Abstract

We show theoretically and experimentally that, in phase-mismatched second-harmonic generation, an effective group-velocity dispersion is induced at the second-harmonic frequency. Experimental results agree quite well with the theoretical predictions. Although large phase mismatch is required to induce appreciable group-velocity dispersion in birefringent nonlinear crystals, similar effects can be observed in quasi-phase-matched structures at much lower phase mismatch. Some implications of the induced dispersion for pulse propagation in quadratic media are discussed.

© 2006 Optical Society of America

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2004 (2)

H. Y. Zhu, T. Wang, W. G. Zheng, P. Yuan, L. J. Qian, and D. Y. Fan, "Efficient second harmonic generation of femtosecond laser at 1 µm," Opt. Express 12, 2150-2155 (2004).
[Crossref] [PubMed]

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]

2003 (3)

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

I. N. Towers, B. A. Malomed, and F. W. Wise, "Light bullets in quadratic media with normal dispersion at the second harmonic," Phys. Rev. Lett. 90, 123902 (2003).
[Crossref] [PubMed]

2002 (1)

2001 (2)

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, "Measurement of modulational instability gain of second-order nonlinear optical eigenmodes in a one-dimensional system," Phys. Rev. Lett. 86, 4528-4531 (2001).
[Crossref] [PubMed]

T. Wang, L. J. Qian, H. Y. Zhu, Z. J. Hou, and F. M. Li, "Beam-quality improved efficient second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Commun. 188, 213-217 (2001).
[Crossref]

2000 (3)

X. Liu, K. Beckwitt, and F. W. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[Crossref]

D. Mihalache, D. Mazilu, L. C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[Crossref]

A. D. Boardman, K. Marinov, D. I. Pushkarov, and A. Shivarova, "Wave-beam coupling in quadratic nonlinear optical waveguides: effects of nonlinearly induced diffraction," Phys. Rev. E 62, 2871-2877 (2000).
[Crossref]

1999 (1)

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4631-4634 (1999).
[Crossref]

1997 (3)

1995 (1)

1992 (1)

1990 (2)

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[Crossref] [PubMed]

L. D. Noordam, H. J. Bakker, M. P. de Boer, and H. B. V. Vandenheuvell, "Second-harmonic generation of femtosecond pulses: observation of phase-mismatch effects," Opt. Lett. 15, 1464-1466 (1990).
[Crossref] [PubMed]

1988 (2)

1981 (1)

Anderson, A.

B. A. Malomed, P. Drummond, H. He, A. Berntson, A. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[Crossref]

Arbore, M. A.

Bakker, H. J.

L. D. Noordam, H. J. Bakker, M. P. de Boer, and H. B. V. Vandenheuvell, "Second-harmonic generation of femtosecond pulses: observation of phase-mismatch effects," Opt. Lett. 15, 1464-1466 (1990).
[Crossref] [PubMed]

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[Crossref] [PubMed]

Beckwitt, K.

X. Liu, K. Beckwitt, and F. W. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[Crossref]

Bellanca, G.

Berntson, A.

B. A. Malomed, P. Drummond, H. He, A. Berntson, A. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[Crossref]

Boardman, A. D.

A. D. Boardman, K. Marinov, D. I. Pushkarov, and A. Shivarova, "Wave-beam coupling in quadratic nonlinear optical waveguides: effects of nonlinearly induced diffraction," Phys. Rev. E 62, 2871-2877 (2000).
[Crossref]

Carlotti, X.

Chou, M. H.

Conti, C.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. Di Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

Crasovan, L. C.

D. Mihalache, D. Mazilu, L. C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[Crossref]

de Boer, M. P.

DeSalvo, R.

Di Trapani, P.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. Di Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

Drummond, P.

B. A. Malomed, P. Drummond, H. He, A. Berntson, A. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[Crossref]

Ducasse, A.

Fan, D. Y.

Fang, H.

