Abstract

We discuss the effect of second harmonic generation via the Čerenkov-like process in nonlinear bulk media and waveguides. We show that in both schemes the Čerenkov harmonic emission represents in fact a nonlinear Bragg diffraction process. It is therefore possible, for the first time, to describe the bulk and waveguide Čerenkov emission uniformly by considering the spatial modulation of the second-order nonlinear polarization. This is also experimentally illustrated by studying the Čerenkov second harmonic generation at the boundary of a nonlinear quadratic medium via the total internal reflection inside the nonlinear crystal.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures,” Japan. J. Appl. Phys.47, 6777–6783 (2009).
    [CrossRef]
  4. Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express18, 16539–16545 (2010).
    [CrossRef] [PubMed]
  5. J. Chen and X. Chen, “Domain wall characterization in ferroelectrics by using localized nonlinearities,” Opt. Express18, 15597–15602 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged Lithium niobate guides,” IEEE J. Quantum Electron.26, 1384–1393 (1990).
    [CrossRef]
  8. S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
    [CrossRef]
  9. X. W. Deng, H. J. Ren, H. Y. Lao, and X. F. Chen, “Research on Cherenkov second-harmonic generation in periodically poled lithium niobate by femtosecond pulses,” J. Opt. Soc. Am. B27, 1475–1480 (2010).
    [CrossRef]
  10. K. Hayata, K. Yanagawa, and M. Koshiba, “Enhancement of the guided-wave second-harmonic generation in the form of Cerenkov radiation,” Appl. Phys. Lett.56, 206–208 (1989).
    [CrossRef]
  11. K. Chikuma and S. Umegaki, “Theory of optical second-harmonic generation in crystal-cored fibers based on phase matching of Cerenkov-type radiation,” J. Opt. Soc. Am. B9, 1083–1091 (1992).
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    [CrossRef] [PubMed]
  15. Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett.98, 241114 (2011).
    [CrossRef]
  16. X. W. Deng, H. J. Ren, H. Lao, and X. F. Chen, “Noncollinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B100, 755–758 (2010).
    [CrossRef]
  17. K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, “Wavelength and position tuning of Čerenkov second-harmonic generation in optical superlattice,” Appl. Phys. Lett.99, 181128 (2011).
    [CrossRef]
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    [CrossRef]
  20. H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett.108, 223901 (2012).
    [CrossRef] [PubMed]
  21. W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple Cerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett.35, 3790–3792 (2010).
    [CrossRef] [PubMed]
  22. S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling process,” Opt. Lett.34, 848–850 (2009).
    [CrossRef] [PubMed]
  23. A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” App. Phys. Lett.85, 375–377 (2004).
    [CrossRef]
  24. S. J. Holmgren, C. Canalias, and V. Pasiskevicius, “Ultrashort single-shot pulse characterization with high spatial resolution using localized nonlinearities in ferroelectric domain walls,” Opt. Lett.32, 1545–1547 (2007).
    [CrossRef] [PubMed]
  25. Y. Sheng, V. Roppo, K. Kalinowski, and W. Krolikowski, “Role of a localized modulation of χ(2)in Cerenkov second-harmonic generation in nonlinear bulk medium,” Opt. Lett.37, 3864–3866 (2012).
    [CrossRef] [PubMed]
  26. V. Berger, “Nonlinear Photonic Crystals,” Phys. Rev. Lett.81, 4136–4139 (1998).
    [CrossRef]
  27. N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett.84, 4345–4348 (2000).
    [CrossRef] [PubMed]
  28. S. M. Saltiel, D. N. Neshev, R. Fischer, W. 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]
  29. A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser and Photon. Rev.4, 355–373 (2010).
    [CrossRef]
  30. J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
    [CrossRef]
  31. N. Bloembergen, “Conservation laws in nonlinear optics,” J. Opt. Soc. Am.70, 1429–1436 (1980).
    [CrossRef]
  32. N. Bloembergen, H. J. Simon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev.181, 1261–1271 (1969).
    [CrossRef]
  33. S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Yu. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett.104, 083902 (2010).
    [CrossRef] [PubMed]
  34. M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
    [CrossRef] [PubMed]
  35. E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase-mismatched second-harmonic generation,” Opt. Express17, 3141–3147 (2009).
    [CrossRef] [PubMed]

