Abstract

Energy redistribution between two subpicosecond laser pulses of 2.5 eV photon energy is observed and studied in congruent, nominally undoped LiNbO3, aiming to reveal the underlying coupling mechanisms. The dependences of pulse amplification on intensity, frequency detuning and pulse duration point to two different contributions of coupling, both based on self-diffraction from a recorded dynamic grating. The first one is caused by a difference in pulse intensities (transient energy transfer) while the second one originates from a difference in pulse frequencies. The latter appears when chirped pulses are mutually delayed in time. A quite high coupling efficiency has been observed in a 280 µm thin crystal: one order of magnitude energy amplification of a weak pulse and nearly 10% net energy enhancement of one pulse for the case of equal input intensities.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2016 (1)

Y. Sivan, S. Rozenberg, A. Halstuch, and A.A. Ishaaya, “Nonlinear wave interactions between short pulses of different spatio-temporal extents,” Sci. Rep. 6, 29010 (2016).
[Crossref] [PubMed]

2015 (4)

H. Badorreck, A. Shumelyuk, S. Nolte, M. Imlau, and S. Odoulov, “Doppler-shifted Raman-Nath diffraction from gratings recorded in LiNbO3 with ultra-short laser pulses of different color,” Opt. Mater. Express 6, 517–522 (2015).
[Crossref]

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K. M. Voit, and M. Imlau, “Interference and holography with femtosecong laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
[Crossref]

H. Badorreck, S. Nolte, F. Freytag, P. Bäune, V. Dieckmann, and M. Imlau, “Scanning nonlinear absorption in lithium niobate over the time regime of small polaron formation,” Opt. Mater. Express 5, 2729–2741 (2015).
[Crossref]

2013 (1)

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experimets,” Phys. Rev. A 87, 053801 (2013).
[Crossref]

2012 (2)

2010 (2)

Y. Liu, M. Durand, S. Chen, A. Houdard, B. Prade, B. Forrestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref] [PubMed]

X. Yang, J. Wu, Y. Tong, L. Ding, Z. Xu, and H. Zheng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett. 97, 071108 (2010).
[Crossref]

2009 (4)

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett. 22, 13–16 (2009).

Y. Zhao, T. E. Witt, and R. J. Gordon, “Efficient energy transfer between laser beams by stimulated Raman scattering,” Phys. Rev. Lett. 103, 173903 (2009).
[Crossref] [PubMed]

C. W. Luo, Y. T. Wang, F. W. Chen, H. C. Shin, and T. Kobayashi, “Eliminate coherence spike in reflection-type pump-probe measurements,” Opt. Express 17, 11321–11327 (2009).
[Crossref] [PubMed]

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron dynamics in lithium niobate upon femtosecond pulse irradiation: Influence of magnesium doping and stoichiometry control,” J. Appl. Phys. 105, 083102 (2009).
[Crossref]

2007 (1)

P. Reckenthaeler, D. Maxien, Th. Woike, and K. Buse, “Separation of optical Kerr and free-carrier nonlinear responses with femtosecond light pulses in LiNbO3 crystals,” Phys. Rev. B 76, 195117 (2007).
[Crossref]

2005 (3)

2000 (2)

1997 (3)

A. Dogariu and D. J. Hagan, “Low frequency Raman gain measurements using chirped pulses,” Opt. Express 1, 73–76 (1997).
[Crossref] [PubMed]

A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland, and N. Bloembergen, “Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B 14, 769–803 (1997).
[Crossref]

N. Tang and R. L. Sutherland, “Time-domain theory for pump-probe experiments with chirped pulses,” J. Opt. Soc. Am. B 14, 3412–3423 (1997).
[Crossref]

1995 (1)

1994 (1)

1993 (1)

G. Rivoire and D. Wang, “Dynamics of CS2 in a large spectral bandwidth stimulated Rayleigh-wing scattering,” J. Chem. Phys. 99, 9460–9464 (1993).
[Crossref]

1989 (1)

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–517 (1989).
[Crossref]

1984 (1)

H. J. Eichler, D. Langhans, and F. Massmann, “Coherence peaks in picosecond sampling experiments,” Opt. Commun. 50, 117–122 (1984).
[Crossref]

1979 (1)

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[Crossref]

1977 (1)

N. Kukhtarev, V. Markov, and S. Odoulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
[Crossref]

1976 (1)

V. Bryksin, A. Groznyj, V. Sidorovich, and D. Stasel’ko, “Efficient amplification of weak light beams by 3D dynamic holograms in media with thermal nonlinearity,” Soviet Physics: Technical Physics Letters,  2, 561 (1976).

