Abstract

We study experimentally the process of the second harmonic generation by two noncollinear beams in quadratic nonlinear crystals with a disordered structure of ferroelectric domains. We show that the second-harmonic radiation is emitted in the form of two cones as well as in a plane representing the cross-correlation of the two fundamental pulses. We demonstrate the implementation of this parametric process for characterisation of femtosecond pulses, enabling the estimation of pulse width, chirp, and front tilt. This is achieved through monitoring the evolution of the autocorrelation trace inside the nonlinear crystal.

© 2008 Optical Society of America

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  1. M. Horowitz, A. Bekker, and B. Fischer, "Broadband second-harmonic generation in SrBaNb2O6 by spread spectrum phase matching with controllable domain gratings," Appl. Phys. Lett. 62, 2619-2621 (1993).
    [CrossRef]
  2. J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase- matchingsecond-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
    [CrossRef]
  3. R. Fischer, D. N. Neshev, S. Saltiel, W. Krolikowski, and Yu. S. Kivshar, "Broadband femtosecond frequency doubling in random media," Appl. Phys. Lett. 89, 191105 (2006).
    [CrossRef]
  4. P. Molina, M. O. Ramirez, and L. E. Bausa, "Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonlinear "Photonic Glass," Adv. Funct. Mat. 18, 709-715 (2008).
    [CrossRef]
  5. M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, "Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible," J. Appl. Phys. 95, 6185-6191 (2004).
    [CrossRef]
  6. A. R. Tunyagi, M. Ulex, and K. Betzler, "Noncollinear optical frequency doubling in strontium barium niobate," Phys. Rev. Lett. 90, 243901 (2003).
    [CrossRef] [PubMed]
  7. A. R. Tunyagi, "Non-Collinear Second Harmonic Generation in Strontium Barium Niobate," PhD thesis, Fachbereich Physik, Universit¨at Osnabr¨uck, Germany (2004).
  8. R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104 (2007).
    [CrossRef]
  9. S. M. Saltiel, D. N. Neshev, R. Fischer, A. Arie, W. Krolikowski, and Yu. S. Kivshar, "Spatiotemporal toroidal waves from the transverse second-harmonic generation," Opt. Lett. 33, 527-529 (2008).
    [CrossRef] [PubMed]
  10. J. Janszky, G. Corradi, and R. N. Gyuzalian, "On a possibility of analysing the temporal characteristics of short pulses," Opt. Commum. 23, 293-298 (1977).
    [CrossRef]
  11. S. M. Saltiel, S. D. Savov, I. V. Tomov, and L. S. Telegin, "Subnanosecond pulse duration measurements by noncollinear second harmonic generation," Opt. Commun. 38, 443-447 (1981).
    [CrossRef]
  12. Y. Ishida, T. Yajima, and A. Watanabe, "A simple monitoring system for single subpicosecond laser pulses," Opt. Commun. 56, 57-60 (1985).
    [CrossRef]
  13. M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
    [CrossRef]
  14. J. Trull, C. Cojocaru, R. Fischer, S. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N Neshev, W. Krolikowski, and Yu. S. Kivshar, "Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures," Opt. Express 15, 15868-15877 (2007).
    [CrossRef] [PubMed]
  15. G. Agrawal, Nonlinear Fiber Optics, Ch. 3, (Academic Press, 2007).
  16. S. Akturk, M. Kimmel, P. O�??Shea, and R. Trebino "Measuring pulse-front tilt in ultrashort pulses using GRENOUILLE," Opt. Express 11, 491-501 (2003).
    [CrossRef] [PubMed]

2008

P. Molina, M. O. Ramirez, and L. E. Bausa, "Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonlinear "Photonic Glass," Adv. Funct. Mat. 18, 709-715 (2008).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, A. Arie, W. Krolikowski, and Yu. S. Kivshar, "Spatiotemporal toroidal waves from the transverse second-harmonic generation," Opt. Lett. 33, 527-529 (2008).
[CrossRef] [PubMed]

