Abstract

The evolution of the difference frequency generation between a planar pump wave and a focused signal wave has been numerically investigated in this paper. We show that, at the difference frequency wave, various beam patterns such as ring and moon-like, are resulted due to the nonuniform distribution of phase velocity in the focused signal wave. The subluminal and superluminal regions can be identified by the intersection of two generated beam profiles that correspond to a pair of phase-mismatches with equal value but opposite signs.

©2007 Optical Society of America

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  1. G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
    [Crossref]
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    [Crossref]
  3. S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
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    [Crossref]
  6. P. Xu, S. H. Ji, S. N. Zhu, X.Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional chi((2)) photonic crystal: A hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93, 133904 (2004).
    [Crossref] [PubMed]
  7. M. Goulkov, O. Shinkarenko, L. Ivleva, P. Lykov, T. Granzow, T. Woike, M. Imlau, and M. Wohlecke, “New parametric scattering in photorefractive Sr0.61Ba0.39Nb2O6 : Cr,” Phys. Rev. Lett. 91, 243903 (2003).
    [Crossref] [PubMed]
  8. G. Giusfredi, D. Mazzotti, P. Cancio, and P. De Natale, “Spatial mode control of radiation generated by frequency difference in periodically poled crystals,” Phys. Rev. Lett. 87, 113901 (2001).
    [Crossref] [PubMed]
  9. X. Y. Xu, V. G. Minogin, K. Lee, Y.Z. Wang, and W. H. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
    [Crossref]
  10. Z. Chen, Y. K. Ho, P. X. Wang, Q. Kong, Y. J. Xie, W. Wang, and J. J. Xu, “A formula on phase velocity of waves and pplication,” Appl. Phys. Lett. 88, 121125 (2006).
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  15. V. Magni, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Comm. 184, 245–255 (2000).
    [Crossref]
  16. G. D. Xu, T. W. Ren, Y. H. Wang, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Third-harmonic generation by use of focused Gaussian beams in an optical superlattice,” J. Opt. Soc. Am. B 20, 360–365 (2003).
    [Crossref]
  17. S. M. Saltiel, K. Koynov, B. Agate, and W. Sibbett, “Second-harmonic generation with focused beams under conditions of large group-velocity mismatch,” J. Opt. Soc. Am. B 21, 591–598 (2004).
    [Crossref]
  18. D. Q. Lu, L. J. Qian, Y. Z. Li, and D.Y. Fan, “Frequency mixing of off-axis focused Gaussian beams: An approach to measure the phase velocity distribution,” Appl. Phys. Lett. 88, 261112 (2006).
    [Crossref]
  19. M. D. Perry, D. Pennington, B. C. Stuart, G. Tietbohl, J. A. Britten, C. Brown, S. Herman, B. Golick, M. Kartz, J. Miller, H.T. Powell, M. Vergino, and V. Yanovsky, “Petawatt laser pulses,” Opt. Lett. 24, 160–162 (1999).
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    [Crossref]
  21. D. Umstadter, S. Y. Chen, A. Maksimchuk, G. Mourou, and R. Wagner, “Nonlinear optics in relativistic plasmas and laser wake field acceleration of electrons,” Science 273, 472–475 (1996).
    [Crossref] [PubMed]
  22. S. M. Saltiel, K. Koynov, B. Agate, and W. Sibbett, “Second-harmonic generation with focused beams under conditions of large group-velocity mismatch,” J. Opt. Soc. Am. B 21, 591–598 (2004)
    [Crossref]

2006 (2)

Z. Chen, Y. K. Ho, P. X. Wang, Q. Kong, Y. J. Xie, W. Wang, and J. J. Xu, “A formula on phase velocity of waves and pplication,” Appl. Phys. Lett. 88, 121125 (2006).
[Crossref]

D. Q. Lu, L. J. Qian, Y. Z. Li, and D.Y. Fan, “Frequency mixing of off-axis focused Gaussian beams: An approach to measure the phase velocity distribution,” Appl. Phys. Lett. 88, 261112 (2006).
[Crossref]

2004 (3)

2003 (2)

G. D. Xu, T. W. Ren, Y. H. Wang, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Third-harmonic generation by use of focused Gaussian beams in an optical superlattice,” J. Opt. Soc. Am. B 20, 360–365 (2003).
[Crossref]

