Abstract

Nominally undoped LiNbO3 crystals feature a pronounced mixed (absorption/refraction) nonlinear response in the blue-green spectrum domain that is sufficient for the excitation of moving dynamic gratings and the observation of selfdiffraction with Doppler shifted higher orders. This type of Raman-Nath selfdiffraction can be successfully used for up- and down- frequency conversion as well as for characterization of the recording pulses.

© 2016 Optical Society of America

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References

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  1. M. Horowitz, B. Fischer, Y. Barad, and Y. Silberberg, “Photorefractive effect in a BaTiO3 crystal at the 1.5-μm wavelength regime by two-photon absorption,” Opt. Lett. 21, 1120–1122 (1996).
    [Crossref] [PubMed]
  2. Hung-Te Hsieh, D. Psaltis, O. Beyer, D. Maxein, C. von Korff Schmising, K. Buse, and B. Sturman, “Femtosecond holography in lithium niobate crystals,” Opt. Lett. 30, 2233–2235 (2005).
    [Crossref] [PubMed]
  3. A. Shumelyuk, M. Imlau, V. Dieckmann, H. Badorreck, A. Grabar, and S. Odoulov, “Self-diffraction from two-photon absorption gratings in Sn2P2S6,” Opt. Lett. 37, 4065–4067 (2012).
    [Crossref] [PubMed]
  4. S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun.  65866 (2015).
    [PubMed]
  5. H. Crespo, J. T. Mendonca, and A. Dos Santos, “Cascaded highly nondegenerate four-wave-mixing phenomenon in transparent isotropic condensed media,” Opt. Lett. 25, 829–831 (2000).
    [Crossref]
  6. J. L. Silva, R. Weigand, and H. M. Crespo, “Octave spanning spectra and pulse synthesis by nondegenerate cascaded four-wave mixing,” Opt. Lett. 34, 2489–2491 (2009).
    [Crossref] [PubMed]
  7. Jinping He, Jun Liu, and Takayoshi Kobayashi, “Tunable multicolored femtosecond pulse generation using Cascaded Four-Wave Mixing in bulk materials,” Appl. Sci. 4, 444–467 (2014).
    [Crossref]
  8. S. Cabuk and A. Mamedov, “A study of the LiNbO3 and LiTaO3 absorption edge,” Tr. J. of Physics,  22, 41–45 (1986).
  9. M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, ”Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-Photon Absorption,” Phys Rev. Lett. 65, 97–99 (1990).
    [Crossref]
  10. 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. Mat. Express 5, 2729–2741 (2015).
    [Crossref]
  11. M. Imlau, V. Dieckmann, H. Badorreck, and A. Shumelyuk, “Tin hypothiodophosphate: Nonlinear response in the sub-100 fs time domain,” Opt. Mater. Express 1, 953–957 (2011).
    [Crossref]
  12. M. Imlau, H. Brüning, B. Schoke, R.-S. Hardt, D. Conradi, and C. Merschjann, “Hologram recording via spatial density modulation of NbLi4+/5+ antisites in lithium niobate,” Opt. Express 19, 15322–15238 (2011).
    [Crossref] [PubMed]
  13. C. M. Cirloganu, L. A. Padilha, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Extremely nondegenerate two-photon absorption in direct-gap semiconductors,” Opt. Express 19, 22951–22960 (2011).
    [Crossref] [PubMed]
  14. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
    [Crossref]
  15. M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
    [Crossref]
  16. Pochi Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quant. Electron.,  25, 484–519 (1989).
    [Crossref]
  17. H.J. Eichler, P. Günter, and D. Pohl, Laser-induced Dynamic Gratings, Springer Series in Optical Sciences, vol. 50, Springer Verlag, Berlin, Heidelberg, 1986.
    [Crossref]
  18. R. Brubaker, Q. Wang, D. Nolte, E. Harmon, and M. Melloch, “Steady-state four-wave mixing in photorefractive quantum wells with femtosecond pulses,” J. Opt. Soc. Am. B 11, 1038–1044 (1994).
    [Crossref]
  19. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, 2000).
    [Crossref]

2015 (3)

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun.  65866 (2015).
[PubMed]

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. Mat. 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]

2014 (1)

Jinping He, Jun Liu, and Takayoshi Kobayashi, “Tunable multicolored femtosecond pulse generation using Cascaded Four-Wave Mixing in bulk materials,” Appl. Sci. 4, 444–467 (2014).
[Crossref]

2012 (1)

2011 (4)

2009 (1)

2005 (1)

2000 (1)

1996 (1)

1994 (1)

1990 (1)

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, ”Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-Photon Absorption,” Phys Rev. Lett. 65, 97–99 (1990).
[Crossref]

1989 (1)

Pochi Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quant. Electron.,  25, 484–519 (1989).
[Crossref]

1986 (1)

S. Cabuk and A. Mamedov, “A study of the LiNbO3 and LiTaO3 absorption edge,” Tr. J. of Physics,  22, 41–45 (1986).

Badorreck, H.