2007

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

J. Trull, C. Cojocaru, R. Fischer, S. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N Neshev, W. Krolikowski, and Yu. S. Kivshar, "Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures," Opt. Express 15, 15868-15877 (2007).
[CrossRef] [PubMed]

2006

R. Fischer, D. N. Neshev, S. Saltiel, W. Krolikowski, and Yu. S. Kivshar, "Broadband femtosecond frequency doubling in random media," Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

2004

M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, "Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible," J. Appl. Phys. 95, 6185-6191 (2004).
[CrossRef]

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
[CrossRef]

2003

S. Akturk, M. Kimmel, P. O�??Shea, and R. Trebino "Measuring pulse-front tilt in ultrashort pulses using GRENOUILLE," Opt. Express 11, 491-501 (2003).
[CrossRef] [PubMed]

A. R. Tunyagi, M. Ulex, and K. Betzler, "Noncollinear optical frequency doubling in strontium barium niobate," Phys. Rev. Lett. 90, 243901 (2003).
[CrossRef] [PubMed]

J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase- matchingsecond-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
[CrossRef]

1993

M. Horowitz, A. Bekker, and B. Fischer, "Broadband second-harmonic generation in SrBaNb2O6 by spread spectrum phase matching with controllable domain gratings," Appl. Phys. Lett. 62, 2619-2621 (1993).
[CrossRef]

1985

Y. Ishida, T. Yajima, and A. Watanabe, "A simple monitoring system for single subpicosecond laser pulses," Opt. Commun. 56, 57-60 (1985).
[CrossRef]

1981

S. M. Saltiel, S. D. Savov, I. V. Tomov, and L. S. Telegin, "Subnanosecond pulse duration measurements by noncollinear second harmonic generation," Opt. Commun. 38, 443-447 (1981).
[CrossRef]

1977

J. Janszky, G. Corradi, and R. N. Gyuzalian, "On a possibility of analysing the temporal characteristics of short pulses," Opt. Commum. 23, 293-298 (1977).
[CrossRef]

Akturk, S.

Arago, C.

J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase- matchingsecond-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
[CrossRef]

Arie, A.

Baudrier-Raybaut, M.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
[CrossRef]

Bausa, L. E.

P. Molina, M. O. Ramirez, and L. E. Bausa, "Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonlinear "Photonic Glass," Adv. Funct. Mat. 18, 709-715 (2008).
[CrossRef]

M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, "Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible," J. Appl. Phys. 95, 6185-6191 (2004).
[CrossRef]

Bekker, A.

M. Horowitz, A. Bekker, and B. Fischer, "Broadband second-harmonic generation in SrBaNb2O6 by spread spectrum phase matching with controllable domain gratings," Appl. Phys. Lett. 62, 2619-2621 (1993).
[CrossRef]

Betzler, K.

A. R. Tunyagi, M. Ulex, and K. Betzler, "Noncollinear optical frequency doubling in strontium barium niobate," Phys. Rev. Lett. 90, 243901 (2003).
[CrossRef] [PubMed]

Cojocaru, C.

Corradi, G.

J. Janszky, G. Corradi, and R. N. Gyuzalian, "On a possibility of analysing the temporal characteristics of short pulses," Opt. Commum. 23, 293-298 (1977).
[CrossRef]

Fischer, B.

M. Horowitz, A. Bekker, and B. Fischer, "Broadband second-harmonic generation in SrBaNb2O6 by spread spectrum phase matching with controllable domain gratings," Appl. Phys. Lett. 62, 2619-2621 (1993).
[CrossRef]

Fischer, R.