M. Goulkov, O. Shinkarenko, L. Ivleva, P. Lykov, T. Granzow, T. Woike, M. Imlau, and M. Wohlecke, “New parametric scattering in photorefractive Sr0.61Ba0.39Nb2O6 : Cr,” Phys. Rev. Lett. 91, 243903 (2003).
[Crossref] [PubMed]

2001 (2)

G. Giusfredi, D. Mazzotti, P. Cancio, and P. De Natale, “Spatial mode control of radiation generated by frequency difference in periodically poled crystals,” Phys. Rev. Lett. 87, 113901 (2001).
[Crossref] [PubMed]

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78, 2253–2255 (2001).
[Crossref]

2000 (1)

V. Magni, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Comm. 184, 245–255 (2000).
[Crossref]

1999 (4)

1998 (2)

1996 (1)

D. Umstadter, S. Y. Chen, A. Maksimchuk, G. Mourou, and R. Wagner, “Nonlinear optics in relativistic plasmas and laser wake field acceleration of electrons,” Science 273, 472–475 (1996).
[Crossref] [PubMed]

1982 (1)

S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
[Crossref]

1968 (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. App. Phys. 39, 3597–3639 (1968).
[Crossref]

1965 (1)

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[Crossref]

Agate, B.

Ashkin, A.

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. ( Cambridge University Press, Cambridge, 1999).

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. App. Phys. 39, 3597–3639 (1968).
[Crossref]

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[Crossref]

Boyd, R. W.

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

Britten, J. A.

Brown, C.

Cancio, P.

G. Giusfredi, D. Mazzotti, P. Cancio, and P. De Natale, “Spatial mode control of radiation generated by frequency difference in periodically poled crystals,” Phys. Rev. Lett. 87, 113901 (2001).
[Crossref] [PubMed]

Cao, N.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78, 2253–2255 (2001).
[Crossref]

Chen, S. Y.

D. Umstadter, S. Y. Chen, A. Maksimchuk, G. Mourou, and R. Wagner, “Nonlinear optics in relativistic plasmas and laser wake field acceleration of electrons,” Science 273, 472–475 (1996).
[Crossref] [PubMed]

Chen, Z.

Z. Chen, Y. K. Ho, P. X. Wang, Q. Kong, Y. J. Xie, W. Wang, and J. J. Xu, “A formula on phase velocity of waves and pplication,” Appl. Phys. Lett. 88, 121125 (2006).
[Crossref]

De Natale, P.

G. Giusfredi, D. Mazzotti, P. Cancio, and P. De Natale, “Spatial mode control of radiation generated by frequency difference in periodically poled crystals,” Phys. Rev. Lett. 87, 113901 (2001).
[Crossref] [PubMed]

Dziedzic, J. M.

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[Crossref]

Esarey, E.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78, 2253–2255 (2001).
[Crossref]

Falk, J.

S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
[Crossref]

Fan, D.Y.

D. Q. Lu, L. J. Qian, Y. Z. Li, and D.Y. Fan, “Frequency mixing of off-axis focused Gaussian beams: An approach to measure the phase velocity distribution,” Appl. Phys. Lett. 88, 261112 (2006).
[Crossref]

Giusfredi, G.

G. Giusfredi, D. Mazzotti, P. Cancio, and P. De Natale, “Spatial mode control of radiation generated by frequency difference in periodically poled crystals,” Phys. Rev. Lett. 87, 113901 (2001).
[Crossref] [PubMed]

Golick, B.

Goulkov, M.

M. Goulkov, O. Shinkarenko, L. Ivleva, P. Lykov, T. Granzow, T. Woike, M. Imlau, and M. Wohlecke, “New parametric scattering in photorefractive Sr0.61Ba0.39Nb2O6 : Cr,” Phys. Rev. Lett. 91, 243903 (2003).
[Crossref] [PubMed]

Granzow, T.

M. Goulkov, O. Shinkarenko, L. Ivleva, P. Lykov, T. Granzow, T. Woike, M. Imlau, and M. Wohlecke, “New parametric scattering in photorefractive Sr0.61Ba0.39Nb2O6 : Cr,” Phys. Rev. Lett. 91, 243903 (2003).
[Crossref] [PubMed]

Guha, S.