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. Mat. Express 5, 2729–2741 (2015).
[Crossref]

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun.  65866 (2015).
[PubMed]

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

A. Shumelyuk, M. Imlau, V. Dieckmann, H. Badorreck, A. Grabar, and S. Odoulov, “Self-diffraction from two-photon absorption gratings in Sn2P2S6,” Opt. Lett. 37, 4065–4067 (2012).
[Crossref] [PubMed]

M. Imlau, V. Dieckmann, H. Badorreck, and A. Shumelyuk, “Tin hypothiodophosphate: Nonlinear response in the sub-100 fs time domain,” Opt. Mater. Express 1, 953–957 (2011).
[Crossref]

Barad, Y.

Bäune, P.

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. Mat. Express 5, 2729–2741 (2015).
[Crossref]

Beyer, O.

Brubaker, R.

Brüning, H.

Buse, K.

Cabuk, S.

S. Cabuk and A. Mamedov, “A study of the LiNbO3 and LiTaO3 absorption edge,” Tr. J. of Physics,  22, 41–45 (1986).

Cirloganu, C. M.

A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

C. M. Cirloganu, L. A. Padilha, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Extremely nondegenerate two-photon absorption in direct-gap semiconductors,” Opt. Express 19, 22951–22960 (2011).
[Crossref] [PubMed]

Conradi, D.

Crespo, H.

Crespo, H. M.

Dieckmann, V.

Dos Santos, A.

Eichler, H.J.

H.J. Eichler, P. Günter, and D. Pohl, Laser-induced Dynamic Gratings, Springer Series in Optical Sciences, vol. 50, Springer Verlag, Berlin, Heidelberg, 1986.
[Crossref]

Fischer, B.

Fishman, A.

A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Fishman, D. A.

Freytag, F.

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. Mat. Express 5, 2729–2741 (2015).
[Crossref]

Grabar, A.

Günter, P.

H.J. Eichler, P. Günter, and D. Pohl, Laser-induced Dynamic Gratings, Springer Series in Optical Sciences, vol. 50, Springer Verlag, Berlin, Heidelberg, 1986.
[Crossref]

Hagan, D. J.

A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

C. M. Cirloganu, L. A. Padilha, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Extremely nondegenerate two-photon absorption in direct-gap semiconductors,” Opt. Express 19, 22951–22960 (2011).
[Crossref] [PubMed]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, ”Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-Photon Absorption,” Phys Rev. Lett. 65, 97–99 (1990).
[Crossref]

Hardt, R.-S.

Harmon, E.

He, Jinping

Jinping He, Jun Liu, and Takayoshi Kobayashi, “Tunable multicolored femtosecond pulse generation using Cascaded Four-Wave Mixing in bulk materials,” Appl. Sci. 4, 444–467 (2014).
[Crossref]

Horowitz, M.

Hsieh, Hung-Te

Imlau, M.

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. Mat. Express 5, 2729–2741 (2015).
[Crossref]

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun.  65866 (2015).
[PubMed]

A. Shumelyuk, M. Imlau, V. Dieckmann, H. Badorreck, A. Grabar, and S. Odoulov, “Self-diffraction from two-photon absorption gratings in Sn2P2S6,” Opt. Lett. 37, 4065–4067 (2012).
[Crossref] [PubMed]

M. Imlau, H. Brüning, B. Schoke, R.-S. Hardt, D. Conradi, and C. Merschjann, “Hologram recording via spatial density modulation of NbLi4+/5+ antisites in lithium niobate,” Opt. Express 19, 15322–15238 (2011).
[Crossref] [PubMed]

M. Imlau, V. Dieckmann, H. Badorreck, and A. Shumelyuk, “Tin hypothiodophosphate: Nonlinear response in the sub-100 fs time domain,” Opt. Mater. Express 1, 953–957 (2011).
[Crossref]

Kobayashi, Takayoshi

Jinping He, Jun Liu, and Takayoshi Kobayashi, “Tunable multicolored femtosecond pulse generation using Cascaded Four-Wave Mixing in bulk materials,” Appl. Sci. 4, 444–467 (2014).
[Crossref]

Liu, Jun

Jinping He, Jun Liu, and Takayoshi Kobayashi, “Tunable multicolored femtosecond pulse generation using Cascaded Four-Wave Mixing in bulk materials,” Appl. Sci. 4, 444–467 (2014).
[Crossref]

Mamedov, A.

S. Cabuk and A. Mamedov, “A study of the LiNbO3 and LiTaO3 absorption edge,” Tr. J. of Physics,  22, 41–45 (1986).

Maxein, D.

Melloch, M.

Mendonca, J. T.

Merschjann, C.

Monroe, M.

A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Nolte, D.

Nolte, S.

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. Mat. Express 5, 2729–2741 (2015).
[Crossref]

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun.  65866 (2015).
[PubMed]

Odoulov, S.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun.  65866 (2015).
[PubMed]

A. Shumelyuk, M. Imlau, V. Dieckmann, H. Badorreck, A. Grabar, and S. Odoulov, “Self-diffraction from two-photon absorption gratings in Sn2P2S6,” Opt. Lett. 37, 4065–4067 (2012).
[Crossref] [PubMed]

Padilha, L. A.