S. M. Saltiel, D. N. Neshev, R. Fischer, A. Arie, W. Krolikowski, and Yu. S. Kivshar, "Spatiotemporal toroidal waves from the transverse second-harmonic generation," Opt. Lett. 33, 527-529 (2008).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

J. Trull, C. Cojocaru, R. Fischer, S. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N Neshev, W. Krolikowski, and Yu. S. Kivshar, "Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures," Opt. Express 15, 15868-15877 (2007).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. Saltiel, W. Krolikowski, and Yu. S. Kivshar, "Broadband femtosecond frequency doubling in random media," Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Garcia Sole, J.

J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase- matchingsecond-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
[CrossRef]

Gonzalo, J. A.

J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase- matchingsecond-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
[CrossRef]

Gyuzalian, R. N.

J. Janszky, G. Corradi, and R. N. Gyuzalian, "On a possibility of analysing the temporal characteristics of short pulses," Opt. Commum. 23, 293-298 (1977).
[CrossRef]

Haidar, R.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
[CrossRef]

Herrero, R.

Horowitz, M.

M. Horowitz, A. Bekker, and B. Fischer, "Broadband second-harmonic generation in SrBaNb2O6 by spread spectrum phase matching with controllable domain gratings," Appl. Phys. Lett. 62, 2619-2621 (1993).
[CrossRef]

Ishida, Y.

Y. Ishida, T. Yajima, and A. Watanabe, "A simple monitoring system for single subpicosecond laser pulses," Opt. Commun. 56, 57-60 (1985).
[CrossRef]

Ivleva, L.

M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, "Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible," J. Appl. Phys. 95, 6185-6191 (2004).
[CrossRef]

Janszky, J.

J. Janszky, G. Corradi, and R. N. Gyuzalian, "On a possibility of analysing the temporal characteristics of short pulses," Opt. Commum. 23, 293-298 (1977).
[CrossRef]

Jaque, D.

M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, "Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible," J. Appl. Phys. 95, 6185-6191 (2004).
[CrossRef]

J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase- matchingsecond-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
[CrossRef]

Kimmel, M.

Kivshar, Yu. S.

S. M. Saltiel, D. N. Neshev, R. Fischer, A. Arie, W. Krolikowski, and Yu. S. Kivshar, "Spatiotemporal toroidal waves from the transverse second-harmonic generation," Opt. Lett. 33, 527-529 (2008).
[CrossRef] [PubMed]

J. Trull, C. Cojocaru, R. Fischer, S. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N Neshev, W. Krolikowski, and Yu. S. Kivshar, "Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures," Opt. Express 15, 15868-15877 (2007).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

R. Fischer, D. N. Neshev, S. Saltiel, W. Krolikowski, and Yu. S. Kivshar, "Broadband femtosecond frequency doubling in random media," Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Krolikowski, W.

S. M. Saltiel, D. N. Neshev, R. Fischer, A. Arie, W. Krolikowski, and Yu. S. Kivshar, "Spatiotemporal toroidal waves from the transverse second-harmonic generation," Opt. Lett. 33, 527-529 (2008).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

J. Trull, C. Cojocaru, R. Fischer, S. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N Neshev, W. Krolikowski, and Yu. S. Kivshar, "Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures," Opt. Express 15, 15868-15877 (2007).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. Saltiel, W. Krolikowski, and Yu. S. Kivshar, "Broadband femtosecond frequency doubling in random media," Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Kupecek, Ph.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
[CrossRef]

Lemasson, Ph.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
[CrossRef]

Molina, P.

P. Molina, M. O. Ramirez, and L. E. Bausa, "Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonlinear "Photonic Glass," Adv. Funct. Mat. 18, 709-715 (2008).
[CrossRef]

Neshev, D. N

Neshev, D. N.

S. M. Saltiel, D. N. Neshev, R. Fischer, A. Arie, W. Krolikowski, and Yu. S. Kivshar, "Spatiotemporal toroidal waves from the transverse second-harmonic generation," Opt. Lett. 33, 527-529 (2008).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

R. Fischer, D. N. Neshev, S. Saltiel, W. Krolikowski, and Yu. S. Kivshar, "Broadband femtosecond frequency doubling in random media," Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

O???Shea, P.