S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
[Crossref]

He, J. L.

P. Xu, S. H. Ji, S. N. Zhu, X.Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional chi((2)) photonic crystal: A hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93, 133904 (2004).
[Crossref] [PubMed]

Herman, S.

Ho, Y. K.

Z. Chen, Y. K. Ho, P. X. Wang, Q. Kong, Y. J. Xie, W. Wang, and J. J. Xu, “A formula on phase velocity of waves and pplication,” Appl. Phys. Lett. 88, 121125 (2006).
[Crossref]

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78, 2253–2255 (2001).
[Crossref]

Imlau, M.

M. Goulkov, O. Shinkarenko, L. Ivleva, P. Lykov, T. Granzow, T. Woike, M. Imlau, and M. Wohlecke, “New parametric scattering in photorefractive Sr0.61Ba0.39Nb2O6 : Cr,” Phys. Rev. Lett. 91, 243903 (2003).
[Crossref] [PubMed]

Ivleva, L.

M. Goulkov, O. Shinkarenko, L. Ivleva, P. Lykov, T. Granzow, T. Woike, M. Imlau, and M. Wohlecke, “New parametric scattering in photorefractive Sr0.61Ba0.39Nb2O6 : Cr,” Phys. Rev. Lett. 91, 243903 (2003).
[Crossref] [PubMed]

Jarutis, V.

Jhe, W. H.

X. Y. Xu, V. G. Minogin, K. Lee, Y.Z. Wang, and W. H. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[Crossref]

Ji, S. H.

P. Xu, S. H. Ji, S. N. Zhu, X.Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional chi((2)) photonic crystal: A hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93, 133904 (2004).
[Crossref] [PubMed]

Kan’an, A. M.

Kartz, M.

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. App. Phys. 39, 3597–3639 (1968).
[Crossref]

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[Crossref]

Kong, Q.

Z. Chen, Y. K. Ho, P. X. Wang, Q. Kong, Y. J. Xie, W. Wang, and J. J. Xu, “A formula on phase velocity of waves and pplication,” Appl. Phys. Lett. 88, 121125 (2006).
[Crossref]

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78, 2253–2255 (2001).
[Crossref]

Koynov, K.

Laurell, F.

Leaird, D. E.

Lee, K.

X. Y. Xu, V. G. Minogin, K. Lee, Y.Z. Wang, and W. H. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[Crossref]

Li, Y. Z.

D. Q. Lu, L. J. Qian, Y. Z. Li, and D.Y. Fan, “Frequency mixing of off-axis focused Gaussian beams: An approach to measure the phase velocity distribution,” Appl. Phys. Lett. 88, 261112 (2006).
[Crossref]

Lu, D. Q.

D. Q. Lu, L. J. Qian, Y. Z. Li, and D.Y. Fan, “Frequency mixing of off-axis focused Gaussian beams: An approach to measure the phase velocity distribution,” Appl. Phys. Lett. 88, 261112 (2006).
[Crossref]

Lykov, P.

M. Goulkov, O. Shinkarenko, L. Ivleva, P. Lykov, T. Granzow, T. Woike, M. Imlau, and M. Wohlecke, “New parametric scattering in photorefractive Sr0.61Ba0.39Nb2O6 : Cr,” Phys. Rev. Lett. 91, 243903 (2003).
[Crossref] [PubMed]

Magni, V.

V. Magni, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Comm. 184, 245–255 (2000).
[Crossref]

Maksimchuk, A.

D. Umstadter, S. Y. Chen, A. Maksimchuk, G. Mourou, and R. Wagner, “Nonlinear optics in relativistic plasmas and laser wake field acceleration of electrons,” Science 273, 472–475 (1996).
[Crossref] [PubMed]

Mazzotti, D.

G. Giusfredi, D. Mazzotti, P. Cancio, and P. De Natale, “Spatial mode control of radiation generated by frequency difference in periodically poled crystals,” Phys. Rev. Lett. 87, 113901 (2001).
[Crossref] [PubMed]

Miller, J.

Ming, N. B.

