Abstract

We study second harmonic generation via nonlinear Raman-Nath diffraction in an optical superlattice that maintains a periodic modulation of the second-order nonlinear coefficient χ(2) in transverse direction but undergoes random modulation in longitudinal direction. We show that the random χ(2) modulation offers a continuous set of reciprocal lattice vectors to compensate for the phase mismatch of nonlinear Raman-Nath diffraction in the longitudinal direction, leading to more efficient harmonic generation for a wide range of wavelengths. We also characterize the intensity dependence of nonlinear Raman-Nath diffraction on the degree of randomness of the optical supperlattice.

© 2013 OSA

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References

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  1. M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–437 (1993).
    [Crossref]
  2. L. E. Myers, R. C. Eckardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2012–2116 (1995).
    [Crossref]
  3. S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
    [Crossref]
  4. R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
    [Crossref] [PubMed]
  5. I. Freund, “Nonlinear diffraction,” Phys. Rev. Lett. 21, 1404–1406 (1968).
    [Crossref]
  6. S. M. Saltiel, D. N. Neshev, R. Fischer, W. K. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
    [Crossref] [PubMed]
  7. S. M. Saltiel, D. N. Neshev, W. K. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34, 848–850 (2009).
    [Crossref] [PubMed]
  8. X. Deng, H. Ren, H. Lao, and X. Chen, “Non-collinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B 100, 755–758 (2010).
    [Crossref]
  9. N. An, H. Ren, Y Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett. 100, 221103 (2012).
    [Crossref]
  10. Y. Sheng, A. Best, H-J. Butt, W. Krolikowksi, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (2010).
    [Crossref] [PubMed]
  11. Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, “Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal,” Opt. Lett. 36, 3266–3268 (2011).
    [Crossref] [PubMed]
  12. Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100, 163904 (2008).
    [Crossref] [PubMed]
  13. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), Chap. 12.
  14. S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. K. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
    [Crossref] [PubMed]
  15. A. Shapira and A. Arie, “Phase-matched nonlinear diffraction,” Opt. Lett. 36, 1933–1935 (2011).
    [Crossref] [PubMed]
  16. 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]
  17. A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photonics J 2, 18–28 (2010).
    [Crossref]
  18. W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Y. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
    [Crossref] [PubMed]
  19. J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D.N. Neshev, R. Vilaseca, K. Staliunas, and Y.S. Kivshar, “Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media,” Appl. Phys. B 95, 609–615 (2009).
    [Crossref]
  20. Th. Woike, T. Granzow, U. Dörfler, Ch. Poesch, M. Wöhlecke, and R. Pankrath, “Refractive indices of congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi A 186, R13–R15 (2001).
    [Crossref]

2012 (1)

N. An, H. Ren, Y Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett. 100, 221103 (2012).
[Crossref]

2011 (2)

2010 (3)

Y. Sheng, A. Best, H-J. Butt, W. Krolikowksi, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (2010).
[Crossref] [PubMed]

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photonics J 2, 18–28 (2010).
[Crossref]

X. Deng, H. Ren, H. Lao, and X. Chen, “Non-collinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B 100, 755–758 (2010).
[Crossref]

2009 (3)

2008 (3)

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100, 163904 (2008).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. K. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. K. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

2005 (1)

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[Crossref] [PubMed]

2004 (1)

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]

2001 (1)

Th. Woike, T. Granzow, U. Dörfler, Ch. Poesch, M. Wöhlecke, and R. Pankrath, “Refractive indices of congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi A 186, R13–R15 (2001).
[Crossref]

1997 (1)

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[Crossref]

1995 (1)

L. E. Myers, R. C. Eckardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2012–2116 (1995).
[Crossref]

1993 (1)

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–437 (1993).
[Crossref]

1968 (1)

I. Freund, “Nonlinear diffraction,” Phys. Rev. Lett. 21, 1404–1406 (1968).
[Crossref]

An, N.

N. An, H. Ren, Y Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett. 100, 221103 (2012).
[Crossref]

Arie, A.

A. Shapira and A. Arie, “Phase-matched nonlinear diffraction,” Opt. Lett. 36, 1933–1935 (2011).
[Crossref] [PubMed]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, “Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal,” Opt. Lett. 36, 3266–3268 (2011).
[Crossref] [PubMed]

Y. Sheng, A. Best, H-J. Butt, W. Krolikowksi, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (2010).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, W. K. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34, 848–850 (2009).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. K. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. K. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[Crossref] [PubMed]

Assanto, G.