2012

2011

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett.98, 241114 (2011).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, “Wavelength and position tuning of Čerenkov second-harmonic generation in optical superlattice,” Appl. Phys. Lett.99, 181128 (2011).
[CrossRef]

2010

2009

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase-mismatched second-harmonic generation,” Opt. Express17, 3141–3147 (2009).
[CrossRef] [PubMed]

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

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures,” Japan. J. Appl. Phys.47, 6777–6783 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
[CrossRef]

2008

S. M. Saltiel, D. N. Neshev, R. Fischer, W. 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]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

2007

2004

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” App. Phys. Lett.85, 375–377 (2004).
[CrossRef]

2000

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett.84, 4345–4348 (2000).
[CrossRef] [PubMed]

1998

V. Berger, “Nonlinear Photonic Crystals,” Phys. Rev. Lett.81, 4136–4139 (1998).
[CrossRef]

1997

1996

G. J. M. Krijnen, W. Tormellas, G. I. Stegeman, H. J. W. M. Hoekstra, and P. V. Lambeck, “Optimization of second harmonic generation and nonlinear phase-shifts in the Cerenkov regime,” IEEE J. Quantum Electron.32, 729–738 (1996).
[CrossRef]

1993

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett.70, 1401–1404 (1993).
[CrossRef] [PubMed]

1992

1990

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged Lithium niobate guides,” IEEE J. Quantum Electron.26, 1384–1393 (1990).
[CrossRef]

1989

K. Hayata, K. Yanagawa, and M. Koshiba, “Enhancement of the guided-wave second-harmonic generation in the form of Cerenkov radiation,” Appl. Phys. Lett.56, 206–208 (1989).
[CrossRef]

1980

1970

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett.17, 447–450 (1970).
[CrossRef]

1969

A. Zembrod, H. Puell, and J. A. Giordmaine, “Surface Radiation from Non-linear Optical Polarisation,” Opto-electron.1, 64–66 (1969).
[CrossRef]

E. Mathieu, “Conditions for quasi Cerenkov radiation, generated by optical second harmonic polarisation in a nonlinear cristal,” Z. Angew. Math. Phys.20, 433–439 (1969).
[CrossRef]

N. Bloembergen, H. J. Simon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev.181, 1261–1271 (1969).
[CrossRef]

1962

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Akozbek, N.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

Alonzo, M.

Amstrong, J. A.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

An, N.

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett.108, 223901 (2012).
[CrossRef] [PubMed]

Arie, A.

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett.98, 241114 (2011).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, “Wavelength and position tuning of Čerenkov second-harmonic generation in optical superlattice,” Appl. Phys. Lett.99, 181128 (2011).
[CrossRef]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple Cerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett.35, 3790–3792 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Yu. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett.104, 083902 (2010).
[CrossRef] [PubMed]

Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express18, 16539–16545 (2010).
[CrossRef] [PubMed]

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser and Photon. Rev.4, 355–373 (2010).
[CrossRef]

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

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures,” Japan. J. Appl. Phys.47, 6777–6783 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. 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]

Ayoub, M.

Bang, O.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Yu. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett.104, 083902 (2010).
[CrossRef] [PubMed]

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

Belardini, A.

Berger, V.

V. Berger, “Nonlinear Photonic Crystals,” Phys. Rev. Lett.81, 4136–4139 (1998).
[CrossRef]

Bertolotti, M.

Best, A.

Bloch, N.

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
[CrossRef]

Bloembergen, N.

N. Bloembergen, “Conservation laws in nonlinear optics,” J. Opt. Soc. Am.70, 1429–1436 (1980).
[CrossRef]

N. Bloembergen, H. J. Simon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev.181, 1261–1271 (1969).
[CrossRef]

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Bloemer, M. J.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

Broderick, N. G. R.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett.84, 4345–4348 (2000).
[CrossRef] [PubMed]

Butt, H.

Canalias, C.

Centini, M.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase-mismatched second-harmonic generation,” Opt. Express17, 3141–3147 (2009).
[CrossRef] [PubMed]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

Chauvet, M.

Chen, J.

Chen, X.

Chen, X. F.