1972 (1)

D. Staebler and J. Amodei, “Coupled wave analysis of holographic storage in LiNbO3,” J. Appl. Pnys. 43, 1042–1049 (1972).
[Crossref]

1969 (1)

M. E. Mack, “Stimulated thermal light scattering in the picosecond regime,” Phys. Rev. Lett. 22, 13–16 (1969).
[Crossref]

1968 (1)

F. Gires, “Résultats expérimentaux sur la reflexion thermique stimulée,” C. R. Acad. Sci. Ser. B t. 266596–600 (1968).

Amodei, J.

D. Staebler and J. Amodei, “Coupled wave analysis of holographic storage in LiNbO3,” J. Appl. Pnys. 43, 1042–1049 (1972).
[Crossref]

Ashihara, S.

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron dynamics in lithium niobate upon femtosecond pulse irradiation: Influence of magnesium doping and stoichiometry control,” J. Appl. Phys. 105, 083102 (2009).
[Crossref]

Badorreck, H.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K. M. Voit, and M. Imlau, “Interference and holography with femtosecong laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

H. Badorreck, S. Nolte, F. Freytag, P. Bäune, V. Dieckmann, and M. Imlau, “Scanning nonlinear absorption in lithium niobate over the time regime of small polaron formation,” Opt. Mater. Express 5, 2729–2741 (2015).
[Crossref]

M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
[Crossref]

H. Badorreck, A. Shumelyuk, S. Nolte, M. Imlau, and S. Odoulov, “Doppler-shifted Raman-Nath diffraction from gratings recorded in LiNbO3 with ultra-short laser pulses of different color,” Opt. Mater. Express 6, 517–522 (2015).
[Crossref]

Bäune, P.

Bernstein, A. C.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett. 22, 13–16 (2009).

Beyer, O.

Bloembergen, N.

A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland, and N. Bloembergen, “Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B 14, 769–803 (1997).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3 ed. (Academic, 2008).

Brubaker, R. M.

Bryksin, V.

V. Bryksin, A. Groznyj, V. Sidorovich, and D. Stasel’ko, “Efficient amplification of weak light beams by 3D dynamic holograms in media with thermal nonlinearity,” Soviet Physics: Technical Physics Letters,  2, 561 (1976).

Buse, K.

Chen, F. W.

Chen, S.

Y. Liu, M. Durand, S. Chen, A. Houdard, B. Prade, B. Forrestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref] [PubMed]

Cheng, Y.-H.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experimets,” Phys. Rev. A 87, 053801 (2013).
[Crossref]

Chevalier, R.

Crespo, H.

Dieckmann, V.

Ding, L.

X. Yang, J. Wu, Y. Tong, L. Ding, Z. Xu, and H. Zheng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett. 97, 071108 (2010).
[Crossref]

Ditmire, T.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett. 22, 13–16 (2009).

Dogariu, A.

A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland, and N. Bloembergen, “Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B 14, 769–803 (1997).
[Crossref]

A. Dogariu and D. J. Hagan, “Low frequency Raman gain measurements using chirped pulses,” Opt. Express 1, 73–76 (1997).
[Crossref] [PubMed]

Dorkenoo, K. D.

Dos Santos, A.

Durand, M.

Y. Liu, M. Durand, S. Chen, A. Houdard, B. Prade, B. Forrestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref] [PubMed]

Dyer, G. M.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett. 22, 13–16 (2009).

Eichler, H. J.

H. J. Eichler, D. Langhans, and F. Massmann, “Coherence peaks in picosecond sampling experiments,” Opt. Commun. 50, 117–122 (1984).
[Crossref]

Forrestier, B.

Y. Liu, M. Durand, S. Chen, A. Houdard, B. Prade, B. Forrestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref] [PubMed]

Freytag, F.

Ge, X.