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photonics J 2, 18–28 (2010).
[Crossref]

Bahabad, A.

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[Crossref] [PubMed]

Bang, O.

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]

Best, A.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), Chap. 12.

Busacca, A.

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photonics J 2, 18–28 (2010).
[Crossref]

Butt, H-J.

Byer, R. L.

L. E. Myers, R. C. Eckardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2012–2116 (1995).
[Crossref]

Chen, X.

N. An, H. Ren, Y Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett. 100, 221103 (2012).
[Crossref]

X. Deng, H. Ren, H. Lao, and X. Chen, “Non-collinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B 100, 755–758 (2010).
[Crossref]

Cojocaru, C.

J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D.N. Neshev, R. Vilaseca, K. Staliunas, and Y.S. Kivshar, “Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media,” Appl. Phys. B 95, 609–615 (2009).
[Crossref]

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Y. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
[Crossref] [PubMed]

Deng, X.

N. An, H. Ren, Y Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett. 100, 221103 (2012).
[Crossref]

X. Deng, H. Ren, H. Lao, and X. Chen, “Non-collinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B 100, 755–758 (2010).
[Crossref]

Dörfler, U.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poesch, M. Wöhlecke, and R. Pankrath, “Refractive indices of congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi A 186, R13–R15 (2001).
[Crossref]

Dumay, D.

J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D.N. Neshev, R. Vilaseca, K. Staliunas, and Y.S. Kivshar, “Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media,” Appl. Phys. B 95, 609–615 (2009).
[Crossref]

Eckardt, R. C.

L. E. Myers, R. C. Eckardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2012–2116 (1995).
[Crossref]

Fejer, M. M.

L. E. Myers, R. C. Eckardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2012–2116 (1995).
[Crossref]

Fischer, R.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. K. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

Freund, I.

I. Freund, “Nonlinear diffraction,” Phys. Rev. Lett. 21, 1404–1406 (1968).
[Crossref]

Gao, Z. D.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100, 163904 (2008).
[Crossref] [PubMed]

Granzow, T.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poesch, M. Wöhlecke, and R. Pankrath, “Refractive indices of congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi A 186, R13–R15 (2001).
[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]

Kalinowski, K.

Kivshar, Y.

Kivshar, Y. S.

S. M. Saltiel, D. N. Neshev, W. K. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34, 848–850 (2009).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. K. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. K. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

Kivshar, Y.S.

J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D.N. Neshev, R. Vilaseca, K. Staliunas, and Y.S. Kivshar, “Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media,” Appl. Phys. B 95, 609–615 (2009).
[Crossref]

Kong, Y.

Koynov, K.

Y. Sheng, A. Best, H-J. Butt, W. Krolikowksi, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (2010).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. K. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

Krolikowksi, W.

Krolikowski, W.

Krolikowski, W. K.

S. M. Saltiel, D. N. Neshev, W. K. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34, 848–850 (2009).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. K. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. K. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

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]

Lao, H.

X. Deng, H. Ren, H. Lao, and X. Chen, “Non-collinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B 100, 755–758 (2010).
[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]

Lifshitz, R.

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[Crossref] [PubMed]

Ming, N. B.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100, 163904 (2008).
[Crossref] [PubMed]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[Crossref]

Morandotti, R.

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photonics J 2, 18–28 (2010).
[Crossref]

Myers, L. E.

L. E. Myers, R. C. Eckardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2012–2116 (1995).
[Crossref]

Nada, N.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–437 (1993).
[Crossref]

Neshev, D. N.

S. M. Saltiel, D. N. Neshev, W. K. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34, 848–850 (2009).
[Crossref] [PubMed]

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Y. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. K. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. K. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

Neshev, D.N.

J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D.N. Neshev, R. Vilaseca, K. Staliunas, and Y.S. Kivshar, “Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media,” Appl. Phys. B 95, 609–615 (2009).
[Crossref]

Pankrath, R.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poesch, M. Wöhlecke, and R. Pankrath, “Refractive indices of congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi A 186, R13–R15 (2001).
[Crossref]

Pasquazi, A.

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photonics J 2, 18–28 (2010).
[Crossref]

Poesch, Ch.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poesch, M. Wöhlecke, and R. Pankrath, “Refractive indices of congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi A 186, R13–R15 (2001).
[Crossref]

Qi, Z.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100, 163904 (2008).
[Crossref] [PubMed]

Ren, H.

