Abstract

Spatial and temporal locking of fundamental and second harmonic pulses was realized by means of photorefractive nonlinearity and highly mismatched harmonic generation. Due to the presence of both phase-locked and unlocked second harmonic pulses, a twin simultonic state was observed. Simultonic filamentation occurring at high pumping rates allowed us to determine a relation between the simulton’s waist and its intensity.

© 2010 OSA

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of Optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
    [CrossRef]
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    [CrossRef] [PubMed]
  5. C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ2: χ2 cascading,” J. Opt. Soc. Am. B 11(12), 2434–2443 (1994).
    [CrossRef]
  6. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
    [CrossRef] [PubMed]
  7. A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52(2), 1670–1674 (1995).
    [CrossRef] [PubMed]
  8. G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
    [CrossRef] [PubMed]
  9. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
    [CrossRef] [PubMed]
  10. E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
    [CrossRef]
  11. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. anomalous dispersion,” Appl. Phys. Lett. 23(3), 142 (1973).
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  12. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23(4), 171 (1973).
    [CrossRef]
  13. P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,” Phys. Rev. Lett. 81(3), 570–573 (1998).
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  16. V. Coda, M. Chauvet, F. Pettazzi, and E. Fazio, “3-D integrated optical interconnect induced by self-focused beam,” Electron. Lett. 42(8), 463–465 (2006).
    [CrossRef]
  17. F. Pettazzi, V. Coda, M. Chauvet, and E. Fazio, “Frequency doubling in self-induced waveguides in lithium niobate,” Opt. Commun. 272(1), 238–241 (2007).
    [CrossRef]
  18. F. Pettazzi, M. Alonzo, M. Centini, A. Petris, V. I. Vlad, M. Chauvet, and E. Fazio, “Self-trapping of low-energy infrared femtosecond beams in lithium niobate,” Phys. Rev. A 76(6), 063818–063821 (2007).
    [CrossRef]
  19. F. Pettazzi, V. Coda, G. Fanjoux, M. Chauvet, and E. Fazio, “Dynamic of second harmonic generation in photovoltaic photorefractive quadratic medium,” J. Opt. Soc. Am. B 27(1), 1–9 (2010).
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    [CrossRef]
  22. M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, “Second Harmonic Generation of Femtosecond Pulses at the Boundary of a Nonlinear Dielectric,” Phys. Rev. Lett. 83(15), 2934–2937 (1999).
    [CrossRef]
  23. V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
    [CrossRef]
  24. 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. Express 17(5), 3141–3147 (2009).
    [CrossRef] [PubMed]
  25. J. Safioui, F. Devaux, and M. Chauvet, “Pyroliton: pyroelectric spatial soliton,” Opt. Express 17(24), 22209–22216 (2009).
    [CrossRef] [PubMed]
  26. J. Safioui, M. Chauvet, F. Devaux, V. Coda, F. Pettazzi, M. Alonzo, and E. Fazio, “Polarization and configuration dependence of beam self-focusing in photorefractive LiNbO3,” J. Opt. Soc. Am. B 26(3), 487–492 (2009).
    [CrossRef]
  27. N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  28. F. Pettazzi, V. Coda, G. Fanjoux, M. Chauvet, and E. Fazio, “Dynamic of second harmonic generation in photovoltaic photorefractive quadratic medium,” J. Opt. Soc. Am. B 27(1), 1–9 (2010).
    [CrossRef]
  29. 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. Express 17(5), 3141–3147 (2009).
    [CrossRef] [PubMed]

2010 (2)

2009 (4)

2007 (3)

F. Pettazzi, V. Coda, M. Chauvet, and E. Fazio, “Frequency doubling in self-induced waveguides in lithium niobate,” Opt. Commun. 272(1), 238–241 (2007).
[CrossRef]

F. Pettazzi, M. Alonzo, M. Centini, A. Petris, V. I. Vlad, M. Chauvet, and E. Fazio, “Self-trapping of low-energy infrared femtosecond beams in lithium niobate,” Phys. Rev. A 76(6), 063818–063821 (2007).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

2006 (1)

V. Coda, M. Chauvet, F. Pettazzi, and E. Fazio, “3-D integrated optical interconnect induced by self-focused beam,” Electron. Lett. 42(8), 463–465 (2006).
[CrossRef]

2004 (1)

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
[CrossRef]

1999 (2)

X. Liu, L. J. Qian, and F. W. Wise, “Generation of spatio-temporal solitons,” Phys. Rev. Lett. 82(23), 4631–4634 (1999).
[CrossRef]