C. Gong, Y. Zheng, Z. Zheng, C. Li, X. Ge, R. Li, and Z. Xu, “Energy trsnsfer between few-cycle laser filamentrs in air,” Appl. Phys. Lett. 101, 251111 (2012).
[Crossref]

Gires, F.

F. Gires, “Résultats expérimentaux sur la reflexion thermique stimulée,” C. R. Acad. Sci. Ser. B t. 266596–600 (1968).

Gong, C.

C. Gong, Y. Zheng, Z. Zheng, C. Li, X. Ge, R. Li, and Z. Xu, “Energy trsnsfer between few-cycle laser filamentrs in air,” Appl. Phys. Lett. 101, 251111 (2012).
[Crossref]

Gordon, R. J.

Y. Zhao, T. E. Witt, and R. J. Gordon, “Efficient energy transfer between laser beams by stimulated Raman scattering,” Phys. Rev. Lett. 103, 173903 (2009).
[Crossref] [PubMed]

Groznyj, A.

V. Bryksin, A. Groznyj, V. Sidorovich, and D. Stasel’ko, “Efficient amplification of weak light beams by 3D dynamic holograms in media with thermal nonlinearity,” Soviet Physics: Technical Physics Letters,  2, 561 (1976).

Grunnet-Jepsen, A.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

Hagan, D. J.

A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland, and N. Bloembergen, “Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B 14, 769–803 (1997).
[Crossref]

A. Dogariu and D. J. Hagan, “Low frequency Raman gain measurements using chirped pulses,” Opt. Express 1, 73–76 (1997).
[Crossref] [PubMed]

Halstuch, A.

Y. Sivan, S. Rozenberg, A. Halstuch, and A.A. Ishaaya, “Nonlinear wave interactions between short pulses of different spatio-temporal extents,” Sci. Rep. 6, 29010 (2016).
[Crossref] [PubMed]

Harmon, E. S.

Hirohashi, J.

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron dynamics in lithium niobate upon femtosecond pulse irradiation: Influence of magnesium doping and stoichiometry control,” J. Appl. Phys. 105, 083102 (2009).
[Crossref]

Houdard, A.

Y. Liu, M. Durand, S. Chen, A. Houdard, B. Prade, B. Forrestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref] [PubMed]

Hsieh, H. T.

Hus, X.

Imlau, M.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K. M. Voit, and M. Imlau, “Interference and holography with femtosecong laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
[Crossref]

H. Badorreck, S. Nolte, F. Freytag, P. Bäune, V. Dieckmann, and M. Imlau, “Scanning nonlinear absorption in lithium niobate over the time regime of small polaron formation,” Opt. Mater. Express 5, 2729–2741 (2015).
[Crossref]

H. Badorreck, A. Shumelyuk, S. Nolte, M. Imlau, and S. Odoulov, “Doppler-shifted Raman-Nath diffraction from gratings recorded in LiNbO3 with ultra-short laser pulses of different color,” Opt. Mater. Express 6, 517–522 (2015).
[Crossref]

Ishaaya, A.A.

Y. Sivan, S. Rozenberg, A. Halstuch, and A.A. Ishaaya, “Nonlinear wave interactions between short pulses of different spatio-temporal extents,” Sci. Rep. 6, 29010 (2016).
[Crossref] [PubMed]

Kattawar, G. W.

Kirkpatrick, S.

R. L. Sutherland, D. G. McLean, and S. Kirkpatrick, Handbook of Nonlinear Optics, 2 ed. (CRC, 2003).
[Crossref]

Klolomenskii, A. A.

Kobayashi, T.

Kukhtarev, N.

N. Kukhtarev, V. Markov, and S. Odoulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
[Crossref]

Kukhtarev, N. V.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[Crossref]

Langhans, D.

H. J. Eichler, D. Langhans, and F. Massmann, “Coherence peaks in picosecond sampling experiments,” Opt. Commun. 50, 117–122 (1984).
[Crossref]

Lecoq, J. P.

Levis, R. J.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experimets,” Phys. Rev. A 87, 053801 (2013).
[Crossref]

Li, C.

C. Gong, Y. Zheng, Z. Zheng, C. Li, X. Ge, R. Li, and Z. Xu, “Energy trsnsfer between few-cycle laser filamentrs in air,” Appl. Phys. Lett. 101, 251111 (2012).
[Crossref]

Li, R.

