Etchepare, N. Minkovski, and S. M. Saltiel, "10−10 temporal contrast for femtosecond ultraintense lasers by cross-polarized wave generation," Opt. Lett. 30, 920-922 (2005).
    [CrossRef] [PubMed]

2005

2004

2002

1997

1995

1994

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors," IEEE J. Quantum Electron. 30, 256-267 (1994).
[CrossRef]

1992

1985

1983

B. Nikolaus, D. Grischkowsky, and A. C. Balant, "Optical pulse reshaping based on the nonlinear birefringence of single-mode optical fibers," Opt. Lett. 8, 189-191 (1983).
[CrossRef] [PubMed]

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, and P. N. Prasad, "Dynamics of third-order nonlinearity of canthaxanthin carotenoid by the optically heterodyned phase-tuned femtosecond optical Kerr gate," J. Chem. Phys. 98, 2524-2533 (1983).
[CrossRef]

1982

1978

K. Sala and M. C. Richardson, "A passive nonresonant technique for pulse contrast enhancement and gain isolation," J. Appl. Phys. 49, 2268-2276 (1978).
[CrossRef]

1977

K. Sala, M. Richardson, and N. Isenor, "Passive mode locking of lasers with the optical Kerr effect modulator," IEEE J. Quantum Electron. QE-13, 915-924 (1977).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (U. of Rochester, 2001).

Aitchison, J. S.

Albert, O.

Andersen, D. R.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors," J. Opt. Soc. Am. B 12, 401-415 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors," IEEE J. Quantum Electron. 30, 256-267 (1994).
[CrossRef]

Arnold, J. M.

Ashkin, A.

Auge-Rochereau, F.

Augé-Rochereau, F.

Auguste, T.

Balant, A. C.

Botineau, I.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Burgy, F.

Chambaret, J. P.

Chambaret, J.-P.

Cheriaux, G.

Chériaux, G.

d'Oliveira, P.

Dvorak, M. D.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors," J. Opt. Soc. Am. B 12, 401-415 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors," IEEE J. Quantum Electron. 30, 256-267 (1994).
[CrossRef]

Etchepare, J.

Falcoz, F.

Gaeta, A. L.

Grischkowsky, D.

Hamoniaux, G.

Harken, D. R.

Herrmann, J.

Homoelle, D.

Horowitz, M.

Husakou, A.

Hutchings, D. C.

Isenor, N.

K. Sala, M. Richardson, and N. Isenor, "Passive mode locking of lasers with the optical Kerr effect modulator," IEEE J. Quantum Electron. QE-13, 915-924 (1977).
[CrossRef]

Jullien, A.

Kalashnikov, M. P.

Lefkir, M.

McCallum, D. S.

Minkovski, N.

Mourou, G.

Nikolaus, B.

Orczyk, M. E.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, and P. N. Prasad, "Dynamics of third-order nonlinearity of canthaxanthin carotenoid by the optically heterodyned phase-tuned femtosecond optical Kerr gate," J. Chem. Phys. 98, 2524-2533 (1983).
[CrossRef]

Otsuka, K.

Petrov, G. I.

Prasad, P. N.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, and P. N. Prasad, "Dynamics of third-order nonlinearity of canthaxanthin carotenoid by the optically heterodyned phase-tuned femtosecond optical Kerr gate," J. Chem. Phys. 98, 2524-2533 (1983).
[CrossRef]

Richardson, M.

K. Sala, M. Richardson, and N. Isenor, "Passive mode locking of lasers with the optical Kerr effect modulator," IEEE J. Quantum Electron. QE-13, 915-924 (1977).
[CrossRef]

Richardson, M. C.

K. Sala and M. C. Richardson, "A passive nonresonant technique for pulse contrast enhancement and gain isolation," J. Appl. Phys. 49, 2268-2276 (1978).
[CrossRef]

Risse, E.

Rivoire, G.

Rousseau, J.-P.

Sala, K.

K. Sala and M. C. Richardson, "A passive nonresonant technique for pulse contrast enhancement and gain isolation," J. Appl. Phys. 49, 2268-2276 (1978).
[CrossRef]

K. Sala, M. Richardson, and N. Isenor, "Passive mode locking of lasers with the optical Kerr effect modulator," IEEE J. Quantum Electron. QE-13, 915-924 (1977).
[CrossRef]

Saltiel, S. M.

Samoc, M.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, and P. N. Prasad, "Dynamics of third-order nonlinearity of canthaxanthin carotenoid by the optically heterodyned phase-tuned femtosecond optical Kerr gate," J. Chem. Phys. 98, 2524-2533 (1983).
[CrossRef]

Sandner, W.