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, “Second Harmonic Generation of Femtosecond Pulses at the Boundary of a Nonlinear Dielectric,” Phys. Rev. Lett. 83(15), 2934–2937 (1999).
[CrossRef]

1998 (1)

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,” Phys. Rev. Lett. 81(3), 570–573 (1998).
[CrossRef]

1995 (2)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[CrossRef] [PubMed]

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52(2), 1670–1674 (1995).
[CrossRef] [PubMed]

1994 (3)

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[CrossRef] [PubMed]

C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ2: χ2 cascading,” J. Opt. Soc. Am. B 11(12), 2434–2443 (1994).
[CrossRef]

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19(20), 1612–1614 (1994).
[CrossRef] [PubMed]

1993 (2)

M. J. Werner and P. D. Drummond, “simulton solutions for the parametric amplifier,” J. Opt. Soc. Am. B 10(12), 2390–2393 (1993).
[CrossRef]

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

1990 (1)

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

1976 (1)

Y. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Sov. Phys. JETP 41, 414–416 (1976).

1973 (2)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. anomalous dispersion,” Appl. Phys. Lett. 23(3), 142 (1973).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23(4), 171 (1973).
[CrossRef]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of Optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[CrossRef]

1962 (1)

N. Bloembergen and P. S. Pershan, “Light Waves at the Boundary of Nonlinear Media,” Phys. Rev. 128(2), 606–622 (1962).
[CrossRef]

Aitchison, J. S.

Akozbek, N.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Alonzo, M.

Belardini, A.

Bertolotti, 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. Express 17(5), 3141–3147 (2009).
[CrossRef] [PubMed]

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. Express 17(5), 3141–3147 (2009).
[CrossRef] [PubMed]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
[CrossRef]

Bloembergen, N.

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, “Second Harmonic Generation of Femtosecond Pulses at the Boundary of a Nonlinear Dielectric,” Phys. Rev. Lett. 83(15), 2934–2937 (1999).
[CrossRef]

N. Bloembergen and P. S. Pershan, “Light Waves at the Boundary of Nonlinear Media,” Phys. Rev. 128(2), 606–622 (1962).
[CrossRef]

Bloemer, M. J.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Buryak, A. V.

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52(2), 1670–1674 (1995).
[CrossRef] [PubMed]

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19(20), 1612–1614 (1994).
[CrossRef] [PubMed]

Caironi, D.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,” Phys. Rev. Lett. 81(3), 570–573 (1998).
[CrossRef]

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. Express 17(5), 3141–3147 (2009).
[CrossRef] [PubMed]

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. Express 17(5), 3141–3147 (2009).
[CrossRef] [PubMed]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

F. Pettazzi, M. Alonzo, M. Centini, A. Petris, V. I. Vlad, M. Chauvet, and E. Fazio, “Self-trapping of low-energy infrared femtosecond beams in lithium niobate,” Phys. Rev. A 76(6), 063818–063821 (2007).
[CrossRef]

Chauvet, M.

F. Pettazzi, V. Coda, G. Fanjoux, M. Chauvet, and E. Fazio, “Dynamic of second harmonic generation in photovoltaic photorefractive quadratic medium,” J. Opt. Soc. Am. B 27(1), 1–9 (2010).
[CrossRef]

F. Pettazzi, V. Coda, G. Fanjoux, M. Chauvet, and E. Fazio, “Dynamic of second harmonic generation in photovoltaic photorefractive quadratic medium,” J. Opt. Soc. Am. B 27(1), 1–9 (2010).
[CrossRef]

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. Express 17(5), 3141–3147 (2009).
[CrossRef] [PubMed]

J. Safioui, F. Devaux, and M. Chauvet, “Pyroliton: pyroelectric spatial soliton,” Opt. Express 17(24), 22209–22216 (2009).
[CrossRef] [PubMed]

J. Safioui, M. Chauvet, F. Devaux, V. Coda, F. Pettazzi, M. Alonzo, and E. Fazio, “Polarization and configuration dependence of beam self-focusing in photorefractive LiNbO3,” J. Opt. Soc. Am. B 26(3), 487–492 (2009).
[CrossRef]

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. Express 17(5), 3141–3147 (2009).
[CrossRef] [PubMed]

F. Pettazzi, V. Coda, M. Chauvet, and E. Fazio, “Frequency doubling in self-induced waveguides in lithium niobate,” Opt. Commun. 272(1), 238–241 (2007).
[CrossRef]

F. Pettazzi, M. Alonzo, M. Centini, A. Petris, V. I. Vlad, M. Chauvet, and E. Fazio, “Self-trapping of low-energy infrared femtosecond beams in lithium niobate,” Phys. Rev. A 76(6), 063818–063821 (2007).
[CrossRef]

V. Coda, M. Chauvet, F. Pettazzi, and E. Fazio, “3-D integrated optical interconnect induced by self-focused beam,” Electron. Lett. 42(8), 463–465 (2006).
[CrossRef]

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of Optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[CrossRef]

Coda, V.