C. Gong, Y. Zheng, Z. Zheng, C. Li, X. Ge, R. Li, and Z. Xu, “Energy trsnsfer between few-cycle laser filamentrs in air,” Appl. Phys. Lett. 101, 251111 (2012).
[Crossref]

Liu, Y.

Y. Liu, M. Durand, S. Chen, A. Houdard, B. Prade, B. Forrestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref] [PubMed]

Luo, C. W.

Mack, M. E.

M. E. Mack, “Stimulated thermal light scattering in the picosecond regime,” Phys. Rev. Lett. 22, 13–16 (1969).
[Crossref]

Markov, V.

N. Kukhtarev, V. Markov, and S. Odoulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
[Crossref]

Massmann, F.

H. J. Eichler, D. Langhans, and F. Massmann, “Coherence peaks in picosecond sampling experiments,” Opt. Commun. 50, 117–122 (1984).
[Crossref]

Maxien, D.

McCole, E. T.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experimets,” Phys. Rev. A 87, 053801 (2013).
[Crossref]

McCormick, M.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett. 22, 13–16 (2009).

McLean, D. G.

R. L. Sutherland, D. G. McLean, and S. Kirkpatrick, Handbook of Nonlinear Optics, 2 ed. (CRC, 2003).
[Crossref]

Melloch, M. R.

Mendonca, J. T.

Merschjann, C.

M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
[Crossref]

Milchberg, H. M.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experimets,” Phys. Rev. A 87, 053801 (2013).
[Crossref]

Mysyrowicz, A.

Y. Liu, M. Durand, S. Chen, A. Houdard, B. Prade, B. Forrestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref] [PubMed]

Nolte, D. D.

Nolte, S.

Odhner, J. H.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experimets,” Phys. Rev. A 87, 053801 (2013).
[Crossref]

Odoulov, S.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K. M. Voit, and M. Imlau, “Interference and holography with femtosecong laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

H. Badorreck, A. Shumelyuk, S. Nolte, M. Imlau, and S. Odoulov, “Doppler-shifted Raman-Nath diffraction from gratings recorded in LiNbO3 with ultra-short laser pulses of different color,” Opt. Mater. Express 6, 517–522 (2015).
[Crossref]

N. Kukhtarev, V. Markov, and S. Odoulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
[Crossref]

Odulov, S. G.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[Crossref]

Palastro, J. P.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experimets,” Phys. Rev. A 87, 053801 (2013).
[Crossref]

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer, 1985).
[Crossref]

Prade, B.

Y. Liu, M. Durand, S. Chen, A. Houdard, B. Prade, B. Forrestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref] [PubMed]

Psaltis, D.

Reckenthaeler, P.

P. Reckenthaeler, D. Maxien, Th. Woike, and K. Buse, “Separation of optical Kerr and free-carrier nonlinear responses with femtosecond light pulses in LiNbO3 crystals,” Phys. Rev. B 76, 195117 (2007).
[Crossref]

Rivoire, G.

K. D. Dorkenoo, D. Wang, N. P. Xuan, J. P. Lecoq, R. Chevalier, and G. Rivoire, “Stimulated Rayleigh-wing scattering with two-beam coupling in CS2,” J. Opt. Soc. Am. B 12, 37–42 (1995).
[Crossref]

G. Rivoire and D. Wang, “Dynamics of CS2 in a large spectral bandwidth stimulated Rayleigh-wing scattering,” J. Chem. Phys. 99, 9460–9464 (1993).
[Crossref]

Rozenberg, S.

Y. Sivan, S. Rozenberg, A. Halstuch, and A.A. Ishaaya, “Nonlinear wave interactions between short pulses of different spatio-temporal extents,” Sci. Rep. 6, 29010 (2016).
[Crossref] [PubMed]

Said, A. A.

A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland, and N. Bloembergen, “Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B 14, 769–803 (1997).
[Crossref]

Sanders, J. C.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett. 22, 13–16 (2009).

Sasamoto, S.

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron dynamics in lithium niobate upon femtosecond pulse irradiation: Influence of magnesium doping and stoichiometry control,” J. Appl. Phys. 105, 083102 (2009).
[Crossref]

Shin, H. C.