Schönnagel, H.

Schroeder, W. A.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors," J. Opt. Soc. Am. B 12, 401-415 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors," IEEE J. Quantum Electron. 30, 256-267 (1994).
[CrossRef]

Silberberg, Y.

Smirl, A. L.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors," J. Opt. Soc. Am. B 12, 401-415 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors," IEEE J. Quantum Electron. 30, 256-267 (1994).
[CrossRef]

Song, J. J.

Stolen, R. H.

Swiatkiewicz, J.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, and P. N. Prasad, "Dynamics of third-order nonlinearity of canthaxanthin carotenoid by the optically heterodyned phase-tuned femtosecond optical Kerr gate," J. Chem. Phys. 98, 2524-2533 (1983).
[CrossRef]

Tapie, J. L.

Wherrett, B. S.

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors," J. Opt. Soc. Am. B 12, 401-415 (1995).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors," IEEE J. Quantum Electron. 30, 256-267 (1994).
[CrossRef]

Winful, H. G.

H. G. Winful, "Self-induced polarization changes in birefringent optical fibers," Appl. Phys. Lett. 47, 213-215 (1985).
[CrossRef]

Yanovsky, V.

Yumoto, J.

Appl. Phys. Lett.

H. G. Winful, "Self-induced polarization changes in birefringent optical fibers," Appl. Phys. Lett. 47, 213-215 (1985).
[CrossRef]

IEEE J. Quantum Electron.

K. Sala, M. Richardson, and N. Isenor, "Passive mode locking of lasers with the optical Kerr effect modulator," IEEE J. Quantum Electron. QE-13, 915-924 (1977).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, "Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors," IEEE J. Quantum Electron. 30, 256-267 (1994).
[CrossRef]

J. Appl. Phys.

K. Sala and M. C. Richardson, "A passive nonresonant technique for pulse contrast enhancement and gain isolation," J. Appl. Phys. 49, 2268-2276 (1978).
[CrossRef]

J. Chem. Phys.

M. E. Orczyk, M. Samoc, J. Swiatkiewicz, and P. N. Prasad, "Dynamics of third-order nonlinearity of canthaxanthin carotenoid by the optically heterodyned phase-tuned femtosecond optical Kerr gate," J. Chem. Phys. 98, 2524-2533 (1983).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

D. Homoelle, A. L. Gaeta, V. Yanovsky, and G. Mourou, "Pulse contrast enhancement of high-energy pulses by use of a gas-filled hollow waveguide," Opt. Lett. 27, 1646-1648 (2002).
[CrossRef]

A. Jullien, F. Auge-Rochereau, G. Cheriaux, J. P. Chambaret, P. d'Oliveira, T. Auguste, and F. Falcoz, "High-efficiency, simple setup for pulse cleaning at the millijoule level by nonlinear induced birefringence," Opt. Lett. 29, 2184-2186 (2004).
[CrossRef] [PubMed]

R. H. Stolen, I. Botineau, and A. Ashkin, "Intensity discrimination of optical pulses with birefringent fibers," Opt. Lett. 7, 512-514 (1982).
[CrossRef] [PubMed]

B. Nikolaus, D. Grischkowsky, and A. C. Balant, "Optical pulse reshaping based on the nonlinear birefringence of single-mode optical fibers," Opt. Lett. 8, 189-191 (1983).
[CrossRef] [PubMed]

M. Horowitz and Y. Silberberg, "Nonlinear filtering by use of intensity-dependent polarization rotation in birefringent fibers," Opt. Lett. 22, 1760-1763 (1997).
[CrossRef]

K. Otsuka, J. Yumoto, and J. J. Song, "Optical bistability based on self-induced polarization-state change in anisotropic Kerr-like media," Opt. Lett. 10, 508-510 (1985).
[CrossRef] [PubMed]

J. L. Tapie and G. Mourou, "Shaping of clean, femtosecond pulses at 1.053 µm for chirped-pulse amplification," Opt. Lett. 17, 136-138 (1992).
[CrossRef]

N. Minkovski, S. M. Saltiel, G. I. Petrov, O. Albert, and J. Etchepare, "Polarization rotation induced by cascaded third-order processes," Opt. Lett. 27, 2025-2027 (2002).
[CrossRef]

A. Jullien, O. Albert, F. Burgy, G. Hamoniaux, J.-P. Rousseau, J.-P. Chambaret, F. Augé-Rochereau, G. Chériaux, J. Etchepare, N. Minkovski, and S. M. Saltiel, "10−10 temporal contrast for femtosecond ultraintense lasers by cross-polarized wave generation," Opt. Lett. 30, 920-922 (2005).
[CrossRef] [PubMed]