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett.108, 223901 (2012).
[CrossRef] [PubMed]

X. W. Deng, H. J. Ren, H. Y. Lao, and X. F. Chen, “Research on Cherenkov second-harmonic generation in periodically poled lithium niobate by femtosecond pulses,” J. Opt. Soc. Am. B27, 1475–1480 (2010).
[CrossRef]

X. W. Deng, H. J. Ren, H. Lao, and X. F. Chen, “Noncollinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B100, 755–758 (2010).
[CrossRef]

Chikuma, K.

Cojocaru, C.

De Micheli, M.

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged Lithium niobate guides,” IEEE J. Quantum Electron.26, 1384–1393 (1990).
[CrossRef]

Deng, X. W.

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett.108, 223901 (2012).
[CrossRef] [PubMed]

X. W. Deng, H. J. Ren, H. Y. Lao, and X. F. Chen, “Research on Cherenkov second-harmonic generation in periodically poled lithium niobate by femtosecond pulses,” J. Opt. Soc. Am. B27, 1475–1480 (2010).
[CrossRef]

X. W. Deng, H. J. Ren, H. Lao, and X. F. Chen, “Noncollinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B100, 755–758 (2010).
[CrossRef]

Denz, C.

Ducuing, J.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Fazio, E.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase-mismatched second-harmonic generation,” Opt. Express17, 3141–3147 (2009).
[CrossRef] [PubMed]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

Fischer, R.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures,” Japan. J. Appl. Phys.47, 6777–6783 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. 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]

Foreman, J. V.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

Fragemann, A.

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” App. Phys. Lett.85, 375–377 (2004).
[CrossRef]

Giordmaine, J. A.

A. Zembrod, H. Puell, and J. A. Giordmaine, “Surface Radiation from Non-linear Optical Polarisation,” Opto-electron.1, 64–66 (1969).
[CrossRef]

Hanna, D. C.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett.84, 4345–4348 (2000).
[CrossRef] [PubMed]

Haus, J. W.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

Hayata, K.

K. Hayata, K. Yanagawa, and M. Koshiba, “Enhancement of the guided-wave second-harmonic generation in the form of Cerenkov radiation,” Appl. Phys. Lett.56, 206–208 (1989).
[CrossRef]

He, Q.

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged Lithium niobate guides,” IEEE J. Quantum Electron.26, 1384–1393 (1990).
[CrossRef]

Herminghaus, S.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett.70, 1401–1404 (1993).
[CrossRef] [PubMed]

Hoekstra, H. J. W. M.

G. J. M. Krijnen, W. Tormellas, G. I. Stegeman, H. J. W. M. Hoekstra, and P. V. Lambeck, “Optimization of second harmonic generation and nonlinear phase-shifts in the Cerenkov regime,” IEEE J. Quantum Electron.32, 729–738 (1996).
[CrossRef]

Holmgren, S. J.

Imbrock, J.

Kalinowski, K.

Kivshar, Y. S.

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
[CrossRef]

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

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures,” Japan. J. Appl. Phys.47, 6777–6783 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. 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, Yu. S.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Yu. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett.104, 083902 (2010).
[CrossRef] [PubMed]

Kong, Q.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Cerenkov-type second harmonic generation in periodically poled ferroelectric crystal,” J. Opt. Soc. Am. B29, 312–318 (2012).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, “Wavelength and position tuning of Čerenkov second-harmonic generation in optical superlattice,” Appl. Phys. Lett.99, 181128 (2011).
[CrossRef]

Kong, Y.

Kong, Y. F.

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett.98, 241114 (2011).
[CrossRef]

Koshiba, M.

K. Hayata, K. Yanagawa, and M. Koshiba, “Enhancement of the guided-wave second-harmonic generation in the form of Cerenkov radiation,” Appl. Phys. Lett.56, 206–208 (1989).
[CrossRef]

Koynov, K.

Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express18, 16539–16545 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
[CrossRef]

Krijnen, G. J. M.

G. J. M. Krijnen, W. Tormellas, G. I. Stegeman, H. J. W. M. Hoekstra, and P. V. Lambeck, “Optimization of second harmonic generation and nonlinear phase-shifts in the Cerenkov regime,” IEEE J. Quantum Electron.32, 729–738 (1996).
[CrossRef]

Krolikowski, W.