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer, 1985).
[Crossref]

Shroeder, H.

Shumelyuk, A.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K. M. Voit, and M. Imlau, “Interference and holography with femtosecong laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

H. Badorreck, A. Shumelyuk, S. Nolte, M. Imlau, and S. Odoulov, “Doppler-shifted Raman-Nath diffraction from gratings recorded in LiNbO3 with ultra-short laser pulses of different color,” Opt. Mater. Express 6, 517–522 (2015).
[Crossref]

Sidorovich, V.

V. Bryksin, A. Groznyj, V. Sidorovich, and D. Stasel’ko, “Efficient amplification of weak light beams by 3D dynamic holograms in media with thermal nonlinearity,” Soviet Physics: Technical Physics Letters,  2, 561 (1976).

Sivan, Y.

Y. Sivan, S. Rozenberg, A. Halstuch, and A.A. Ishaaya, “Nonlinear wave interactions between short pulses of different spatio-temporal extents,” Sci. Rep. 6, 29010 (2016).
[Crossref] [PubMed]

Smolorz, S.

Sokolov, A. V.

Solymar, L.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

Soskin, M. S.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[Crossref]

Springer, M.

Staebler, D.

D. Staebler and J. Amodei, “Coupled wave analysis of holographic storage in LiNbO3,” J. Appl. Pnys. 43, 1042–1049 (1972).
[Crossref]

Stasel’ko, D.

V. Bryksin, A. Groznyj, V. Sidorovich, and D. Stasel’ko, “Efficient amplification of weak light beams by 3D dynamic holograms in media with thermal nonlinearity,” Soviet Physics: Technical Physics Letters,  2, 561 (1976).

Strohbaber, J.

Stryker, B. D.

Sturman, B.

Sutherland, R. L.

Tang, N.

Tong, Y.

X. Yang, J. Wu, Y. Tong, L. Ding, Z. Xu, and H. Zheng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett. 97, 071108 (2010).
[Crossref]

Träger, F.

F. Träger, Springer Handbook of Lasers and Optics2 ed. (Springer Science & Business Media, 2012), Chap. 12.
[Crossref]

Trebino, R.

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer Science & Business Media, 2012).

Trendafilova, C.

Van Stryland, E. W.

A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland, and N. Bloembergen, “Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B 14, 769–803 (1997).
[Crossref]

Vinetskii, V. L.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[Crossref]

Voit, K. M.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K. M. Voit, and M. Imlau, “Interference and holography with femtosecong laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

von Korff Schmising, C.

Wahlstrand, J. K.

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experimets,” Phys. Rev. A 87, 053801 (2013).
[Crossref]

Wang, D.

K. D. Dorkenoo, D. Wang, N. P. Xuan, J. P. Lecoq, R. Chevalier, and G. Rivoire, “Stimulated Rayleigh-wing scattering with two-beam coupling in CS2,” J. Opt. Soc. Am. B 12, 37–42 (1995).
[Crossref]

G. Rivoire and D. Wang, “Dynamics of CS2 in a large spectral bandwidth stimulated Rayleigh-wing scattering,” J. Chem. Phys. 99, 9460–9464 (1993).
[Crossref]

Wang, Q. N.

Wang, Y. T.

Webb, D. J.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

Wise, F.

Witt, T. E.

Y. Zhao, T. E. Witt, and R. J. Gordon, “Efficient energy transfer between laser beams by stimulated Raman scattering,” Phys. Rev. Lett. 103, 173903 (2009).
[Crossref] [PubMed]

Woerdman, J. P.

J. P. Woerdman, “Some optical and electrical properties of a laser-generated free-carrier plasma in Si (Thesis),” Philips Res. ReptsSuppl. #7 (1971).

Woike, Th.

P. Reckenthaeler, D. Maxien, Th. Woike, and K. Buse, “Separation of optical Kerr and free-carrier nonlinear responses with femtosecond light pulses in LiNbO3 crystals,” Phys. Rev. B 76, 195117 (2007).
[Crossref]

Wu, J.

X. Yang, J. Wu, Y. Tong, L. Ding, Z. Xu, and H. Zheng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett. 97, 071108 (2010).
[Crossref]

Xia, T.