Crosignani, B.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[CrossRef] [PubMed]

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

Danielius, R.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,” Phys. Rev. Lett. 81(3), 570–573 (1998).
[CrossRef]

de Ceglia, D.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Devaux, F.

Di Porto, P.

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

Di Trapani, P.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,” Phys. Rev. Lett. 81(3), 570–573 (1998).
[CrossRef]

DiPorto, P.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[CrossRef] [PubMed]

Drummond, P. D.

Dubietis, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,” Phys. Rev. Lett. 81(3), 570–573 (1998).
[CrossRef]

Duree, G.

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

Fanjoux, G.

Fazio, E.

F. Pettazzi, V. Coda, G. Fanjoux, M. Chauvet, and E. Fazio, “Dynamic of second harmonic generation in photovoltaic photorefractive quadratic medium,” J. Opt. Soc. Am. B 27(1), 1–9 (2010).
[CrossRef]

F. Pettazzi, V. Coda, G. Fanjoux, M. Chauvet, and E. Fazio, “Dynamic of second harmonic generation in photovoltaic photorefractive quadratic medium,” J. Opt. Soc. Am. B 27(1), 1–9 (2010).
[CrossRef]

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. Express 17(5), 3141–3147 (2009).
[CrossRef] [PubMed]

J. Safioui, M. Chauvet, F. Devaux, V. Coda, F. Pettazzi, M. Alonzo, and E. Fazio, “Polarization and configuration dependence of beam self-focusing in photorefractive LiNbO3,” J. Opt. Soc. Am. B 26(3), 487–492 (2009).
[CrossRef]

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. Express 17(5), 3141–3147 (2009).
[CrossRef] [PubMed]

F. Pettazzi, V. Coda, M. Chauvet, and E. Fazio, “Frequency doubling in self-induced waveguides in lithium niobate,” Opt. Commun. 272(1), 238–241 (2007).
[CrossRef]

F. Pettazzi, M. Alonzo, M. Centini, A. Petris, V. I. Vlad, M. Chauvet, and E. Fazio, “Self-trapping of low-energy infrared femtosecond beams in lithium niobate,” Phys. Rev. A 76(6), 063818–063821 (2007).
[CrossRef]

V. Coda, M. Chauvet, F. Pettazzi, and E. Fazio, “3-D integrated optical interconnect induced by self-focused beam,” Electron. Lett. 42(8), 463–465 (2006).
[CrossRef]

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of Optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[CrossRef]

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[CrossRef] [PubMed]

Hasegawa, A.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23(4), 171 (1973).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. anomalous dispersion,” Appl. Phys. Lett. 23(3), 142 (1973).
[CrossRef]

Haus, J. W.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Jackel, J. L.

Kandidov, V. P.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Karamzin, Y. N.

Y. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Sov. Phys. JETP 41, 414–416 (1976).

Kivshar, Y. S.

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52(2), 1670–1674 (1995).
[CrossRef] [PubMed]

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19(20), 1612–1614 (1994).
[CrossRef] [PubMed]

Kosareva, O. G.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Leaird, D. E.

Liu, X.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of spatio-temporal solitons,” Phys. Rev. Lett. 82(23), 4631–4634 (1999).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[CrossRef] [PubMed]

C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ2: χ2 cascading,” J. Opt. Soc. Am. B 11(12), 2434–2443 (1994).
[CrossRef]

Mlejnek, M.

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, “Second Harmonic Generation of Femtosecond Pulses at the Boundary of a Nonlinear Dielectric,” Phys. Rev. Lett. 83(15), 2934–2937 (1999).
[CrossRef]

Moloney, J. V.

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, “Second Harmonic Generation of Femtosecond Pulses at the Boundary of a Nonlinear Dielectric,” Phys. Rev. Lett. 83(15), 2934–2937 (1999).
[CrossRef]

Neurgaonkar, R.

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

Odoulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Oliver, M. K.