Y. Sheng, V. Roppo, K. Kalinowski, and W. Krolikowski, “Role of a localized modulation of χ(2)in Cerenkov second-harmonic generation in nonlinear bulk medium,” Opt. Lett.37, 3864–3866 (2012).
[CrossRef] [PubMed]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett.37, 1832–1834 (2012).
[CrossRef] [PubMed]

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Cerenkov-type second harmonic generation in periodically poled ferroelectric crystal,” J. Opt. Soc. Am. B29, 312–318 (2012).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, “Wavelength and position tuning of Čerenkov second-harmonic generation in optical superlattice,” Appl. Phys. Lett.99, 181128 (2011).
[CrossRef]

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett.98, 241114 (2011).
[CrossRef]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple Cerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett.35, 3790–3792 (2010).
[CrossRef] [PubMed]

Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express18, 16539–16545 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Yu. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett.104, 083902 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures,” Japan. J. Appl. Phys.47, 6777–6783 (2009).
[CrossRef]

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

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. 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]

Lambeck, P. V.

G. J. M. Krijnen, W. Tormellas, G. I. Stegeman, H. J. W. M. Hoekstra, and P. V. Lambeck, “Optimization of second harmonic generation and nonlinear phase-shifts in the Cerenkov regime,” IEEE J. Quantum Electron.32, 729–738 (1996).
[CrossRef]

Lao, H.

X. W. Deng, H. J. Ren, H. Lao, and X. F. Chen, “Noncollinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B100, 755–758 (2010).
[CrossRef]

Lao, H. Y.

Laurell, F.

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” App. Phys. Lett.85, 375–377 (2004).
[CrossRef]

Lee, C. H.

N. Bloembergen, H. J. Simon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev.181, 1261–1271 (1969).
[CrossRef]

Li, M. J.

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged Lithium niobate guides,” IEEE J. Quantum Electron.26, 1384–1393 (1990).
[CrossRef]

Martin, R. J.

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett.17, 447–450 (1970).
[CrossRef]

Mathieu, E.

E. Mathieu, “Conditions for quasi Cerenkov radiation, generated by optical second harmonic polarisation in a nonlinear cristal,” Z. Angew. Math. Phys.20, 433–439 (1969).
[CrossRef]

Neshev, D. N.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Yu. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett.104, 083902 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures,” Japan. J. Appl. Phys.47, 6777–6783 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
[CrossRef]

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

S. M. Saltiel, D. N. Neshev, R. Fischer, W. 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]

Offerhaus, H. L.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett.84, 4345–4348 (2000).
[CrossRef] [PubMed]

Ostrowsky, D. B.

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged Lithium niobate guides,” IEEE J. Quantum Electron.26, 1384–1393 (1990).
[CrossRef]

Pasiskevicius, V.

S. J. Holmgren, C. Canalias, and V. Pasiskevicius, “Ultrashort single-shot pulse characterization with high spatial resolution using localized nonlinearities in ferroelectric domain walls,” Opt. Lett.32, 1545–1547 (2007).
[CrossRef] [PubMed]

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” App. Phys. Lett.85, 375–377 (2004).
[CrossRef]

Pershan, P. S.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Pettazzi, F.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase-mismatched second-harmonic generation,” Opt. Express17, 3141–3147 (2009).
[CrossRef] [PubMed]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

Puell, H.

A. Zembrod, H. Puell, and J. A. Giordmaine, “Surface Radiation from Non-linear Optical Polarisation,” Opto-electron.1, 64–66 (1969).
[CrossRef]

Reinisch, R.

Ren, H. J.

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett.108, 223901 (2012).
[CrossRef] [PubMed]

X. W. Deng, H. J. Ren, H. Y. Lao, and X. F. Chen, “Research on Cherenkov second-harmonic generation in periodically poled lithium niobate by femtosecond pulses,” J. Opt. Soc. Am. B27, 1475–1480 (2010).
[CrossRef]

X. W. Deng, H. J. Ren, H. Lao, and X. F. Chen, “Noncollinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B100, 755–758 (2010).
[CrossRef]

Richardson, D. J.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett.84, 4345–4348 (2000).
[CrossRef] [PubMed]

Roedig, P.

Roppo, V.