A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland, and N. Bloembergen, “Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B 14, 769–803 (1997).
[Crossref]

Xu, Z.

C. Gong, Y. Zheng, Z. Zheng, C. Li, X. Ge, R. Li, and Z. Xu, “Energy trsnsfer between few-cycle laser filamentrs in air,” Appl. Phys. Lett. 101, 251111 (2012).
[Crossref]

X. Yang, J. Wu, Y. Tong, L. Ding, Z. Xu, and H. Zheng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett. 97, 071108 (2010).
[Crossref]

Xuan, N. P.

Yang, X.

X. Yang, J. Wu, Y. Tong, L. Ding, Z. Xu, and H. Zheng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett. 97, 071108 (2010).
[Crossref]

Yariv, A.

P. Yeh and A. Yariv, Optical Waves in Crystals, Wiley Series in Pure and Applied Optics (Wiley, 1984).

Yeh, P.

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–517 (1989).
[Crossref]

P. Yeh, Introduction to Photorefractive Nonlinear Optics, Wiley series in pure and applied optics (Wiley, 1993).

P. Yeh and A. Yariv, Optical Waves in Crystals, Wiley Series in Pure and Applied Optics (Wiley, 1984).

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer, 1985).
[Crossref]

Zhao, Y.

Y. Zhao, T. E. Witt, and R. J. Gordon, “Efficient energy transfer between laser beams by stimulated Raman scattering,” Phys. Rev. Lett. 103, 173903 (2009).
[Crossref] [PubMed]

Zheng, H.

X. Yang, J. Wu, Y. Tong, L. Ding, Z. Xu, and H. Zheng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett. 97, 071108 (2010).
[Crossref]

Zheng, Y.

C. Gong, Y. Zheng, Z. Zheng, C. Li, X. Ge, R. Li, and Z. Xu, “Energy trsnsfer between few-cycle laser filamentrs in air,” Appl. Phys. Lett. 101, 251111 (2012).
[Crossref]

Zheng, Z.

C. Gong, Y. Zheng, Z. Zheng, C. Li, X. Ge, R. Li, and Z. Xu, “Energy trsnsfer between few-cycle laser filamentrs in air,” Appl. Phys. Lett. 101, 251111 (2012).
[Crossref]

Zhi, M.

Appl. Phys. Lett. (2)

X. Yang, J. Wu, Y. Tong, L. Ding, Z. Xu, and H. Zheng, “Femtosecond laser pulse energy transfer induced by plasma grating due to filament interaction in air,” Appl. Phys. Lett. 97, 071108 (2010).
[Crossref]

C. Gong, Y. Zheng, Z. Zheng, C. Li, X. Ge, R. Li, and Z. Xu, “Energy trsnsfer between few-cycle laser filamentrs in air,” Appl. Phys. Lett. 101, 251111 (2012).
[Crossref]

Appl. Phys. Rev. (1)

M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
[Crossref]

C. R. Acad. Sci. Ser. B t. (1)

F. Gires, “Résultats expérimentaux sur la reflexion thermique stimulée,” C. R. Acad. Sci. Ser. B t. 266596–600 (1968).

IEEE J. Quantum Electron. (1)

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–517 (1989).
[Crossref]

J. Appl. Phys. (1)

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron dynamics in lithium niobate upon femtosecond pulse irradiation: Influence of magnesium doping and stoichiometry control,” J. Appl. Phys. 105, 083102 (2009).
[Crossref]

J. Appl. Pnys. (1)

D. Staebler and J. Amodei, “Coupled wave analysis of holographic storage in LiNbO3,” J. Appl. Pnys. 43, 1042–1049 (1972).
[Crossref]

J. Chem. Phys. (1)

G. Rivoire and D. Wang, “Dynamics of CS2 in a large spectral bandwidth stimulated Rayleigh-wing scattering,” J. Chem. Phys. 99, 9460–9464 (1993).
[Crossref]

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

Nat. Commun. (1)

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K. M. Voit, and M. Imlau, “Interference and holography with femtosecong laser pulses of different colours,” Nat. Commun. 6, 5866 (2015).
[Crossref]

Opt. Commun. (2)