N. An, H. Ren, Y Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett. 100, 221103 (2012).
[Crossref]

X. Deng, H. Ren, H. Lao, and X. Chen, “Non-collinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B 100, 755–758 (2010).
[Crossref]

Roppo, V.

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]

Saitoh, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–437 (1993).
[Crossref]

Saltiel, S.

J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D.N. Neshev, R. Vilaseca, K. Staliunas, and Y.S. Kivshar, “Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media,” Appl. Phys. B 95, 609–615 (2009).
[Crossref]

Saltiel, S. M.

S. M. Saltiel, D. N. Neshev, W. K. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34, 848–850 (2009).
[Crossref] [PubMed]

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Y. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. K. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. K. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

Shapira, A.

Sheng, Y.

Shiloh, R.

Staliunas, K.

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Y. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
[Crossref] [PubMed]

J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D.N. Neshev, R. Vilaseca, K. Staliunas, and Y.S. Kivshar, “Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media,” Appl. Phys. B 95, 609–615 (2009).
[Crossref]

Stivala, S.

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photonics J 2, 18–28 (2010).
[Crossref]

Trull, J.

J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D.N. Neshev, R. Vilaseca, K. Staliunas, and Y.S. Kivshar, “Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media,” Appl. Phys. B 95, 609–615 (2009).
[Crossref]

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Y. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
[Crossref] [PubMed]

Vilaseca, R.

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Y. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
[Crossref] [PubMed]

J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D.N. Neshev, R. Vilaseca, K. Staliunas, and Y.S. Kivshar, “Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media,” Appl. Phys. B 95, 609–615 (2009).
[Crossref]

Voloch-Bloch, N.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. K. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

Wang, W.

Watanabe, K.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–437 (1993).
[Crossref]

Wöhlecke, M.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poesch, M. Wöhlecke, and R. Pankrath, “Refractive indices of congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi A 186, R13–R15 (2001).
[Crossref]

Woike, Th.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poesch, M. Wöhlecke, and R. Pankrath, “Refractive indices of congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi A 186, R13–R15 (2001).
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Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), Chap. 12.

Yamada, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–437 (1993).
[Crossref]

Zhang, Y.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100, 163904 (2008).
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Zheng, Y

N. An, H. Ren, Y Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett. 100, 221103 (2012).
[Crossref]

Zhu, S. N.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100, 163904 (2008).
[Crossref] [PubMed]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[Crossref]

Zhu, Y. Y.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[Crossref]

Appl. Phys. B (2)

X. Deng, H. Ren, H. Lao, and X. Chen, “Non-collinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B 100, 755–758 (2010).
[Crossref]

J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D.N. Neshev, R. Vilaseca, K. Staliunas, and Y.S. Kivshar, “Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media,” Appl. Phys. B 95, 609–615 (2009).
[Crossref]

Appl. Phys. Lett. (2)

N. An, H. Ren, Y Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett. 100, 221103 (2012).
[Crossref]

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–437 (1993).
[Crossref]

IEEE Photonics J (1)

A. Pasquazi, A. Busacca, S. Stivala, R. Morandotti, and G. Assanto, “Nonlinear disorder mapping through three-wave mixing,” IEEE Photonics J 2, 18–28 (2010).
[Crossref]

J. Opt. Soc. Am. B (1)

L. E. Myers, R. C. Eckardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2012–2116 (1995).
[Crossref]

Nature (London) (1)

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. Express (2)

Opt. Lett. (3)

Phys. Rev. Lett. (5)

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. K. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100, 163904 (2008).
[Crossref] [PubMed]

R. Lifshitz, A. Arie, and A. Bahabad, “Photonic quasicrystals for nonlinear optical frequency conversion,” Phys. Rev. Lett. 95, 133901 (2005).
[Crossref] [PubMed]

I. Freund, “Nonlinear diffraction,” Phys. Rev. Lett. 21, 1404–1406 (1968).
[Crossref]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. K. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
[Crossref] [PubMed]

Phys. Status Solidi A (1)

Th. Woike, T. Granzow, U. Dörfler, Ch. Poesch, M. Wöhlecke, and R. Pankrath, “Refractive indices of congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi A 186, R13–R15 (2001).
[Crossref]

Science (1)

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[Crossref]

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), Chap. 12.

