Abstract

We present an extensive investigation of the polarization properties of a femtosecond-laser-induced white-light (WL) continuum generated in a cubic crystal (CaF2). The WL spectrum and threshold energies have been examined for input polarizations with various degrees of ellipticity. For linear input polarization, the WL spectrum shows strong depolarization around the input wavelength, while the preservation of the input polarization is pronounced toward the blue spectral region. The observed depolarization effect has been elucidated in the framework of current models for WL generation.

© 2007 Optical Society of America

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  1. R. R. Alfano, ed., The Supercontinuum Laser Source (Springer, 1989).
  2. A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
    [CrossRef]
  3. M. Raytchev, E. Pandurski, I. Buchvarov, C. Modrakowski, and T. Fiebig, J. Phys. Chem. A 107, 4592 (2003).
    [CrossRef]
  4. A. Baltuska, T. Fuji, and T. Kobayashi, Opt. Lett. 27, 306 (2002).
    [CrossRef]
  5. P. Tzankov, T. Fiebig, and I. Buchvarov, Appl. Phys. Lett. 82, 517 (2003).
    [CrossRef]
  6. A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000).
    [CrossRef] [PubMed]
  7. H. Ward and L. Berge, Phys. Rev. Lett. 90, 053901 (2003).
    [CrossRef] [PubMed]
  8. V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
    [CrossRef]
  9. J. E. Rothenberg, Opt. Lett. 17, 1340 (1992).
    [CrossRef] [PubMed]
  10. N. Bloembergen, Opt. Commun. 8, 285 (1973).
    [CrossRef]
  11. M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Appl. Phys. B 77, 185 (2003).
    [CrossRef]
  12. A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. B 71, 125435 (2005).
    [CrossRef]
  13. I. Golub, Opt. Lett. 15, 305 (1990).
    [CrossRef] [PubMed]
  14. K. Midorikawa, H. Kawano, A. Suda, C. Nagura, and M. Obara, Appl. Phys. Lett. 80, 923 (2002).
    [CrossRef]
  15. M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. E 64, 046607 (2001).
    [CrossRef]
  16. A. K. Dharmadhikari, E. A. Rajgara, and D. Mathur, Opt. Lett. 31, 2184 (2006).
    [CrossRef] [PubMed]
  17. P. Tzankov, I. Buchvarov, and T. Fiebig, Opt. Commun. 203, 107 (2002).
    [CrossRef]
  18. D. C. Hutchings, Opt. Lett. 20, 1607 (1995).
    [CrossRef] [PubMed]
  19. D. C. Hutchings and B. S. Wherrett, Phys. Rev. B 52, 8150 (1995).
    [CrossRef]
  20. Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).
  21. ρ(λ)∼[sin2(ΔphivNL(λ)/2)sin2(2α)]−1∼(ΔphivNL(λ)/2)−2∼[(2π/λ)LΔnbrn(α)]−2∼λ2, where ΔphivNL(λ) is the nonlinear phase shift, λ is the wavelength, L is the interaction length, and Δnbrn is the effective nonlinear refraction index of the induced birefringence.
  22. A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. E 73, 016608 (2006).
    [CrossRef]
  23. The obtained ratio between the WL energy thresholds for circular and linear polarization is ∼3/2, which matches the ratio between the corresponding nonlinear indices of refraction (n2). It is relevant for our experimental observations and also that for other groups that WLG threshold power is slightly above the SF threshold, i.e., it is also proportional to ∼1/n2.

2006 (2)

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

A. K. Dharmadhikari, E. A. Rajgara, and D. Mathur, Opt. Lett. 31, 2184 (2006).
[CrossRef] [PubMed]

2005 (1)

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. B 71, 125435 (2005).
[CrossRef]

2003 (5)

M. Raytchev, E. Pandurski, I. Buchvarov, C. Modrakowski, and T. Fiebig, J. Phys. Chem. A 107, 4592 (2003).
[CrossRef]

P. Tzankov, T. Fiebig, and I. Buchvarov, Appl. Phys. Lett. 82, 517 (2003).
[CrossRef]

H. Ward and L. Berge, Phys. Rev. Lett. 90, 053901 (2003).
[CrossRef] [PubMed]

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
[CrossRef]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Appl. Phys. B 77, 185 (2003).
[CrossRef]

2002 (3)

A. Baltuska, T. Fuji, and T. Kobayashi, Opt. Lett. 27, 306 (2002).
[CrossRef]

P. Tzankov, I. Buchvarov, and T. Fiebig, Opt. Commun. 203, 107 (2002).
[CrossRef]

K. Midorikawa, H. Kawano, A. Suda, C. Nagura, and M. Obara, Appl. Phys. Lett. 80, 923 (2002).
[CrossRef]

2001 (1)