Pershan, P. S.

N. Bloembergen and P. S. Pershan, “Light Waves at the Boundary of Nonlinear Media,” Phys. Rev. 128(2), 606–622 (1962).
[CrossRef]

Petris, A.

F. Pettazzi, M. Alonzo, M. Centini, A. Petris, V. I. Vlad, M. Chauvet, and E. Fazio, “Self-trapping of low-energy infrared femtosecond beams in lithium niobate,” Phys. Rev. A 76(6), 063818–063821 (2007).
[CrossRef]

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
[CrossRef]

Pettazzi, F.

F. Pettazzi, V. Coda, G. Fanjoux, M. Chauvet, and E. Fazio, “Dynamic of second harmonic generation in photovoltaic photorefractive quadratic medium,” J. Opt. Soc. Am. B 27(1), 1–9 (2010).
[CrossRef]

F. Pettazzi, V. Coda, G. Fanjoux, M. Chauvet, and E. Fazio, “Dynamic of second harmonic generation in photovoltaic photorefractive quadratic medium,” J. Opt. Soc. Am. B 27(1), 1–9 (2010).
[CrossRef]

J. Safioui, M. Chauvet, F. Devaux, V. Coda, F. Pettazzi, M. Alonzo, and E. Fazio, “Polarization and configuration dependence of beam self-focusing in photorefractive LiNbO3,” J. Opt. Soc. Am. B 26(3), 487–492 (2009).
[CrossRef]

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. Express 17(5), 3141–3147 (2009).
[CrossRef] [PubMed]

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. Express 17(5), 3141–3147 (2009).
[CrossRef] [PubMed]

F. Pettazzi, M. Alonzo, M. Centini, A. Petris, V. I. Vlad, M. Chauvet, and E. Fazio, “Self-trapping of low-energy infrared femtosecond beams in lithium niobate,” Phys. Rev. A 76(6), 063818–063821 (2007).
[CrossRef]

F. Pettazzi, V. Coda, M. Chauvet, and E. Fazio, “Frequency doubling in self-induced waveguides in lithium niobate,” Opt. Commun. 272(1), 238–241 (2007).
[CrossRef]

V. Coda, M. Chauvet, F. Pettazzi, and E. Fazio, “3-D integrated optical interconnect induced by self-focused beam,” Electron. Lett. 42(8), 463–465 (2006).
[CrossRef]

Piskarskas, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,” Phys. Rev. Lett. 81(3), 570–573 (1998).
[CrossRef]

Qian, L. J.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of spatio-temporal solitons,” Phys. Rev. Lett. 82(23), 4631–4634 (1999).
[CrossRef]

Ramadan, W.

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
[CrossRef]

Renzi, F.

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
[CrossRef]

Rinaldi, R.

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
[CrossRef]

Roppo, V.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Safioui, J.

Salamo, G.

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

Scalora, M.

Schiek, R.

Segev, M.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[CrossRef] [PubMed]

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

Sharp, E.

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

Shultz, J.

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

Sibilia, C.

Silberberg, Y.

Smith, P. W. E.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Steblina, V. V.

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52(2), 1670–1674 (1995).
[CrossRef] [PubMed]

Stegeman, G. I.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[CrossRef] [PubMed]

Sukhorukov, A. P.

Y. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Sov. Phys. JETP 41, 414–416 (1976).

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. anomalous dispersion,” Appl. Phys. Lett. 23(3), 142 (1973).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23(4), 171 (1973).
[CrossRef]

Torner, L.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[CrossRef] [PubMed]

C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ2: χ2 cascading,” J. Opt. Soc. Am. B 11(12), 2434–2443 (1994).
[CrossRef]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[CrossRef] [PubMed]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of Optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[CrossRef]

Valiulis, G.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,” Phys. Rev. Lett. 81(3), 570–573 (1998).
[CrossRef]

Valley, G. C.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[CrossRef] [PubMed]

VanStryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[CrossRef] [PubMed]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Vlad, V. I.

F. Pettazzi, M. Alonzo, M. Centini, A. Petris, V. I. Vlad, M. Chauvet, and E. Fazio, “Self-trapping of low-energy infrared femtosecond beams in lithium niobate,” Phys. Rev. A 76(6), 063818–063821 (2007).
[CrossRef]

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
[CrossRef]

Vogel, E. M.

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[CrossRef] [PubMed]

Weiner, A. M.

Werner, M. J.

Wise, F. W.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of spatio-temporal solitons,” Phys. Rev. Lett. 82(23), 4631–4634 (1999).
[CrossRef]

Wright, E. M.

