Abstract

We develop a rapid and efficient numeric technique for the design of arbitrary quasi-phase matched lattices for parametric generation of single and multiple pulses with any prescribed amplitude and phase profiles from fundamental frequency excitation in the regime of pump depletion. We examine the case of simultaneous of 2nd and 3rd harmonic generation in arbitrary quasi-phase matched gratings taking into account the group velocity mismatch and dispersion.

© 2009 Optical Society of America

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  1. D. S. Hum and M. M. Fejer, "Quasi-phasematching," C. R. Phys. 8,180-198 (2007).
    [CrossRef]
  2. H. Miao, S. Yang, C. Langrock, R. V. Roussev, M. M. Fejer, and A. M. Weiner, "Ultralow power second-harmonic generation frequency-resolved optical gating using aperiodically poled lithium niobate waveguides," J. Opt. Soc. Am. B 25,A41-A53 (2008).
    [CrossRef]
  3. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation - Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2653 (1992).
    [CrossRef]
  4. M. A. Arbore, O. Marco, and M. M. Fejer, "Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Lett. 22, 865-867 (1997).
    [CrossRef] [PubMed]
  5. D. Artigas and D. T. Reid, "Efficient femtosecond optical parametric oscillators based on aperiodically poled nonlinear crystals," Opt. Lett. 27, 851-853 (2002).
    [CrossRef]
  6. D. Artigas, D. T. Reid, M. M. Fejer, and L. Torner, "Pulse compression and gain enhancement in a degenerate optical parametric amplifier based on aperiodically poled crystals," Opt. Lett. 27, 442-44 (2002).
    [CrossRef]
  7. O. Bang, C. Balslev-Clausen, P. L. Christiansen, and L. Torner, "Engineering competing nonlinearities," Opt. Lett. 24, 1413-1415 (1999).
    [CrossRef]
  8. G. Leo, A. Amoroso, L. Colace, G. Assanto, R. V. Roussev, and M. M. Fejer, "Low-threshold spatial solitons in reverse-proton-exchanged periodically poled lithium niobate waveguides," Opt. Lett. 29, 1778-1780 (2004).
    [CrossRef] [PubMed]
  9. J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
    [CrossRef]
  10. K. Gallo, G. Assanto, and G. I. Stegeman, "Efficient Wavelength Shifting over the Erbium Amplifier Bandwidth Via Cascaded Second Order Processes in Lithium Niobate Waveguides," Appl. Phys. Lett. 71, 1020-1022 (1997).
    [CrossRef]
  11. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, "All-optical diode in a periodically-poled Lithium Niobate waveguide," Appl. Phys. Lett. 79, 314-316 (2001).
    [CrossRef]
  12. W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
    [CrossRef]
  13. D. T. Reid, "Engineered quasi-phase-matching for second-garmonic generation," J. Opt. A: Pure Appl. Opt. 5, S97-S102 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. I. V. Shutov and A. S. Chirkin, "Consecutive high-order harmonic generation and formation of subfemtosecond in aperiodical nonlinear photonic crystals," Phys. Rev. A 78, 013827-013833 (2008).
    [CrossRef]
  18. U. K. Sapaev and D. T. Reid, "General second-harmonic pulse shaping in grating-engineered quasi-phasematched nonlinear crystals," Opt. Express 13, 3264-3276 (2005), www.opticsinfobase.org/abstract.cfm?&uri=oe-13-9-3264.
    [CrossRef] [PubMed]
  19. U. K. Sapaev and G. Assanto, "Femtosecond pulse synthesis by efficient second-harmonic generation in engineered quasi phase matching gratings," Opt. Express 15, 7448-7457 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?uri=OE-15-12-7448.
    [CrossRef] [PubMed]
  20. M. Conforti, F. Baronio, and C. De Angelis, "From femtosecond infrared to picosecond visible pulses: temporal shaping with high-efficiency conversion," Opt. Lett. 32, 1779-1781 (2007).
    [CrossRef] [PubMed]
  21. L. Kornaszewski, M. Kohler, U. K. Sapaev, and D. T. Reid, "Designer Femtosecond Pulse Shaping Using Grating- Engineered Quasi-Phasematching in Lithium Niobate," Opt. Lett. 33, 378-380 (2008).
    [CrossRef] [PubMed]
  22. Y. Zang and B-Y. Gu, "Optimal design of aperiodically poled lithium niobate crystals for multiple wavelengths parametric amplification," Opt. Commun. 192, 417-425 (2001).
    [CrossRef]
  23. R. Buffa, "Transient second-harmonic generation with spatially non-uniform nonlinear coefficients," Opt. Lett. 27, 1058-1060 (2002).
    [CrossRef]
  24. X. Liu and Y. Li, "Optimal design of DFG-based wavelength conversion based on hybrid genetic algorithm," Opt. Express 11, 1677-1688 (2003), www.opticsinfobase.org/oe/abstract.cfm?uri=OE-11-14-1677.
    [CrossRef] [PubMed]
  25. X. Chen, F. Wu, X. Zeng, Y. Chen, Yu. Xia, and Yi. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818-013821 (2004).
    [CrossRef]