Y. Sheng, V. Roppo, K. Kalinowski, and W. Krolikowski, “Role of a localized modulation of χ(2)in Cerenkov second-harmonic generation in nonlinear bulk medium,” Opt. Lett.37, 3864–3866 (2012).
[CrossRef] [PubMed]

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Cerenkov-type second harmonic generation in periodically poled ferroelectric crystal,” J. Opt. Soc. Am. B29, 312–318 (2012).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, “Wavelength and position tuning of Čerenkov second-harmonic generation in optical superlattice,” Appl. Phys. Lett.99, 181128 (2011).
[CrossRef]

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett.98, 241114 (2011).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

Ross, G. W.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett.84, 4345–4348 (2000).
[CrossRef] [PubMed]

Saltiel, S. M.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Yu. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett.104, 083902 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures,” Japan. J. Appl. Phys.47, 6777–6783 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
[CrossRef]

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

S. M. Saltiel, D. N. Neshev, R. Fischer, W. 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]

Scalora, M.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase-mismatched second-harmonic generation,” Opt. Express17, 3141–3147 (2009).
[CrossRef] [PubMed]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

Sheng, Y.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Cerenkov-type second harmonic generation in periodically poled ferroelectric crystal,” J. Opt. Soc. Am. B29, 312–318 (2012).
[CrossRef]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett.37, 1832–1834 (2012).
[CrossRef] [PubMed]

Y. Sheng, V. Roppo, K. Kalinowski, and W. Krolikowski, “Role of a localized modulation of χ(2)in Cerenkov second-harmonic generation in nonlinear bulk medium,” Opt. Lett.37, 3864–3866 (2012).
[CrossRef] [PubMed]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, “Wavelength and position tuning of Čerenkov second-harmonic generation in optical superlattice,” Appl. Phys. Lett.99, 181128 (2011).
[CrossRef]

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett.98, 241114 (2011).
[CrossRef]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple Cerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett.35, 3790–3792 (2010).
[CrossRef] [PubMed]

Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express18, 16539–16545 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
[CrossRef]

Shiloh, R.

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett.98, 241114 (2011).
[CrossRef]

Sibilia, C.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase-mismatched second-harmonic generation,” Opt. Express17, 3141–3147 (2009).
[CrossRef] [PubMed]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett.101, 113905 (2008).
[CrossRef] [PubMed]

Simon, H. J.

N. Bloembergen, H. J. Simon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev.181, 1261–1271 (1969).
[CrossRef]

Stegeman, G. I.

G. J. M. Krijnen, W. Tormellas, G. I. Stegeman, H. J. W. M. Hoekstra, and P. V. Lambeck, “Optimization of second harmonic generation and nonlinear phase-shifts in the Cerenkov regime,” IEEE J. Quantum Electron.32, 729–738 (1996).
[CrossRef]

Tien, P. K.

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett.17, 447–450 (1970).
[CrossRef]

Tormellas, W.

G. J. M. Krijnen, W. Tormellas, G. I. Stegeman, H. J. W. M. Hoekstra, and P. V. Lambeck, “Optimization of second harmonic generation and nonlinear phase-shifts in the Cerenkov regime,” IEEE J. Quantum Electron.32, 729–738 (1996).
[CrossRef]

Ulrich, R.

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett.17, 447–450 (1970).
[CrossRef]

Umegaki, S.

Vitrant, G.

Voloch, N.

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser and Photon. Rev.4, 355–373 (2010).
[CrossRef]

Voloch-Bloch, N.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Yu. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett.104, 083902 (2010).
[CrossRef] [PubMed]

Wang, Q.

Wang, W.

Wang, W. J.

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett.98, 241114 (2011).
[CrossRef]

Wulle, T.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett.70, 1401–1404 (1993).
[CrossRef] [PubMed]

Yanagawa, K.

K. Hayata, K. Yanagawa, and M. Koshiba, “Enhancement of the guided-wave second-harmonic generation in the form of Cerenkov radiation,” Appl. Phys. Lett.56, 206–208 (1989).
[CrossRef]

Zembrod, A.

A. Zembrod, H. Puell, and J. A. Giordmaine, “Surface Radiation from Non-linear Optical Polarisation,” Opto-electron.1, 64–66 (1969).
[CrossRef]

Zheng, Y. L.

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett.108, 223901 (2012).
[CrossRef] [PubMed]

App. Phys. Lett.

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” App. Phys. Lett.85, 375–377 (2004).
[CrossRef]

Appl. Phys. B

X. W. Deng, H. J. Ren, H. Lao, and X. F. Chen, “Noncollinear efficient continuous optical frequency doubling in periodically poled lithium niobate,” Appl. Phys. B100, 755–758 (2010).
[CrossRef]

Appl. Phys. Lett.