P. Xu, S. H. Ji, S. N. Zhu, X.Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional chi((2)) photonic crystal: A hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93, 133904 (2004).
[Crossref] [PubMed]

G. D. Xu, T. W. Ren, Y. H. Wang, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, “Third-harmonic generation by use of focused Gaussian beams in an optical superlattice,” J. Opt. Soc. Am. B 20, 360–365 (2003).
[Crossref]

Minogin, V. G.

X. Y. Xu, V. G. Minogin, K. Lee, Y.Z. Wang, and W. H. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[Crossref]

Mourou, G.

D. Umstadter, S. Y. Chen, A. Maksimchuk, G. Mourou, and R. Wagner, “Nonlinear optics in relativistic plasmas and laser wake field acceleration of electrons,” Science 273, 472–475 (1996).
[Crossref] [PubMed]

Nishida, Y.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78, 2253–2255 (2001).
[Crossref]

Pasiskevicius, V.

Pennington, D.

Perry, M. D.

Piskarskas, A.

Powell, H.T.

Qian, L. J.

D. Q. Lu, L. J. Qian, Y. Z. Li, and D.Y. Fan, “Frequency mixing of off-axis focused Gaussian beams: An approach to measure the phase velocity distribution,” Appl. Phys. Lett. 88, 261112 (2006).
[Crossref]

Ren, T. W.

Saltiel, S. M.

Sessler, A. M.

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78, 2253–2255 (2001).
[Crossref]

Shinkarenko, O.

M. Goulkov, O. Shinkarenko, L. Ivleva, P. Lykov, T. Granzow, T. Woike, M. Imlau, and M. Wohlecke, “New parametric scattering in photorefractive Sr0.61Ba0.39Nb2O6 : Cr,” Phys. Rev. Lett. 91, 243903 (2003).
[Crossref] [PubMed]

Sibbett, W.

Smilgevicius, V.

Stabinis, A.

Stuart, B. C.

Sun, J.

P. Xu, S. H. Ji, S. N. Zhu, X.Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional chi((2)) photonic crystal: A hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93, 133904 (2004).
[Crossref] [PubMed]

Tellefsen, J.

Tietbohl, G.

Umstadter, D.

D. Umstadter, S. Y. Chen, A. Maksimchuk, G. Mourou, and R. Wagner, “Nonlinear optics in relativistic plasmas and laser wake field acceleration of electrons,” Science 273, 472–475 (1996).
[Crossref] [PubMed]

Vergino, M.

Wagner, R.

D. Umstadter, S. Y. Chen, A. Maksimchuk, G. Mourou, and R. Wagner, “Nonlinear optics in relativistic plasmas and laser wake field acceleration of electrons,” Science 273, 472–475 (1996).
[Crossref] [PubMed]

Wang, H. T.

P. Xu, S. H. Ji, S. N. Zhu, X.Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional chi((2)) photonic crystal: A hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93, 133904 (2004).
[Crossref] [PubMed]

Wang, P. X.

Z. Chen, Y. K. Ho, P. X. Wang, Q. Kong, Y. J. Xie, W. Wang, and J. J. Xu, “A formula on phase velocity of waves and pplication,” Appl. Phys. Lett. 88, 121125 (2006).
[Crossref]

P. X. Wang, Y. K. Ho, X. Q. Yuan, Q. Kong, N. Cao, A. M. Sessler, E. Esarey, and Y. Nishida, “Vacuum electron acceleration by an intense laser,” Appl. Phys. Lett. 78, 2253–2255 (2001).
[Crossref]

Wang, S.

Wang, W.

Z. Chen, Y. K. Ho, P. X. Wang, Q. Kong, Y. J. Xie, W. Wang, and J. J. Xu, “A formula on phase velocity of waves and pplication,” Appl. Phys. Lett. 88, 121125 (2006).
[Crossref]

Wang, Y. H.

Wang, Y.Z.

X. Y. Xu, V. G. Minogin, K. Lee, Y.Z. Wang, and W. H. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[Crossref]

Weiner, A. M.

Wohlecke, M.

M. Goulkov, O. Shinkarenko, L. Ivleva, P. Lykov, T. Granzow, T. Woike, M. Imlau, and M. Wohlecke, “New parametric scattering in photorefractive Sr0.61Ba0.39Nb2O6 : Cr,” Phys. Rev. Lett. 91, 243903 (2003).
[Crossref] [PubMed]

Woike, T.