Other

G. P. Agrawal, Nonlinear Fiber Optics (U. of Rochester, 2001).

R. W. Boyd, Nonlinear Optics (Academic, 1992).

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Figures (7)

Fig. 1
Fig. 1

Experimental arrangements for measuring XPW generation in a BaF 2 crystal. The input and output polarizers are crossed. (a) Scheme with elliptically polarized input light that involves two crossed λ 4 plates. (b) Scheme with linearly polarized input light without λ 4 plates. Angles α and β are defined on Fig. 2

Fig. 2
Fig. 2

Fields involved in the process and frames used in the model. The three frames are (a) input and output polarization directions, (b) f and s axes of the input γ 4 plate rotated at angle α with respect to frame a, (c) x and y crystallographic axes of the cubic crystal rotated at angle β with respect to frame b. The dashed thick arrows represent the input fields, and the solid thick arrows are output fields (see the text for further details).

Fig. 3
Fig. 3

Contribution of the different processes to the efficiency of the XPW generation obtained by numerical solution of system (1). (a)–(c) Low input intensity ( γ 0 a 0 2 L = 0.3 ) ; (d)–(f) high input intensity ( γ 0 a 0 2 L = 2 ) .

Fig. 4
Fig. 4

(a) Experimental setup for measuring nonlinear ellipse rotation. (b) Variation of the measured rotation of the main ellipse axis as a function of sample rotation around its [001] axis. Input pulse energy is 12.5 μ J . The input λ 4 plate is rotated at α = 22.5 ° . The curve is a guide for the eye. (c) Theoretical prediction for the ellipse rotation as obtained by numerical solution of system (1) for normalized intensity level γ 0 a 0 2 L = 0.7 and σ = 1.2 . The dashed line is the amount of nonlinear ellipse rotation for isotropic media with σ = 0 .

Fig. 5
Fig. 5

(a) Variation of the experimentally measured XPW signal as a function of sample rotation around its [001] axis for a BaF 2 crystal for two different values of α for λ 4 plates. The input pulse energy is 12 μ J . Circles, α = 22.5 ° ; triangles, α = 18 ° . The curves are corrected for imperfect crossing of the λ 4 plates. The curve with squares is obtained with the scheme without λ 4 plates [Fig. 1b]. (b) Theoretical prediction for the efficiency of the XPW generation as obtained by numerical solution of system (1) for normalized intensity level γ 0 a 0 2 L = 1.5 and σ = 1.2 . Dark curve, α = 22.5 ° ; gray curve, α = 18 ° ; dotted curve, α = 0 ° . The dashed line is the nonlinear ellipse rotation for the isotropic media with σ = 0 when α = 22.5 ° .

Fig. 6
Fig. 6

(a) Variation of the measured XPW generation efficiency as a function of input energy for a BaF 2 crystal with the two schemes shown on Fig. 1: filled circles, E-XPW scheme [Fig. 1a]; open squares, L-XPW scheme [Fig. 1b]. Angle α = 22.5 ° for the scheme on Fig. 1a. In both measurements, the angle β is optimized for maximum efficiency. The curves are guides for the eye. (b) The respective theoretical predictions as obtained by numerical solution of system (1). Solid curve, E-XPW scheme [Fig. 1a]; dotted curve, L-XPW scheme [fig. 1b]. The dashed curve is the XPW generation efficiency for the scheme on Fig. 2a for isotropic media with σ = 0 .

Fig. 7
Fig. 7

Experimental spectra for XPW generation (10% efficiency) obtained by the L-XPW scheme (solid curve) and E-XPW scheme (dashed curve) compared with initial laser spectrum (gray curve).

Equations (4)

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d A d z = i γ 1 A 2 A i γ 2 ( B 2 B A 2 B * 2 A 2 B ) + i γ 3 ( 2 B 2 A + B 2 A * ) ,
d B d z = i γ 1 B 2 B + i γ 2 ( A 2 A B 2 A * 2 B 2 A ) + i γ 3 ( 2 A 2 B + A 2 B * ) ,
γ 1 = γ 0 [ 1 σ 2 sin 2 ( 2 β ) ] , γ 2 = γ 0 σ 4 sin ( 4 β ) ,
γ 3 = γ 0 [ σ 2 sin 2 ( 2 β ) + 1 σ 3 ] , γ 0 = ( 6 π 8 λ n ) χ x x x x ( 3 ) ,

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