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Figures (5)

Fig. 1
Fig. 1

(a) Nonlinear diffraction with fundamental beam propagating perpendicularly to the alternating direction of the sign of second order susceptibility χ(2) in an optical superlattice. Phase matching diagram for (b) nonlinear Bragg diffraction, (c) nonlinear Raman-Nath diffraction, and (d) nonlinear Čerenkov diffraction. NL stands for nonlinear; l, m, n are integers.

Fig. 2
Fig. 2

(a) Schematic of two-dimensional optical superlattice with a periodic χ(2) modulation in the transverse direction (y) and a random distribution along the longitudinal direction (x). (b)–(c): Fourier spectra of the superlattices with different degrees of randomness in the x direction: σ =0 μm and σ =1.2 μm, respectively (for better visualization of reciprocal vectors involved in the first-order (m = ±1) nonlinear Raman-Nath diffraction, colors are oversaturated). The absolute value of (q, G0) which represents the first-order Raman-Nath diffraction is shown in Figs. 2(d)–2(f) for increasing degrees of randomness: σ =0 μm, σ =0.6μm, and σ =1.2μm.

Fig. 3
Fig. 3

The average intensity of the first-order nonlinear Raman-Nath diffraction signal in the randomized QPM structure as a function of the wavelength of the incident fundamental beam. The dashed line and dot-dashed line represents randomized structure with σ =1.2μm and σ =0.6μm, respectively, while the solid line corresponds to the fully periodic case (σ = 0μm). The average intensity has been calculated by averaging over 512 realizations of the random domain structure. In all simulations the propagation distance was 1480μm.

Fig. 4
Fig. 4

Far field spatial average intensity distribution of the first-order Raman-Nath second harmonic wave as a function of propagation distance in nonlinear χ(2) structures with different degree of randomness and different incident wavelengths (λ). (a) λ =1.35μm, σ =0μm; (b) λ =1.45μm, σ =0μm; (c) λ =1.35μm, σ =1.2μm; (d) λ =1.45μm, σ =1.2μm. The average intensity was obtained by averaging over 512 realizations of domain structure.

Fig. 5
Fig. 5

Intensity of the first-order Raman-Nath second harmonic beam (averaged over 512 random realizations) as a function of the propagation distance, for few values of the degree of randomness σ at two values of the fundamental wavelengths λ =1.40μm (a) and λ =1.35μm (b).

Equations (13)

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g ( x , y ) = m = 0 , ± 1 , e i m G 0 y g ˜ ( x , m G 0 ) = m = 0 , ± 1 , e i m G 0 y q g ˜ ( q , m G 0 ) e i q x d q ,
( x + i 2 k 2 2 y 2 ) A 2 ( x , y ) = i β 2 g ( x , y ) A 1 2 ( y ) e i Δ k x ,
( x i k y 2 2 k 2 ) A ˜ 2 ( x , k y ) = i β 2 g ( x , y ) A 1 2 ( y ) e i k y y e i Δ k x d y .
G ˜ 2 ( x , k y ) x = i β 2 w A o 2 π / 2 e i ( Δ k k y 2 / 2 k 2 ) x m = 0 , ± 1 , g ˜ ( x , m G 0 ) e w 2 ( m G 0 + k y ) 2 / 8
G ˜ 2 ( x , k y ) = β 2 w A o 2 x π / 2 e i x ( Δ k k y 2 / 2 k 2 + q ) / 2 × m = 0 , ± 1 , q g ˜ ( q , m G 0 ) sinc ( x ( Δ k k y 2 / 2 k 2 + q ) / 2 ) d q × e w 2 ( m G 0 + k y ) 2 / 8 ,
S ˜ 2 ( x , k y ) = π Γ 2 x 2 / 2 ( m = 0 , ± 1 , q g ˜ ( q , m G 0 ) sinc ( x ( Δ k k y 2 / 2 k 2 + q ) / 2 ) d q × e w 2 ( m G 0 + k y ) 2 / 8 ) 2
m G 0 + k y = 0
Δ k k y 2 / 2 k 2 + q = k 2 cos α m 2 k 1 + q
q = 2 k 1 k 2 cos α m ,
g ( x , y ) = 1 + l = 0 , 2 , 4 , 2 M ( f ( x ) 1 ) Π y l , y l + 1 ( y ) ,
f ( x ) = k = 0 N ( 1 ) k Π x k , x k + 1 ( x ) ,
y l + 1 = y l + Λ / 2 ,
x k + 1 = x k + N k ( ρ 0 , σ ) ,

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