H. J. Eichler, D. Langhans, and F. Massmann, “Coherence peaks in picosecond sampling experiments,” Opt. Commun. 50, 117–122 (1984).
[Crossref]

N. Kukhtarev, V. Markov, and S. Odoulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Opt. Mater. Express (2)

Phys. Rev. A (1)

J. K. Wahlstrand, J. H. Odhner, E. T. McCole, Y.-H. Cheng, J. P. Palastro, R. J. Levis, and H. M. Milchberg, “Effect of two-beam coupling in strong-field optical pump-probe experimets,” Phys. Rev. A 87, 053801 (2013).
[Crossref]

Phys. Rev. B (1)

P. Reckenthaeler, D. Maxien, Th. Woike, and K. Buse, “Separation of optical Kerr and free-carrier nonlinear responses with femtosecond light pulses in LiNbO3 crystals,” Phys. Rev. B 76, 195117 (2007).
[Crossref]

Phys. Rev. Lett. (4)

M. E. Mack, “Stimulated thermal light scattering in the picosecond regime,” Phys. Rev. Lett. 22, 13–16 (1969).
[Crossref]

Y. Liu, M. Durand, S. Chen, A. Houdard, B. Prade, B. Forrestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105, 055003 (2010).
[Crossref] [PubMed]

Y. Zhao, T. E. Witt, and R. J. Gordon, “Efficient energy transfer between laser beams by stimulated Raman scattering,” Phys. Rev. Lett. 103, 173903 (2009).
[Crossref] [PubMed]

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett. 22, 13–16 (2009).

Sci. Rep. (1)

Y. Sivan, S. Rozenberg, A. Halstuch, and A.A. Ishaaya, “Nonlinear wave interactions between short pulses of different spatio-temporal extents,” Sci. Rep. 6, 29010 (2016).
[Crossref] [PubMed]

Sov. Phys. Usp. (1)

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[Crossref]

Soviet Physics: Technical Physics Letters (1)

V. Bryksin, A. Groznyj, V. Sidorovich, and D. Stasel’ko, “Efficient amplification of weak light beams by 3D dynamic holograms in media with thermal nonlinearity,” Soviet Physics: Technical Physics Letters,  2, 561 (1976).

Other (10)

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer, 1985).
[Crossref]

F. Träger, Springer Handbook of Lasers and Optics2 ed. (Springer Science & Business Media, 2012), Chap. 12.
[Crossref]

P. Yeh and A. Yariv, Optical Waves in Crystals, Wiley Series in Pure and Applied Optics (Wiley, 1984).

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

P. Yeh, Introduction to Photorefractive Nonlinear Optics, Wiley series in pure and applied optics (Wiley, 1993).

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications, Vol. 1–3, Springer series in Optical Science, (Springer, 2007).

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer Science & Business Media, 2012).

R. L. Sutherland, D. G. McLean, and S. Kirkpatrick, Handbook of Nonlinear Optics, 2 ed. (CRC, 2003).
[Crossref]

R. W. Boyd, Nonlinear Optics, 3 ed. (Academic, 2008).

J. P. Woerdman, “Some optical and electrical properties of a laser-generated free-carrier plasma in Si (Thesis),” Philips Res. ReptsSuppl. #7 (1971).

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Figures (8)