M. Goulkov, O. Shinkarenko, L. Ivleva, P. Lykov, T. Granzow, T. Woike, M. Imlau, and M. Wohlecke, “New parametric scattering in photorefractive Sr0.61Ba0.39Nb2O6 : Cr,” Phys. Rev. Lett. 91, 243903 (2003).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. ( Cambridge University Press, Cambridge, 1999).

Wu, F. J.

S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
[Crossref]

Xie, Y. J.

Z. Chen, Y. K. Ho, P. X. Wang, Q. Kong, Y. J. Xie, W. Wang, and J. J. Xu, “A formula on phase velocity of waves and pplication,” Appl. Phys. Lett. 88, 121125 (2006).
[Crossref]

Xu, G. D.

Xu, J. J.

Z. Chen, Y. K. Ho, P. X. Wang, Q. Kong, Y. J. Xie, W. Wang, and J. J. Xu, “A formula on phase velocity of waves and pplication,” Appl. Phys. Lett. 88, 121125 (2006).
[Crossref]

Xu, P.

P. Xu, S. H. Ji, S. N. Zhu, X.Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional chi((2)) photonic crystal: A hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93, 133904 (2004).
[Crossref] [PubMed]

Xu, X. Y.

X. Y. Xu, V. G. Minogin, K. Lee, Y.Z. Wang, and W. H. Jhe, “Guiding cold atoms in a hollow laser beam,” Phys. Rev. A 60, 4796–4804 (1999).
[Crossref]

Yanovsky, V.

Yu, S.

Yu, X.Q.

P. Xu, S. H. Ji, S. N. Zhu, X.Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional chi((2)) photonic crystal: A hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93, 133904 (2004).
[Crossref] [PubMed]

Yuan, X. Q.

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Supplementary Material (4)

» Media 1: GIF (674 KB)     
» Media 2: GIF (729 KB)     
» Media 3: GIF (804 KB)     
» Media 4: GIF (1010 KB)     

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Figures (5)

Fig. 1.
Fig. 1. Longitudinal distributions of the normalized phase velocity v´=(vPZ/c-1)×104 at different radial positions for a focused Gaussian beam with w0=10 λ.

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Fig. 2.
Fig. 2. Movies of the evolutions of the DF beam. (a) (675 KB) ΔkL = 8 ; [Media 1] (b) (729 KB) ΔkL = -8. [Media 2]

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Fig. 3.
Fig. 3. (a)(805 KB) The same as Fig. 2(a) except the signal beam is EGSW; [Media 3] (b) (1011 KB) the same as Fig. 2(a) except the signal beam is HGSB. [Media 4]

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Fig. 4.
Fig. 4. (a) The DF beams generated from a planar pump wave and a Gaussian signal beam when Δk = 0 . The solid line (diamond symbol) and the dashed line (dotted line) respectively presents the intensity and the instantaneous phase distribution of the DF beam generated in process I (II). The parameters are the same as those in Fig. 2(a) except Δk , L and the entrance (exist) plane. (b) The dynamics of the property shown in (a).

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Fig. 5.
Fig. 5. The intensity distribution of the DF beam for various phase mismatching conditions. where n = ΔknL / 0.25 , L = zRc / 2 , the entrance plane is z =0 , other parameters are the same as those in Fig. 2(a).

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Tables (1)

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Table 1. Parameters used in Fig. 2.

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Equations (7)

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v pz r z = ω k − ∂ z φ ( z ) − kr 2 2 R 2 ( z ) ∂ z R ( z ) ,
( ∂ z + i 2 k p ∇ ⊥ 2 ) A p = − iσ p A s A g exp ( i Δ kz ) ,
( ∂ z + i 2 k s ∇ ⊥ 2 ) A s = − iσ s A p A g * exp ( − i Δ kz ) ,
( ∂ z + i 2 k g ∇ ⊥ 2 ) A g = − iσ g A p A s * exp ( − i Δ kz ) ,
δk ≃ k p ( V pz ( s ) c − 1 ) ,
Dk = δk + Δ k .
A g ( − z 0 + h ) = ih σ g A p A s * ( − z 0 ) ,

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