Ramirez, M. O.

P. Molina, M. O. Ramirez, and L. E. Bausa, "Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonlinear "Photonic Glass," Adv. Funct. Mat. 18, 709-715 (2008).
[CrossRef]

M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, "Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible," J. Appl. Phys. 95, 6185-6191 (2004).
[CrossRef]

Romero, J. J.

J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase- matchingsecond-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
[CrossRef]

Rosencher, E.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
[CrossRef]

Saltiel, S.

Saltiel, S. M.

S. M. Saltiel, D. N. Neshev, R. Fischer, A. Arie, W. Krolikowski, and Yu. S. Kivshar, "Spatiotemporal toroidal waves from the transverse second-harmonic generation," Opt. Lett. 33, 527-529 (2008).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

S. M. Saltiel, S. D. Savov, I. V. Tomov, and L. S. Telegin, "Subnanosecond pulse duration measurements by noncollinear second harmonic generation," Opt. Commun. 38, 443-447 (1981).
[CrossRef]

Savov, S. D.

S. M. Saltiel, S. D. Savov, I. V. Tomov, and L. S. Telegin, "Subnanosecond pulse duration measurements by noncollinear second harmonic generation," Opt. Commun. 38, 443-447 (1981).
[CrossRef]

Staliunas, K.

Sukhorukov, A. A.

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

Telegin, L. S.

S. M. Saltiel, S. D. Savov, I. V. Tomov, and L. S. Telegin, "Subnanosecond pulse duration measurements by noncollinear second harmonic generation," Opt. Commun. 38, 443-447 (1981).
[CrossRef]

Tomov, I. V.

S. M. Saltiel, S. D. Savov, I. V. Tomov, and L. S. Telegin, "Subnanosecond pulse duration measurements by noncollinear second harmonic generation," Opt. Commun. 38, 443-447 (1981).
[CrossRef]

Trebino, R.

Trull, J.

Tunyagi, A. R.

A. R. Tunyagi, M. Ulex, and K. Betzler, "Noncollinear optical frequency doubling in strontium barium niobate," Phys. Rev. Lett. 90, 243901 (2003).
[CrossRef] [PubMed]

Ulex, M.

A. R. Tunyagi, M. Ulex, and K. Betzler, "Noncollinear optical frequency doubling in strontium barium niobate," Phys. Rev. Lett. 90, 243901 (2003).
[CrossRef] [PubMed]

Vilaseca, R.

Watanabe, A.

Y. Ishida, T. Yajima, and A. Watanabe, "A simple monitoring system for single subpicosecond laser pulses," Opt. Commun. 56, 57-60 (1985).
[CrossRef]

Yajima, T.

Y. Ishida, T. Yajima, and A. Watanabe, "A simple monitoring system for single subpicosecond laser pulses," Opt. Commun. 56, 57-60 (1985).
[CrossRef]

Adv. Funct. Mat.

P. Molina, M. O. Ramirez, and L. E. Bausa, "Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonlinear "Photonic Glass," Adv. Funct. Mat. 18, 709-715 (2008).
[CrossRef]

Appl. Phys. Lett.

M. Horowitz, A. Bekker, and B. Fischer, "Broadband second-harmonic generation in SrBaNb2O6 by spread spectrum phase matching with controllable domain gratings," Appl. Phys. Lett. 62, 2619-2621 (1993).
[CrossRef]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

R. Fischer, D. N. Neshev, S. Saltiel, W. Krolikowski, and Yu. S. Kivshar, "Broadband femtosecond frequency doubling in random media," Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

J. Appl. Phys.

J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase- matchingsecond-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
[CrossRef]

M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, "Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible," J. Appl. Phys. 95, 6185-6191 (2004).
[CrossRef]

Nature (London)

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
[CrossRef]

Opt. Commum.