Fig. 1
Fig. 1 Schematic of the experimental setup: variable neutral density filter (VF), double grating compressor/stretcher (GCS), glass plate (GP), 50/50 beamsplitter (BS), compensator plate (CP), optical delay line (DL), mirror (M), D-shaped mirror (DM), λ/2-waveplate, lenses f = 500 mm (L1,2), full crossing angle in air 2θ, lithium niobate sample (LN) with the polar c-axis normal to the plane of drawing, and silicon detectors (Dref, Dpu and Dpr).
Fig. 2
Fig. 2 Pulse delay dependence of the normalized probe pulse transmission with parallel (T, black dots) and orthogonal polarization (T, red squares). The inset shows the gain G (green squares) evaluated from Eq. (3). The total peak intensity of the two pulses is I ≈ 635 GW/cm2 with a peak intensity ratio of R ≈ 100, pulses duration of τc = (80 ± 5) fs and beam radii of r = (55 ± 5) µm.
Fig. 3
Fig. 3 Gain Gmax versus total pulse peak intensity I. Black and red symbols show the data for the intensity ratios R ≈ 1000 and R ≈ 100, respectively, for pulses with durations τc = (80 ± 5) fs and beam radii r = (55 ± 5) µm. For intensities below 300 GW/cm2 the measured data can be fitted with Gmax-1 ∝ Im. For R = 1000 such a fit gives m = 2.5 (green line); the gray shaded area is limited by functions with the exponents 2 < m < 4.
Fig. 4
Fig. 4 Gain Gt = 0) versus peak intensity ratio R in a log-log plot. Right and left branches show the experimentally measured gain for weak probe and weak pump pulses, respectively. The total peak intensity of two pulses is I ≈ 630 GW/cm2 (blue) and I ≈ 380 GW/cm2 (green) with pulses duration τc = (80 ± 5) fs and beam radii r = (55 ± 5 µm. Solid and dashed lines are plotted as a guide to the eye.
Fig. 5
Fig. 5 Pulse delay dependences of (a) normalized transmission Tt) for pump and probe pulses and (b) gain G(δt) evaluated according Eq. (5) (with flipped curve δt = −Δt for the data Tpu). Each pulse has an energy of W = (5.1 ± 0.1) µJ, a pulse duration of τc ≈ 235 fs and a bandwidth of Δω = 3.7 × 1013 rad/s. The beam radii are r ≈ 160 µm and the sum of the peak intensities of both pulses is I ≈ 100 GW/cm2.
Fig. 6
Fig. 6 Pulse delay dependence of gain G(δt) for (a) pulses with a negative frequency chirp and energies W = (2.6 ± 0.1) µJ and (b) pulses with a positive frequency chirp and energies W < 2 µJ. Identical pulses are used, with central wavelengths λ = 590 nm, bandwidths of Δω = 4.0 × 1013 rad/s and durations τc ≈ 200 fs. The pulse frequency detuning Ω estimated according to Eq. (4) is shown as the upper x-axis. Red and green colors mark two interacting pulses.
Fig. 7
Fig. 7 (a) Pulse duration dependences of largest gain Gmax (red dots) and pulse temporal mismatch that ensures this largest gain Δtmax (black squares). The red dotted lines are guiding the eye, while the black dotted line is a linear fit. (b) Pulse duration dependences of the chirp coefficient ω ˙ (gray shaded curve) and pulse frequency difference that provides the maximum gain Ωmax (blue squares), extracted from the data plotted in (a). The blue dotted line represents Ω ¯ max, the mean value of data above τc = 300 fs. A hyperbolic dependence ∝ 1/τc (black dots) shows the asymptotic behavior of the chirp coefficient ω ˙ for long pulses. Both pulses have the same central wavelengths λ = 488 nm and bandwidths of Δω = 3.7 × 1013 rad/s.
Fig. 8
Fig. 8 Gain of a weak probe pulse G-1 versus probe-pump pulse frequency detuning Ω = ωprωpu (black squares). Blue and red solid lines show qualitatively the expected contributions to the overall gain from transient beam-coupling and coupling from a moving grating (see text).

Equations (8)

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

I = 16 ln ( 2 ) π 3 W r 2 τ c .
ω ˙ = ( Δ ω / τ c ) 1 ( τ 0 / τ c ) 2 .
G ( Δ t ) = T ( Δ t ) T ( Δ t ) = A ( Δ t ) G ( Δ t ) A ( Δ t ) ,
Ω ( Δ t ) = ω pr , pu ( t Δ t ) ω pr , pu ( t ) = ω ˙ Δ t .
G pr ( Δ t ) = 2 P ( Δ t ) 1 + P ( Δ t ) , G pu ( Δ t ) = 2 1 + P ( Δ t ) .
Ω max = Δ ω τ c ϵ τ c = Δ ω ϵ .
g g 0 Ω τ c 1 + Ω 2 τ c 2 ,
I pr I pr ( 0 ) I pr ( 0 ) = 4 Φ 2 [ I pu ( 0 ) I pr ( 0 ) I pu ( 0 ) + I pr ( 0 ) ] exp ( t τ r ) [ 1 ( t τ r ) exp ( t τ r ) ] .

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