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, “Wavelength and position tuning of Čerenkov second-harmonic generation in optical superlattice,” Appl. Phys. Lett.99, 181128 (2011).
[CrossRef]

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett.17, 447–450 (1970).
[CrossRef]

K. Hayata, K. Yanagawa, and M. Koshiba, “Enhancement of the guided-wave second-harmonic generation in the form of Cerenkov radiation,” Appl. Phys. Lett.56, 206–208 (1989).
[CrossRef]

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2)nonlinear photonic crystal,” Appl. Phys. Lett.98, 241114 (2011).
[CrossRef]

IEEE J. Quantum Electron.

G. J. M. Krijnen, W. Tormellas, G. I. Stegeman, H. J. W. M. Hoekstra, and P. V. Lambeck, “Optimization of second harmonic generation and nonlinear phase-shifts in the Cerenkov regime,” IEEE J. Quantum Electron.32, 729–738 (1996).
[CrossRef]

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged Lithium niobate guides,” IEEE J. Quantum Electron.26, 1384–1393 (1990).
[CrossRef]

IEEE J. Quantum. Electron.

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum. Electron.45, 1465–1472 (2009).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Japan. J. Appl. Phys.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic Bessel beams by transverse phase-matching in annular periodically poled structures,” Japan. J. Appl. Phys.47, 6777–6783 (2009).
[CrossRef]

Laser and Photon. Rev.

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser and Photon. Rev.4, 355–373 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Opto-electron.

A. Zembrod, H. Puell, and J. A. Giordmaine, “Surface Radiation from Non-linear Optical Polarisation,” Opto-electron.1, 64–66 (1969).
[CrossRef]

Phys. Rev.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

N. Bloembergen, H. J. Simon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev.181, 1261–1271 (1969).
[CrossRef]

Phys. Rev. Lett.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Yu. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett.104, 083902 (2010).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

(a) Experimentally recorded Čerenkov conical SH emission from an as-grown strontium barium niobate crystal illuminated by the fundamental beam at λ =800nm. (b) Phase matching diagram for SHG in normally dispersive medium. The circle represents wavevectors of the SH. We can distinguish the typical collinear and the general non-collinear second harmonic emission. The Čerenkov SH emission is the special case when the emission angle is defined by the fulfillment of the longitudinal phase matching condition.

Fig. 2
Fig. 2

(a) Scheme of Čerenkov SH emission in a 1D periodically poled LiNbO3 crystal using fundamental beam at λ =1300nm. The right inset shows experimentally recorded far-field SH image. The SH spots at small angles (θRN) represent the Raman-Nath emission while the spot at bigger angles θC are the Čerenkov SH. The SH beams are generally emitted as doublets with orthogonal polarization because of birefringence of the crystal. See Fig. 3(a) for the corresponding phase-matching scheme. (b) Schematic representation of Čerenkov SH emission via spatially localized modulation of nonlinearity. The right inset shows experimentally recorded far-field SH image [4]. Unlike the case depicted in Fig. 2(a), here only the Čerenkov SH spots are visible. See Fig. 3(b) for the corresponding phase matching diagram.

Fig. 3
Fig. 3

Phase matching diagrams of the Čerenkov SHG in: (a) 1D periodically modulated nonlinearity, as shown in Fig. 2(a). The phase-mismatched emissions at small angles given by the action of the single reciprocal lattice vector are the Raman-Nath SHs. (b) localized nonlinear modulation, as shown in Fig. 2(b). c) general case with fundamental beam illuminating χ(2) modulation at an oblique angle. In this last case, even if both Čerenkov signals are still emitted symmetrically with respect to the normal to nonlinearity modulation, they differ in intensity as they are formed using different reciprocal vectors (G1 and G2).

Fig. 4
Fig. 4

Numerically simulated fundamental (left) and generated second harmonic (rigt) in a nonlinear medium with a periodically modulated nonlinearity in transverse direction. The short period of the modulation (Λ = 0.2μm in this case) ensures that the reciprocal lattice vectors corresponding to the periodic χ(2) modulation cannot fulfil the Bragg condition. However, the Čerenkov SH signal is still clearly emitted at kc ≈ ±5μm−1. Here we assumed the refractive index to be n1(λ = 1.2μm) =1.125 and n2(λ = 0.6μm)=1.179.