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, "Measurement of modulational instability gain of second-order nonlinear optical eigenmodes in a one-dimensional system," Phys. Rev. Lett. 86, 4528-4531 (2001).
[Crossref] [PubMed]

Fejer, M. M.

Ferro, P.

Freysz, E.

Galvanauskas, A.

Hache, F.

Hagan, D. J.

Harter, D.

He, H.

B. A. Malomed, P. Drummond, H. He, A. Berntson, A. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[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]

Hou, Z. J.

T. Wang, L. J. Qian, H. Y. Zhu, Z. J. Hou, and F. M. Li, "Beam-quality improved efficient second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Commun. 188, 213-217 (2001).
[Crossref]

Ivanov, A.

Jedrkiewicz, O.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. Di Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[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]

Kothari, N. C.

Kuipers, L.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[Crossref] [PubMed]

Lagendijk, A.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[Crossref] [PubMed]

Lederer, F.

D. Mihalache, D. Mazilu, L. C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[Crossref]

Li, F. M.

T. Wang, L. J. Qian, H. Y. Zhu, Z. J. Hou, and F. M. Li, "Beam-quality improved efficient second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Commun. 188, 213-217 (2001).
[Crossref]

Lisak, M.

B. A. Malomed, P. Drummond, H. He, A. Berntson, A. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[Crossref]

Liu, X.

X. Liu, K. Beckwitt, and F. W. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[Crossref]

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4631-4634 (1999).
[Crossref]

Malendevich, R.

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, "Measurement of modulational instability gain of second-order nonlinear optical eigenmodes in a one-dimensional system," Phys. Rev. Lett. 86, 4528-4531 (2001).
[Crossref] [PubMed]

Malomed, B. A.

I. N. Towers, B. A. Malomed, and F. W. Wise, "Light bullets in quadratic media with normal dispersion at the second harmonic," Phys. Rev. Lett. 90, 123902 (2003).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, L. C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[Crossref]

B. A. Malomed, P. Drummond, H. He, A. Berntson, A. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[Crossref]

Manassah, J. T.

Marinov, K.

A. D. Boardman, K. Marinov, D. I. Pushkarov, and A. Shivarova, "Wave-beam coupling in quadratic nonlinear optical waveguides: effects of nonlinearly induced diffraction," Phys. Rev. E 62, 2871-2877 (2000).
[Crossref]

Mazilu, D.

D. Mihalache, D. Mazilu, L. C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[Crossref]

Mihalache, D.

D. Mihalache, D. Mazilu, L. C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[Crossref]

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]

Noordam, L. D.

Piskarskas, A.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

Planken, P. C.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[Crossref] [PubMed]

Pushkarov, D. I.

A. D. Boardman, K. Marinov, D. I. Pushkarov, and A. Shivarova, "Wave-beam coupling in quadratic nonlinear optical waveguides: effects of nonlinearly induced diffraction," Phys. Rev. E 62, 2871-2877 (2000).
[Crossref]

Qian, L. J.

H. Y. Zhu, T. Wang, W. G. Zheng, P. Yuan, L. J. Qian, and D. Y. Fan, "Efficient second harmonic generation of femtosecond laser at 1 µm," Opt. Express 12, 2150-2155 (2004).
[Crossref] [PubMed]

T. Wang, L. J. Qian, H. Y. Zhu, Z. J. Hou, and F. M. Li, "Beam-quality improved efficient second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Commun. 188, 213-217 (2001).
[Crossref]

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4631-4634 (1999).
[Crossref]

Rassoul, R. M.

Schiek, R.

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, "Measurement of modulational instability gain of second-order nonlinear optical eigenmodes in a one-dimensional system," Phys. Rev. Lett. 86, 4528-4531 (2001).
[Crossref] [PubMed]

Sheik-Bahae, M.

Shivarova, A.

A. D. Boardman, K. Marinov, D. I. Pushkarov, and A. Shivarova, "Wave-beam coupling in quadratic nonlinear optical waveguides: effects of nonlinearly induced diffraction," Phys. Rev. E 62, 2871-2877 (2000).
[Crossref]

Stegeman, G.