A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

C. M. Cirloganu, L. A. Padilha, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Extremely nondegenerate two-photon absorption in direct-gap semiconductors,” Opt. Express 19, 22951–22960 (2011).
[Crossref] [PubMed]

Pohl, D.

H.J. Eichler, P. Günter, and D. Pohl, Laser-induced Dynamic Gratings, Springer Series in Optical Sciences, vol. 50, Springer Verlag, Berlin, Heidelberg, 1986.
[Crossref]

Psaltis, D.

Schoke, B.

Sheik-Bahae, M.

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, ”Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-Photon Absorption,” Phys Rev. Lett. 65, 97–99 (1990).
[Crossref]

Shumelyuk, A.

Silberberg, Y.

Silva, J. L.

Sturman, B.

Trebino, R.

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, 2000).
[Crossref]

Van Stryland, E. W.

A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

C. M. Cirloganu, L. A. Padilha, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Extremely nondegenerate two-photon absorption in direct-gap semiconductors,” Opt. Express 19, 22951–22960 (2011).
[Crossref] [PubMed]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, ”Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-Photon Absorption,” Phys Rev. Lett. 65, 97–99 (1990).
[Crossref]

Voit, K.-M.

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun.  65866 (2015).
[PubMed]

von Korff Schmising, C.

Wang, Q.

Webster, S.

A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

C. M. Cirloganu, L. A. Padilha, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Extremely nondegenerate two-photon absorption in direct-gap semiconductors,” Opt. Express 19, 22951–22960 (2011).
[Crossref] [PubMed]

Weigand, R.

Yeh, Pochi

Pochi Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quant. Electron.,  25, 484–519 (1989).
[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]

Appl. Sci. (1)

Jinping He, Jun Liu, and Takayoshi Kobayashi, “Tunable multicolored femtosecond pulse generation using Cascaded Four-Wave Mixing in bulk materials,” Appl. Sci. 4, 444–467 (2014).
[Crossref]

IEEE J. Quant. Electron. (1)

Pochi Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quant. Electron.,  25, 484–519 (1989).
[Crossref]

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

Nat. Commun (1)

S. Odoulov, A. Shumelyuk, H. Badorreck, S. Nolte, K.-M. Voit, and M. Imlau, “Interference and holography with femtosecond laser pulses of different colours,” Nat. Commun.  65866 (2015).
[PubMed]

Nat. Photonics (1)

A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-gap semiconductors using extreme nondegenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

Opt. Mat. Express (1)

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. Mat. Express 5, 2729–2741 (2015).
[Crossref]

Opt. Mater. Express (1)

Phys Rev. Lett. (1)

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, ”Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-Photon Absorption,” Phys Rev. Lett. 65, 97–99 (1990).
[Crossref]

Tr. J. of Physics (1)

S. Cabuk and A. Mamedov, “A study of the LiNbO3 and LiTaO3 absorption edge,” Tr. J. of Physics,  22, 41–45 (1986).

Other (2)

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, 2000).
[Crossref]

H.J. Eichler, P. Günter, and D. Pohl, Laser-induced Dynamic Gratings, Springer Series in Optical Sciences, vol. 50, Springer Verlag, Berlin, Heidelberg, 1986.
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

(a) Experimental geometry: the incident beams 1 and 2 create a moving grating in the LiNbO3 sample (LN), two diffracted beams 3 and 4 appear at the output in addition to transmitted beams 1 and 2. These beams form four colored spots in the far-field pattern shown in the upper left inset to this picture. (b) Schematic presentation of the wavevector diagram. The fragments of circles show the xy-crossections of Ewald surfaces for the uniaxial crystal LiNbO3, with radii equal to ki = ωini/c for waves of different colors.

Fig. 2
Fig. 2

Frequencies (a) and propagation angles (b) of four beams behind the sample versus frequency detuning of beam 2. Vertically polarized light beams impinge upon the 200 μm-thick y-cut LiNbO3 plate in a plane parallel to the polar axis.

Fig. 3
Fig. 3

Intensities (a) and spectral positions (b) of the diffracted pulses 3, 4 versus time delay between the recording pulses with the wavelengths λ1 = 489 nm and λ2 = 509 nm.

Equations (5)

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

K = k 1 k 2 ,
k 3 = k 2 K , k 4 = k 1 + K ,
ω 3 = ω 2 Ω , ω 4 = ω 1 + Ω ,
ω 3 , 4 ( Δ t ) = ω 3 , 4 ( 0 ) + d ω 3 , 4 d ( Δ t ) Δ t + d 2 ω 3 , 4 d ( Δ t ) 2 ( Δ t ) 2 + .
d ω d t = 1 3 d Ω 4 3 d ( Δ t ) = 1 3 ( d ω 4 d ( Δ t ) d ω 3 d ( Δ t ) ) .

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