M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. E 64, 046607 (2001).
[CrossRef]

2000 (1)

A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000).
[CrossRef] [PubMed]

1998 (1)

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

1995 (2)

D. C. Hutchings and B. S. Wherrett, Phys. Rev. B 52, 8150 (1995).
[CrossRef]

D. C. Hutchings, Opt. Lett. 20, 1607 (1995).
[CrossRef] [PubMed]

1992 (1)

1990 (1)

1973 (1)

N. Bloembergen, Opt. Commun. 8, 285 (1973).
[CrossRef]

Akozbek, N.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
[CrossRef]

Alfano, R. R.

R. R. Alfano, ed., The Supercontinuum Laser Source (Springer, 1989).

Baltuska, A.

Becker, A.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
[CrossRef]

Berge, L.

H. Ward and L. Berge, Phys. Rev. Lett. 90, 053901 (2003).
[CrossRef] [PubMed]

Bloembergen, N.

N. Bloembergen, Opt. Commun. 8, 285 (1973).
[CrossRef]

Bowden, C. M.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
[CrossRef]

Brodeur, A.

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

Buchvarov, I.

P. Tzankov, T. Fiebig, and I. Buchvarov, Appl. Phys. Lett. 82, 517 (2003).
[CrossRef]

M. Raytchev, E. Pandurski, I. Buchvarov, C. Modrakowski, and T. Fiebig, J. Phys. Chem. A 107, 4592 (2003).
[CrossRef]

P. Tzankov, I. Buchvarov, and T. Fiebig, Opt. Commun. 203, 107 (2002).
[CrossRef]

Chin, S. L.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
[CrossRef]

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

Couairon, A.

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. B 71, 125435 (2005).
[CrossRef]

Dharmadhikari, A. K.

Di Trapani, P.

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

Dubietis, A.

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

Faccio, D.

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

Fiebig, T.

P. Tzankov, T. Fiebig, and I. Buchvarov, Appl. Phys. Lett. 82, 517 (2003).
[CrossRef]

M. Raytchev, E. Pandurski, I. Buchvarov, C. Modrakowski, and T. Fiebig, J. Phys. Chem. A 107, 4592 (2003).
[CrossRef]

P. Tzankov, I. Buchvarov, and T. Fiebig, Opt. Commun. 203, 107 (2002).
[CrossRef]

Franco, M.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. B 71, 125435 (2005).
[CrossRef]

Fuji, T.

Gaeta, A. L.

A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000).
[CrossRef] [PubMed]

Gaizauskas, E.

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

Golub, I.

Golubtsov, I. S.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
[CrossRef]

Hutchings, D. C.

D. C. Hutchings and B. S. Wherrett, Phys. Rev. B 52, 8150 (1995).
[CrossRef]

D. C. Hutchings, Opt. Lett. 20, 1607 (1995).
[CrossRef] [PubMed]

Kandidov, V. P.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
[CrossRef]

Katona, G.

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Appl. Phys. B 77, 185 (2003).
[CrossRef]

Kawano, H.

K. Midorikawa, H. Kawano, A. Suda, C. Nagura, and M. Obara, Appl. Phys. Lett. 80, 923 (2002).
[CrossRef]

Kobayashi, T.

Kolesik, M.

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Appl. Phys. B 77, 185 (2003).
[CrossRef]

M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. E 64, 046607 (2001).
[CrossRef]

Kosareva, O. G.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
[CrossRef]

Liu, W.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
[CrossRef]

Mathur, D.

Midorikawa, K.

K. Midorikawa, H. Kawano, A. Suda, C. Nagura, and M. Obara, Appl. Phys. Lett. 80, 923 (2002).
[CrossRef]

Modrakowski, C.

M. Raytchev, E. Pandurski, I. Buchvarov, C. Modrakowski, and T. Fiebig, J. Phys. Chem. A 107, 4592 (2003).
[CrossRef]

Moloney, J. V.

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Appl. Phys. B 77, 185 (2003).
[CrossRef]

M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. E 64, 046607 (2001).
[CrossRef]

Mysyrowicz, A.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. B 71, 125435 (2005).
[CrossRef]

Nagura, C.

K. Midorikawa, H. Kawano, A. Suda, C. Nagura, and M. Obara, Appl. Phys. Lett. 80, 923 (2002).
[CrossRef]

Obara, M.