Fig. 5
Fig. 5

Illustrating of the concept of Čerenkov SH emission in a waveguide. FF and SH denote fundamental and second harmonic beams, respectively. Here fundamental beam propagates as guided mode while second harmonic is a radiation mode of the waveguiding structure. The graph depicts also the phase matching diagram corresponding to this physical situation with the reciprocal vector G⃗ provided by the jump of the nonlinearity (see sec.III–IV for details). The dashed line indicates that the SH cannot propagates into the air because of the total internal refection.

Fig. 6
Fig. 6

Normalized strength of Čerenkov signal excited by the fundamental mode of the symmetric waveguide as a function of the waveguide width (2d). Line represents result obtained by using simple analytical approach based on the transverse modulation of the nonlinearity [Eqs. (15) and (17)]. Points depict results evaluated by numerically solving the propagation equations Eq. (5) in waveguide geometry. Solid and dashed lines correspond to the nonlinearity located in the guiding layer and substrate, respectively.

Fig. 7
Fig. 7

Numerically simulated SHG in waveguide geometry (waveguide width 2d = 1μm) with uniform second order nonlinearity. Left (right) - evolution of the intensity of the fundamental (second harmonic) beam. The Čerenkov SH signal is emitted at kc ≈ ±5μm−1.

Fig. 8
Fig. 8

SH emission via total internal reflection in nonlinear medium. (a) Experimental setup. Red line represents the fundamental frequency (FF) beam. Green lines represent the SH beams: VSH - virtual SH, CSH - Čerenkov SH, FSH - forward SH. αS - FF incidence angle, αD - detector position angle. P - polarizer, F - short pass filter, DET - detector. (b) The phase matching condition for the Čerenkov SHG. (c) The image of the observed SH generated at the boundary between nonlinear crystal and air. The red dashed line indicates the FF, green lines represent generated SH. The intense red diffusive spots are the observed SH beams as seen on the paper screen (no FF filter used here). (i) lithium niobate crystal, (ii)–((iv) CCD images (linear scale) of the second harmonic (FF beam filtered out): (ii) VSH, (iii) CSH and (iv) FSH.

Fig. 9
Fig. 9

Experimentally measured angular positions (detector angle αD) of second harmonic signals as function of FF incident angle αS (outside the crystal). Experimental data is shown as triangles while lines depict theory.

Equations (17)

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k 2 z 2 k 1 z = 0 ,
k 2 x 2 k 1 x = Δ k x ,
k 2 cos θ 2 k 1 = 0 ,
k 2 sin θ G = Δ k x .
E 1 z = i 2 k 1 2 E 1 x 2 i ω 1 2 χ ( 2 ) ( x ) k 1 c 2 E 1 * E 2 e i ( k 2 2 k 1 ) z , E 2 z = i 2 k 2 2 E 2 x 2 i ω 2 2 χ ( 2 ) ( x ) 2 k 2 c 2 E 1 2 e i ( 2 k 1 k 2 ) z .
E S H z χ ( 2 ) ( x ) E 1 2 ( x , z ) e i k c x d x ,
k 2 2 k 1 = G .
E ( x , z ) = E ( x ) e i β z ,
E ( x ) = { A 0 / ( 1 + κ 2 / γ 2 ) exp ( κ ( x + d ) ) x d A 0 cos ( γ x ) | x | d A 0 / ( 1 + κ 2 / γ 2 ) exp ( κ ( x d ) ) x d .
κ 2 = β 2 k 0 2 n 1 2
γ 2 = k 0 2 n 0 2 β 2
κ γ = tan ( γ d ) ,
k c 2 + 4 β 2 = k 2 2 .
χ ( 2 ) ( x ) = { χ 0 ( 2 ) for | x | d 0 otherwise .
E S H d d χ 0 ( 2 ) A 0 2 cos 2 ( γ x ) e i k c x d x = A 0 2 χ 0 ( 2 ) ( sin ( k c d ) k c + sin ( 2 γ + k c ) d 2 γ + k c + sin ( k c 2 γ ) d k c 2 γ )
χ ( 2 ) ( x ) = { χ 0 ( 2 ) for x d 0 otherwise
E S H d χ 0 ( 2 ) A 1 2 e 2 κ ( x + d ) e i k c x d x = A 0 2 χ 0 ( 2 ) 1 + κ 2 / γ 2 e i k c d 2 κ + i k c

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