2008 (5)

2007 (4)

2005 (1)

2004 (4)

A. H. Norton and C. M. de Sterke, "Aperiodic 1-dimensional structures for quasi-phase matching," Opt. Express 12, 841-846 (2004), http://www.opticsinfobase.org/abstract.cfm?id=148641.
[CrossRef] [PubMed]

G. Leo, A. Amoroso, L. Colace, G. Assanto, R. V. Roussev, and M. M. Fejer, "Low-threshold spatial solitons in reverse-proton-exchanged periodically poled lithium niobate waveguides," Opt. Lett. 29, 1778-1780 (2004).
[CrossRef] [PubMed]

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

X. Chen, F. Wu, X. Zeng, Y. Chen, Yu. Xia, and Yi. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818-013821 (2004).
[CrossRef]

2003 (2)

2002 (3)

2001 (2)

Y. Zang and B-Y. Gu, "Optimal design of aperiodically poled lithium niobate crystals for multiple wavelengths parametric amplification," Opt. Commun. 192, 417-425 (2001).
[CrossRef]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, "All-optical diode in a periodically-poled Lithium Niobate waveguide," Appl. Phys. Lett. 79, 314-316 (2001).
[CrossRef]

1999 (1)

1997 (2)

K. Gallo, G. Assanto, and G. I. Stegeman, "Efficient Wavelength Shifting over the Erbium Amplifier Bandwidth Via Cascaded Second Order Processes in Lithium Niobate Waveguides," Appl. Phys. Lett. 71, 1020-1022 (1997).
[CrossRef]

M. A. Arbore, O. Marco, and M. M. Fejer, "Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Lett. 22, 865-867 (1997).
[CrossRef] [PubMed]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation - Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2653 (1992).
[CrossRef]

Amoroso, A.

Arbore, M. A.

Artigas, D.

Assanto, G.

Balslev-Clausen, C.

Bang, O.

Baronio, F.

Büchter, D.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Buffa, R.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation - Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2653 (1992).
[CrossRef]

Chen, X.

X. Chen, F. Wu, X. Zeng, Y. Chen, Yu. Xia, and Yi. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818-013821 (2004).
[CrossRef]

Chen, Y.

X. Chen, F. Wu, X. Zeng, Y. Chen, Yu. Xia, and Yi. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818-013821 (2004).
[CrossRef]

Chen, Yi.

X. Chen, F. Wu, X. Zeng, Y. Chen, Yu. Xia, and Yi. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818-013821 (2004).
[CrossRef]

Chirkin, A. S.

I. V. Shutov and A. S. Chirkin, "Consecutive high-order harmonic generation and formation of subfemtosecond in aperiodical nonlinear photonic crystals," Phys. Rev. A 78, 013827-013833 (2008).
[CrossRef]

Christiansen,, P. L.

Colace, L.

Conforti, M.

De Angelis, C.

de Sterke, C. M.

Du, J.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

Fejer, M. M.

Gallo, K.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, "All-optical diode in a periodically-poled Lithium Niobate waveguide," Appl. Phys. Lett. 79, 314-316 (2001).
[CrossRef]

K. Gallo, G. Assanto, and G. I. Stegeman, "Efficient Wavelength Shifting over the Erbium Amplifier Bandwidth Via Cascaded Second Order Processes in Lithium Niobate Waveguides," Appl. Phys. Lett. 71, 1020-1022 (1997).
[CrossRef]

Grundkötter, W.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Gu, B-Y.

Y. Zang and B-Y. Gu, "Optimal design of aperiodically poled lithium niobate crystals for multiple wavelengths parametric amplification," Opt. Commun. 192, 417-425 (2001).
[CrossRef]

He, J. L.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

Herrmann, H.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Hu, H.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Hum, D. S.

D. S. Hum and M. M. Fejer, "Quasi-phasematching," C. R. Phys. 8,180-198 (2007).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation - Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2653 (1992).
[CrossRef]

Kohler, M.

Kornaszewski, L.

Langrock, C.

Leo, G.

Li, Y.

Liao, J.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

Liu, H.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

Liu, X.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation - Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2653 (1992).
[CrossRef]

Marco, O.

Miao, H.

Min, Y.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Ming, N. B.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

Norton, A. H.

Nouroozi, R.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Orlov, S.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Parameswaran, K. R.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, "All-optical diode in a periodically-poled Lithium Niobate waveguide," Appl. Phys. Lett. 79, 314-316 (2001).
[CrossRef]

Quiring, V.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Reid, D. T.