J. Janszky, G. Corradi, and R. N. Gyuzalian, "On a possibility of analysing the temporal characteristics of short pulses," Opt. Commum. 23, 293-298 (1977).
[CrossRef]

Opt. Commun.

S. M. Saltiel, S. D. Savov, I. V. Tomov, and L. S. Telegin, "Subnanosecond pulse duration measurements by noncollinear second harmonic generation," Opt. Commun. 38, 443-447 (1981).
[CrossRef]

Y. Ishida, T. Yajima, and A. Watanabe, "A simple monitoring system for single subpicosecond laser pulses," Opt. Commun. 56, 57-60 (1985).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

A. R. Tunyagi, M. Ulex, and K. Betzler, "Noncollinear optical frequency doubling in strontium barium niobate," Phys. Rev. Lett. 90, 243901 (2003).
[CrossRef] [PubMed]

Other

A. R. Tunyagi, "Non-Collinear Second Harmonic Generation in Strontium Barium Niobate," PhD thesis, Fachbereich Physik, Universit¨at Osnabr¨uck, Germany (2004).

G. Agrawal, Nonlinear Fiber Optics, Ch. 3, (Academic Press, 2007).

Supplementary Material (3)

» Media 1: MOV (22 KB)     
» Media 2: MOV (309 KB)     
» Media 3: MOV (3872 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of the phase-matching diagram demonstrating the planar emission of the SH wave via interaction of two noncollinear pumps with bisector coinciding with crystal axis X. Gi being the reciprocal vectors of the disordered nonlinear crystal. (b) Overlap of the beams A and B and the overlap of the short pulses forming a narrow line inside the crystal.

Fig. 2.
Fig. 2.

Photographic images of the SH emission in the transverse (a) and forward (b) directions via noncollinear waves interaction. The middle line in both photos corresponds to the planar SH emission as a result of the mixing of the two beams/pulses A and B (λ=810 nm). These central traces disappear if one of the input beams (A or B) is blocked or if the pulses do not overlap inside the crystal. The two arcs on both sides of the central lines represent the conical emission from each individual pump beam [3, 4, 6]. Media 1 shows images recorded in forward direction: right beam (A) blocked; left beam (B) blocked; both beams ON - big delay between the femtosecond pulses; both beams ON - no delay between the femtosecond pulses.

Fig. 3.
Fig. 3.

Left: The AC trace of transversely emitted SHG from two intersecting fundamental beams. The movie Media 2 associated with this photo shows the change of the position of the AC trace with variation of the delay between the pulses. Each step corresponds to 104 fs delay. Right: Detailed profile of the AC trace.

Fig. 4.
Fig. 4.

(a-b) Comparison of the thicknesses of the planar SH emission in the case of (a) nanosecond and (b) femtosecond pulses; (c) cross-correlation of a single and double femtosecond pulses. The delay between two constituent pulses in the doublet is 837 fs. (d) The Media 3 illustrates schematically the formation of AC trace, cross-correlation trace, and pulse-front tilt.

Fig. 5.
Fig. 5.

Left: Increase of the FWHM width of the AC trace as a function of the distance from the input face of the SBN crystal for three different alignments of the femtosecond laser. The lines represent the predicted AC trace broadening for the cases without input chirp, with a linear input chirp of C=0.55, and with a linear input chirp of C=1.3. Right: Measured spectra of the fundamental and SH signals.

Equations (4)

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Δ z = τ u ( 2 sin α ) ,
β = cos 1 [ ( 2 k 1 k 2 ) sin α ] .
Δ z ( x ) Δ z 0 = τ chirp ( x ) τ 0 ,
τ chirp ( x ) = τ 0 ( 1 + 4 ln 2 C β 2 x τ 0 2 ) 2 + ( 4 ln 2 β 2 x τ 0 2 ) 2 ,

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