K. Midorikawa, H. Kawano, A. Suda, C. Nagura, and M. Obara, Appl. Phys. Lett. 80, 923 (2002).
[CrossRef]

Pandurski, E.

M. Raytchev, E. Pandurski, I. Buchvarov, C. Modrakowski, and T. Fiebig, J. Phys. Chem. A 107, 4592 (2003).
[CrossRef]

Prade, B.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. B 71, 125435 (2005).
[CrossRef]

Rajgara, E. A.

Raytchev, M.

M. Raytchev, E. Pandurski, I. Buchvarov, C. Modrakowski, and T. Fiebig, J. Phys. Chem. A 107, 4592 (2003).
[CrossRef]

Rothenberg, J. E.

Suda, A.

K. Midorikawa, H. Kawano, A. Suda, C. Nagura, and M. Obara, Appl. Phys. Lett. 80, 923 (2002).
[CrossRef]

Sudrie, L.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. B 71, 125435 (2005).
[CrossRef]

Svirko, Y. P.

Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).

Tzankov, P.

P. Tzankov, T. Fiebig, and I. Buchvarov, Appl. Phys. Lett. 82, 517 (2003).
[CrossRef]

P. Tzankov, I. Buchvarov, and T. Fiebig, Opt. Commun. 203, 107 (2002).
[CrossRef]

Ward, H.

H. Ward and L. Berge, Phys. Rev. Lett. 90, 053901 (2003).
[CrossRef] [PubMed]

Wherrett, B. S.

D. C. Hutchings and B. S. Wherrett, Phys. Rev. B 52, 8150 (1995).
[CrossRef]

Wright, E. M.

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Appl. Phys. B 77, 185 (2003).
[CrossRef]

M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. E 64, 046607 (2001).
[CrossRef]

Zheludev, N. I.

Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).

Appl. Phys. B (2)

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, Appl. Phys. B 77, 149 (2003).
[CrossRef]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Appl. Phys. B 77, 185 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

P. Tzankov, T. Fiebig, and I. Buchvarov, Appl. Phys. Lett. 82, 517 (2003).
[CrossRef]

K. Midorikawa, H. Kawano, A. Suda, C. Nagura, and M. Obara, Appl. Phys. Lett. 80, 923 (2002).
[CrossRef]

J. Phys. Chem. A (1)

M. Raytchev, E. Pandurski, I. Buchvarov, C. Modrakowski, and T. Fiebig, J. Phys. Chem. A 107, 4592 (2003).
[CrossRef]

Opt. Commun. (2)

P. Tzankov, I. Buchvarov, and T. Fiebig, Opt. Commun. 203, 107 (2002).
[CrossRef]

N. Bloembergen, Opt. Commun. 8, 285 (1973).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. B (2)

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. B 71, 125435 (2005).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, Phys. Rev. B 52, 8150 (1995).
[CrossRef]

Phys. Rev. E (2)

M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. E 64, 046607 (2001).
[CrossRef]

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000).
[CrossRef] [PubMed]

H. Ward and L. Berge, Phys. Rev. Lett. 90, 053901 (2003).
[CrossRef] [PubMed]

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

Other (4)

R. R. Alfano, ed., The Supercontinuum Laser Source (Springer, 1989).

The obtained ratio between the WL energy thresholds for circular and linear polarization is ∼3/2, which matches the ratio between the corresponding nonlinear indices of refraction (n2). It is relevant for our experimental observations and also that for other groups that WLG threshold power is slightly above the SF threshold, i.e., it is also proportional to ∼1/n2.

Y. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley, 1998).

ρ(λ)∼[sin2(ΔphivNL(λ)/2)sin2(2α)]−1∼(ΔphivNL(λ)/2)−2∼[(2π/λ)LΔnbrn(α)]−2∼λ2, where ΔphivNL(λ) is the nonlinear phase shift, λ is the wavelength, L is the interaction length, and Δnbrn is the effective nonlinear refraction index of the induced birefringence.

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Figures (2)

Fig. 1
Fig. 1

Polarization ratios (solid curves) and WL spectrum (dotted curve) generated with linearly polarized input pulses at various input energies. The WL threshold energy was 2.2 μ J . The inset shows the polarization ratios at α = 0 ° , 13 ° and integrated over a full rotation period, respectively. The rotation of the CaF 2 plate was replaced by a translational motion only for the measurements at α = 0 ° and 13°.

Fig. 2
Fig. 2

WL spectra at various elliptical input polarizations, corresponding to different wave-plate rotation angles θ. The inset shows the WL intensity at 500 nm versus the input pulse energy for linear (triangles) and circular (circles) input polarizations.

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