Reza, S.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Ricken, R.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Roussev, R. V.

Sapaev, U. K.

Shutov, I. V.

I. V. Shutov and A. S. Chirkin, "Consecutive high-order harmonic generation and formation of subfemtosecond in aperiodical nonlinear photonic crystals," Phys. Rev. A 78, 013827-013833 (2008).
[CrossRef]

Sohler, W.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Stegeman, G. I.

K. Gallo, G. Assanto, and G. I. Stegeman, "Efficient Wavelength Shifting over the Erbium Amplifier Bandwidth Via Cascaded Second Order Processes in Lithium Niobate Waveguides," Appl. Phys. Lett. 71, 1020-1022 (1997).
[CrossRef]

Suche, H.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Torner, L.

Vannahme, C.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Wang, H. T.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

Weiner, A. M.

Wu, F.

X. Chen, F. Wu, X. Zeng, Y. Chen, Yu. Xia, and Yi. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818-013821 (2004).
[CrossRef]

Xia, Yu.

X. Chen, F. Wu, X. Zeng, Y. Chen, Yu. Xia, and Yi. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818-013821 (2004).
[CrossRef]

Xu, F.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

Yang, S.

Zang, Y.

Y. Zang and B-Y. Gu, "Optimal design of aperiodically poled lithium niobate crystals for multiple wavelengths parametric amplification," Opt. Commun. 192, 417-425 (2001).
[CrossRef]

Zeng, X.

X. Chen, F. Wu, X. Zeng, Y. Chen, Yu. Xia, and Yi. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818-013821 (2004).
[CrossRef]

Zhu, S. N.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

Zhu, Y. Y.

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

Appl. Phys. B (1)

J. Liao, J. L. He, H. Liu, J. Du, F. Xu, H. T. Wang, S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Red, yellow, green and blue-four-color light from a single, aperiodically poled LiTaO3 crystal," Appl. Phys. B 78, 265-267 (2004).
[CrossRef]

Appl. Phys. Lett. (2)

K. Gallo, G. Assanto, and G. I. Stegeman, "Efficient Wavelength Shifting over the Erbium Amplifier Bandwidth Via Cascaded Second Order Processes in Lithium Niobate Waveguides," Appl. Phys. Lett. 71, 1020-1022 (1997).
[CrossRef]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, "All-optical diode in a periodically-poled Lithium Niobate waveguide," Appl. Phys. Lett. 79, 314-316 (2001).
[CrossRef]

C. R. Phys. (1)

D. S. Hum and M. M. Fejer, "Quasi-phasematching," C. R. Phys. 8,180-198 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation - Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2653 (1992).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

D. T. Reid, "Engineered quasi-phase-matching for second-garmonic generation," J. Opt. A: Pure Appl. Opt. 5, S97-S102 (2003).
[CrossRef]

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

Opt. Commun. (1)

Y. Zang and B-Y. Gu, "Optimal design of aperiodically poled lithium niobate crystals for multiple wavelengths parametric amplification," Opt. Commun. 192, 417-425 (2001).
[CrossRef]

Opt. Express (5)

Opt. Lett. (8)

L. Kornaszewski, M. Kohler, U. K. Sapaev, and D. T. Reid, "Designer Femtosecond Pulse Shaping Using Grating- Engineered Quasi-Phasematching in Lithium Niobate," Opt. Lett. 33, 378-380 (2008).
[CrossRef] [PubMed]

M. Conforti, F. Baronio, and C. De Angelis, "From femtosecond infrared to picosecond visible pulses: temporal shaping with high-efficiency conversion," Opt. Lett. 32, 1779-1781 (2007).
[CrossRef] [PubMed]

G. Leo, A. Amoroso, L. Colace, G. Assanto, R. V. Roussev, and M. M. Fejer, "Low-threshold spatial solitons in reverse-proton-exchanged periodically poled lithium niobate waveguides," Opt. Lett. 29, 1778-1780 (2004).
[CrossRef] [PubMed]

M. A. Arbore, O. Marco, and M. M. Fejer, "Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings," Opt. Lett. 22, 865-867 (1997).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

D. Artigas and D. T. Reid, "Efficient femtosecond optical parametric oscillators based on aperiodically poled nonlinear crystals," Opt. Lett. 27, 851-853 (2002).
[CrossRef]

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[CrossRef]

Opt. Photon. News (1)

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, and Y. Min, "Integrated Optical Devices in Lithium Niobate," Opt. Photon. News 19, 24-31 (2008).
[CrossRef]

Opt. Spectr. (1)