Stegeman, G. I.

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, "Measurement of modulational instability gain of second-order nonlinear optical eigenmodes in a one-dimensional system," Phys. Rev. Lett. 86, 4528-4531 (2001).
[Crossref] [PubMed]

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]

Torner, L.

D. Mihalache, D. Mazilu, L. C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[Crossref]

Towers, I. N.

I. N. Towers, B. A. Malomed, and F. W. Wise, "Light bullets in quadratic media with normal dispersion at the second harmonic," Phys. Rev. Lett. 90, 123902 (2003).
[Crossref] [PubMed]

Trebino, R.

Trillo, S.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. Di Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

S. Trillo and P. Ferro, "Modulational instability in second-harmonic generation," Opt. Lett. 20, 438-440 (1995).
[Crossref] [PubMed]

Trull, J.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. Di Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

Valiulis, G.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

S. Trillo, C. Conti, P. Di Trapani, O. Jedrkiewicz, J. Trull, G. Valiulis, and G. Bellanca, "Colored conical emission by means of second-harmonic generation," Opt. Lett. 27, 1451-1453 (2002).
[Crossref]

Van Stryland, E. W.

Vandenheuvell, H. B.

Vanherzeele, H.

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, T.

H. Y. Zhu, T. Wang, W. G. Zheng, P. Yuan, L. J. Qian, and D. Y. Fan, "Efficient second harmonic generation of femtosecond laser at 1 µm," Opt. Express 12, 2150-2155 (2004).
[Crossref] [PubMed]

T. Wang, L. J. Qian, H. Y. Zhu, Z. J. Hou, and F. M. Li, "Beam-quality improved efficient second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Commun. 188, 213-217 (2001).
[Crossref]

Wise, F. W.

I. N. Towers, B. A. Malomed, and F. W. Wise, "Light bullets in quadratic media with normal dispersion at the second harmonic," Phys. Rev. Lett. 90, 123902 (2003).
[Crossref] [PubMed]

X. Liu, K. Beckwitt, and F. W. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[Crossref]

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4631-4634 (1999).
[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]

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, P.

Zheng, W. G.

Zhu, H. Y.

H. Y. Zhu, T. Wang, W. G. Zheng, P. Yuan, L. J. Qian, and D. Y. Fan, "Efficient second harmonic generation of femtosecond laser at 1 µm," Opt. Express 12, 2150-2155 (2004).
[Crossref] [PubMed]

T. Wang, L. J. Qian, H. Y. Zhu, Z. J. Hou, and F. M. Li, "Beam-quality improved efficient second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Commun. 188, 213-217 (2001).
[Crossref]

Zhu, S. N.

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]

Zhu, Y. Y.

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]

Appl. Opt. (2)

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

Opt. Commun. (1)

T. Wang, L. J. Qian, H. Y. Zhu, Z. J. Hou, and F. M. Li, "Beam-quality improved efficient second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Commun. 188, 213-217 (2001).
[Crossref]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (1)

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[Crossref] [PubMed]

Phys. Rev. E (4)

D. Mihalache, D. Mazilu, L. C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[Crossref]

X. Liu, K. Beckwitt, and F. W. Wise, "Two-dimensional optical spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 1328-1340 (2000).
[Crossref]

A. D. Boardman, K. Marinov, D. I. Pushkarov, and A. Shivarova, "Wave-beam coupling in quadratic nonlinear optical waveguides: effects of nonlinearly induced diffraction," Phys. Rev. E 62, 2871-2877 (2000).
[Crossref]

B. A. Malomed, P. Drummond, H. He, A. Berntson, A. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[Crossref]

Phys. Rev. Lett. (6)

I. N. Towers, B. A. Malomed, and F. W. Wise, "Light bullets in quadratic media with normal dispersion at the second harmonic," Phys. Rev. Lett. 90, 123902 (2003).
[Crossref] [PubMed]

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]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[Crossref] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4631-4634 (1999).
[Crossref]

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, "Measurement of modulational instability gain of second-order nonlinear optical eigenmodes in a one-dimensional system," Phys. Rev. Lett. 86, 4528-4531 (2001).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Calculated SH (solid curve) and FH (dashed curve) intensity profiles after propagation through six dispersion lengths. There are no GVM and no material dispersion at the SH. The dotted curve is the launched FH pulse. Inset: peak intensity of the SH pulse versus propagation distance. The nonlinear length is much larger than the crystal length ( L nl L ) , and the phase mismatch Δ k L = 100 π .