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, “Second Harmonic Generation of Femtosecond Pulses at the Boundary of a Nonlinear Dielectric,” Phys. Rev. Lett. 83(15), 2934–2937 (1999).
[CrossRef]

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[CrossRef] [PubMed]

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. anomalous dispersion,” Appl. Phys. Lett. 23(3), 142 (1973).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23(4), 171 (1973).
[CrossRef]

Electron. Lett. (1)

V. Coda, M. Chauvet, F. Pettazzi, and E. Fazio, “3-D integrated optical interconnect induced by self-focused beam,” Electron. Lett. 42(8), 463–465 (2006).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

J. Opt. Soc. Am. B (5)

Opt. Commun. (1)

F. Pettazzi, V. Coda, M. Chauvet, and E. Fazio, “Frequency doubling in self-induced waveguides in lithium niobate,” Opt. Commun. 272(1), 238–241 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. (1)

N. Bloembergen and P. S. Pershan, “Light Waves at the Boundary of Nonlinear Media,” Phys. Rev. 128(2), 606–622 (1962).
[CrossRef]

Phys. Rev. A (3)

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52(2), 1670–1674 (1995).
[CrossRef] [PubMed]

F. Pettazzi, M. Alonzo, M. Centini, A. Petris, V. I. Vlad, M. Chauvet, and E. Fazio, “Self-trapping of low-energy infrared femtosecond beams in lithium niobate,” Phys. Rev. A 76(6), 063818–063821 (2007).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Phys. Rev. Lett. (7)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[CrossRef] [PubMed]

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,” Phys. Rev. Lett. 81(3), 570–573 (1998).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, “Generation of spatio-temporal solitons,” Phys. Rev. Lett. 82(23), 4631–4634 (1999).
[CrossRef]

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of Optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[CrossRef]

G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[CrossRef] [PubMed]

M. Mlejnek, E. M. Wright, J. V. Moloney, and N. Bloembergen, “Second Harmonic Generation of Femtosecond Pulses at the Boundary of a Nonlinear Dielectric,” Phys. Rev. Lett. 83(15), 2934–2937 (1999).
[CrossRef]

Sov. Phys. JETP (1)

Y. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Sov. Phys. JETP 41, 414–416 (1976).

Other (1)

V.G. Dmitriev, G.G. Gurzadyan, D.N. Nikogosyan, Handbook of Nonlinear Optical Crystals. 2nd edition, (Springer).

Supplementary Material (2)

» Media 1: MPG (1416 KB)     
» Media 2: MPG (1302 KB)     

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Figures (8)

Fig. 1
Fig. 1

The used samples had tilted input faces in order to separate the two generated second-harmonic pulses since the beginning.

Fig. 2
Fig. 2

The experimental set-up.

Fig. 3
Fig. 3

transverse shape of 800nm beam at 120 μW of input power.

Fig. 4
Fig. 4

Evolution in time of the beams (Media 1) and simulton formation at 160 μW of input pump power. The whole experiment shown in the movie has a length of 5 min in real. Some frames have been selected to better visualize the phenomenon: A) after 20 sec, B)2 min 52 sec, C) 3 min 23 sec, D) 4 min 28 sec.

Fig. 5
Fig. 5

Numerical simulation of the simulton formation.

Fig. 6
Fig. 6

Twin simulton profile.

Fig. 7
Fig. 7

Filamentation experiment (Media 2) with a RGB detail of the filamented beam. the phenomenon was obtained pumping with 60 GW/cm2.

Fig. 8
Fig. 8

Experimental relation between simulton hyperbolic waists and intensities.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

2 E ω 1 c 2 ε × 2 E ω t 2 = 1 c 2 2 t 2 d ( ω ; 2 ω , ω ) : E 2 ω E ω *
2 E 2 ω 1 c 2 ε × 2 E 2 ω t 2 = 1 c 2 2 t 2 ( d ( 2 ω ; ω , ω ) : E ω E ω + n 0 2 R : E S C 1 + | E 2 ω | E b a c k g r o u n d E 2 ω )
N D + t = σ | E 2 ω | 2 ( N D N D + ) ξ n e N D +
ρ = e ( N D + N A n e )
( ε : E S C ) = ρ
ρ t + J = 0
J = e μ n e E S C + μ K B T n e + β P V ( N D N D + ) | E 2 ω | 2 c ^
y = 1.8 + 1.6   e x 11.1 .

Metrics