U. K. Sapaev, "Optimum formation of the response of aperiodic nonlinear crystals in the process of second harmonic generation," Opt. Spectr. 102, 939-943 (2007).
[CrossRef]

Phys. Rev. A (2)

I. V. Shutov and A. S. Chirkin, "Consecutive high-order harmonic generation and formation of subfemtosecond in aperiodical nonlinear photonic crystals," Phys. Rev. A 78, 013827-013833 (2008).
[CrossRef]

X. Chen, F. Wu, X. Zeng, Y. Chen, Yu. Xia, and Yi. Chen, "Multiple quasi-phase-matching in a nonperiodic domain-inverted optical superlattice," Phys. Rev. A 69, 013818-013821 (2004).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(Left) time evolutions of the intensity distributions of FF (red) at z=L (solid line) and at z=0 (dashed line), SH (blue line), TH (green line) pulses and target SH pulse (blue “o” symbols). (Center) Energy evolutions of the interacting harmonics versus designed QPM grating length (red, blue, green and black lines correspond to fundamental, 2nd, 3rd harmonics and the sum of their energies). (Right) QPM domain size distribution (relative to the unperturbed qo ) versus domain number N.

Fig. 2.
Fig. 2.

Generation of optimized 3rd harmonic profile: lines are defined as in Fig. 1. The green line with symbols “o” is the 3rd harmonic target pulse.

Fig. 3.
Fig. 3.

Generation of optimized of 2nd and 3rd harmonic pulses: lines are defined as in Figs. 1-2.

Fig. 4.
Fig. 4.

Generation of optimized of 2nd and 3rd harmonic pulses for a real experimental case in Lithium Niobate (see text): lines and colors are as in Figs. 1–3.

Equations (15)

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A 1 z + v 1 A 1 t + i β 1 2 2 A 1 t 2 = i γ 1 ρ ( z ) ( A 1 * A 2 p 1 + A 2 * A 3 p 2 )
A 2 z + v 2 A 2 t + i β 2 2 2 A 2 t 2 = i γ 2 ρ ( z ) ( A 1 2 p 1 * + 2 A 1 * A 3 p 2 )
A 3 z + i β 3 2 2 A 3 t 2 = i 3 γ 3 ρ ( z ) A 1 A 2 p 2 *
A 1 ( z , t ) z = 0 = A o exp ( 0.5 ( t / τ o ) 2 ) , A 2 ( z , t ) z = 0 = 0 , A 3 ( z , t ) z = 0 = 0
J = J 1 + J 2 + c . c .
J 1 = 1 2 + dt [ [ A 2 ( z = L , t ) A 2 T ( t ) ] 2 + [ A 3 ( z = L , t ) A 3 T ( t ) ] 2 ]
J 2 = 0 L dz + dt { f 1 [ A 1 z + v 1 A 1 t + i β 1 2 2 A 1 t 2 + i γ 1 ρ ( z ) ( A 1 * A 2 p 1 + A 2 * A 3 p 2 ) ] } +
0 L dz + dt { f 2 [ A 2 z + v 2 A 2 t + i β 2 2 2 A 2 t 2 + i γ 2 ρ ( z ) ( A 1 2 p 1 * + 2 A 3 A 1 * p 2 ) ] } +
0 L dz + dt { f 3 [ A 3 z + i β 3 2 2 A 3 t 2 + i 3 γ 3 ρ ( z ) A 2 A 1 p 2 * ] }
f 1 z + v 1 f 1 t + i β 1 2 2 f 1 t 2 = i γ 1 ρ ( z ) [ p 1 ( A 2 * f 1 * 2 A 1 f 2 ) + p 2 ( 2 A 3 * f 2 * 3 A 2 f 3 ) ]
f 2 z + v 2 f 2 t + i β 2 2 2 f 2 t 2 = i γ 2 ρ ( z ) [ p 2 ( A 3 * f 1 * 3 A 1 f 3 ) p 1 * A 1 * f 1 ]
f 3 z + i β 3 2 2 f 3 t 2 = i γ 3 ρ ( z ) p 2 * [ ( A 2 * f 1 + 2 A 1 * f 2 ) ]
f 1 ( z , t ) z = L = 0 ; f 2 ( z , t ) z = L = A 2 ( z = L , t ) A 2 T ( t ) ; f 3 ( z , t ) z = L = A 3 ( z = L , t ) A 3 T ( t )
δJ δρ ( z ) = [ F 1 + F 2 + F 3 + F 1 * + F 2 * + F 3 * ] dt
F 1 = i γ 1 f 1 ( A 1 * A 2 p 1 + A 2 * A 3 p 2 ) , F 2 = i γ 3 f 2 ( A 1 2 p 1 * + 2 A 1 * A 3 p 2 ) and F 3 = i 3 γ 3 f 3 A 1 A 2 p 2 *

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