Fig. 2
Fig. 2

Calculated SH (solid curve) and FH (dashed curve) intensity profiles after propagation through six dispersion lengths in the presence of GVM. There is no material dispersion at the SH. The dotted curve is the launched FH pulse. All the parameters of the simulations are the same as in Fig. 1, except L gvm = 0.1 L and Δ k L = 10000 π .

Fig. 3
Fig. 3

(a) SH (solid curve) and FH (dashed curve) intensity profiles after propagation through six dispersion lengths under QPM. There is no material dispersion at the SH. The dotted curve is the launched FH pulse. (b) Peak intensity of the chirped SH component with propagation in the nonlinear crystal. The inset is an enlarged plot of the same thing. All the parameters of the simulations are the same as in Fig. 2, except the domain period of the QPM structure Λ = L 250 , Δ k QPM L = 100 π , and the material dispersion is chosen so that Δ k L = 400 π .

Fig. 4
Fig. 4

(a) Calculated and (b) measured SH pulses at phase matching ( Δ k = 0 ) . The dashed curve in (a) is the output at the FH wavelength. As a comparison, the calculated SH pulse is also plotted in the case of negligible dispersion at the FH frequency [dotted curve in (a)].

Fig. 5
Fig. 5

(a) Calculated and (b) measured SH pulses with large phase mismatch ( Δ K L = 100 π ) . The dashed line in (a) is the output at the FH wavelength.

Equations (10)

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E 1 z i β 1 2 2 E 1 t 2 = i L nl g ( z ) E 1 * E 2 exp ( i Δ k z ) ,
E 2 z + Δ u 1 E 2 t i β 2 2 2 E 2 t 2 = i L nl g ( z ) E 1 2 exp ( i Δ k z ) .
L nl = 2 n c ω 0 χ ( 2 ) E 0
E 1 ( ω , z ) = E 0 exp [ ( ω τ 2 ) 2 + i β 1 ω 2 z ] ,
E 1 ( t , z ) = E 0 [ τ 2 + ( 4 β 1 z τ 2 ) 2 ] 1 2 exp [ t 2 ( τ 2 i 4 β 1 z ) ] .
z E 2 ( ω , z ) = i L nl exp ( i Δ k z ) [ E 1 ( t , z ) ] 2 exp ( i ω t ) d t = i E 0 2 2 L nl [ τ 2 + ( 4 β 1 z τ ) 2 ] 1 2 exp ( i Δ k z ) exp [ ( ω τ 2 2 ) 2 + i β 1 2 ω 2 z ] .
z E 2 ( ω , z ) = i E 0 2 2 L nl τ exp [ ( ω τ 2 2 ) 2 ] exp [ i ( Δ k + 1 2 β 1 ω 2 ) z ] .
E 2 ( ω , z ) = A exp [ ( ω τ 2 2 ) 2 ] exp [ i ( Δ k + 1 2 β 1 ω 2 ) z ] 1 Δ k + 1 2 β 1 ω 2 ,
E 2 ( ω , z ) 2 = A 2 z 2 exp [ ( ω τ 2 ) 2 ] { sin c [ z 2 ( Δ k + 1 2 β 1 ω 2 ) ] } 2 ,
E 2 ( ω , z ) = A i Δ k exp ( i Δ k z ) exp [ ( ω τ 2 2 ) 2 + i β 1 2 ω 2 z ] A i Δ k exp [ ( ω τ 2 2 ) 2 ] .

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