Abstract

A detailed numerical comparison of the bandwidth–efficiency trade-off for second-harmonic generation (SHG) achieved by the formation of two-dimensional quadratic spatial solitons versus the more conventional method of gentle focusing in the middle of a nonlinear crystal is presented. Numerical simulations for type II SHG in potassium titanyl phosphate with constant wave-vector mismatch show that the 3-dB drop-off in SHG conversion efficiency can be many multiples of π in detuning from the phase-match condition over a large range of walk-off angles and focal positions.

© 1998 Optical Society of America

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References

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  1. R. W. Boyd, Nonlinear Optics (Academic, New York, 1994); P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118 (1961);J. A. Armstrong, N. Bloemergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [Crossref]
  2. K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green second harmonic generation laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
    [Crossref]
  3. Reviewed recently in G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) Cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” J. Opt. Quantum Electron. 28, 1691–1740 (1996).
    [Crossref]
  4. 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, 5036–5039 (1995).
    [Crossref] [PubMed]
  5. L. Torner, “Stationary solitary waves with second-order nonlinearities,” Opt. Commun. 114, 136–140 (1995).
    [Crossref]
  6. H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
    [Crossref]
  7. See, e.g., G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1989), Chap. 2.
  8. R. A. Fuerst, M. T. G. Canva, D. Baboiu, and G. I. Stegeman, “Properties of type II quadratic soliton excited by imbalanced fundamental waves,” Opt. Lett. 22, 1748–1750 (1997).
    [Crossref]
  9. J. P. Feve, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
    [Crossref]
  10. L. Torner, C. B. Clausen, and M. M. Fejer, “Adiabatic shaping of quadratic solitons,” Opt. Lett. 23, 903 (1998).
    [Crossref]

1998 (1)

1997 (1)

1996 (1)

Reviewed recently in G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) Cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” J. Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

1995 (3)

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, 5036–5039 (1995).
[Crossref] [PubMed]

L. Torner, “Stationary solitary waves with second-order nonlinearities,” Opt. Commun. 114, 136–140 (1995).
[Crossref]

J. P. Feve, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
[Crossref]

1992 (2)

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green second harmonic generation laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[Crossref]

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

Agrawal, G. P.

See, e.g., G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1989), Chap. 2.

Andou, T.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green second harmonic generation laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[Crossref]

Baboiu, D.

Boulanger, B.

J. P. Feve, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, New York, 1994); P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118 (1961);J. A. Armstrong, N. Bloemergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[Crossref]

Canva, M. T. G.

Clausen, C. B.

Fejer, M. M.

Feve, J. P.

J. P. Feve, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
[Crossref]

Fuerst, R. A.

Hagan, D. J.

Reviewed recently in G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) Cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” J. Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

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, 5036–5039 (1995).
[Crossref] [PubMed]

Huang, C. H.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

Jia, S. Q.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

Jiang, A. D.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

Lin, W. X.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

Marnier, G.

J. P. Feve, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
[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, 5036–5039 (1995).
[Crossref] [PubMed]

Miyai, T.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green second harmonic generation laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[Crossref]

Muraoka, K.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green second harmonic generation laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[Crossref]

Nakamura, J.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green second harmonic generation laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[Crossref]

Shen, D. Z.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

Shen, H. Y.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

Stegeman, G. I.

R. A. Fuerst, M. T. G. Canva, D. Baboiu, and G. I. Stegeman, “Properties of type II quadratic soliton excited by imbalanced fundamental waves,” Opt. Lett. 22, 1748–1750 (1997).
[Crossref]

Reviewed recently in G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) Cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” J. Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

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, 5036–5039 (1995).
[Crossref] [PubMed]

Sugiyama, H.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green second harmonic generation laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[Crossref]

Takahashi, M.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green second harmonic generation laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[Crossref]

Tatsuno, K.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green second harmonic generation laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[Crossref]

Torner, L.

L. Torner, C. B. Clausen, and M. M. Fejer, “Adiabatic shaping of quadratic solitons,” Opt. Lett. 23, 903 (1998).
[Crossref]

Reviewed recently in G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) Cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” J. Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

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, 5036–5039 (1995).
[Crossref] [PubMed]

L. Torner, “Stationary solitary waves with second-order nonlinearities,” Opt. Commun. 114, 136–140 (1995).
[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, 5036–5039 (1995).
[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, 5036–5039 (1995).
[Crossref] [PubMed]

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, 5036–5039 (1995).
[Crossref] [PubMed]

Yu, G. F.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

Zeng, R. R.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

Zeng, Z. D.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

Zhou, Y. P.

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

IEEE J. Quantum Electron. (2)

H. Y. Shen, Y. P. Zhou, W. X. Lin, Z. D. Zeng, R. R. Zeng, G. F. Yu, C. H. Huang, A. D. Jiang, S. Q. Jia, and D. Z. Shen, “Second harmonic generation and sum frequency mixing of dual wavelength Nd:YALO3 laser in flux grown KTiOPO4 crystal,” IEEE J. Quantum Electron. 28, 48–51 (1992).
[Crossref]

J. P. Feve, B. Boulanger, and G. Marnier, “Experimental study of walk-off attenuation for type II second-harmonic-generation in KTP,” IEEE J. Quantum Electron. 31, 1569–1571 (1995).
[Crossref]

J. Opt. Quantum Electron. (1)

Reviewed recently in G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) Cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” J. Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

Jpn. J. Appl. Phys. (1)

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green second harmonic generation laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[Crossref]

Opt. Commun. (1)

L. Torner, “Stationary solitary waves with second-order nonlinearities,” Opt. Commun. 114, 136–140 (1995).
[Crossref]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

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, 5036–5039 (1995).
[Crossref] [PubMed]

Other (2)

R. W. Boyd, Nonlinear Optics (Academic, New York, 1994); P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118 (1961);J. A. Armstrong, N. Bloemergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[Crossref]

See, e.g., G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1989), Chap. 2.

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Figures (5)

Fig. 1
Fig. 1

Conversion efficiency as a function of phase mismatch. For the solid curve, the input beams were 20 μm at the entrance face of the crystal with the peak intensity of each input fundamental beam set to 7.5 GW/cm2. The other curves indicate conventional SHG with the input beams focused at the center of the crystal. There are four different beam waists corresponding to 20, 100, 200, and 500 μm with peak intensities of 5, 0.2, 0.05, and 0.008 GW/cm2, respectively.

Fig. 2
Fig. 2

Percentage of output power in the three interacting fields relative to the total input field, for the case of SHG with solitons. The peak fundamental powers were 7.5 GW/cm2.

Fig. 3
Fig. 3

Conversion efficiency as a function of walk-off angle of the extraordinary polarized fundamental field at phase match. The peak input intensity of each fundamental was 10, 0.4, 0.1, and 0.016 GW/cm2 for 20-, 100-, 200-, and 500-μm beam waists, respectively.

Fig. 4
Fig. 4

Influence of focal position on conversion efficiency. The solid curve identifies SHG with spatial-soliton formation. The other traces illustrate the efficiency as a function of focal position for conventional SHG.

Fig. 5
Fig. 5

Beam profiles of the second-harmonic wave at the output face for a 0.6-deg walk-off angle: (a) The beam waist for soliton generation was 20 μm, and the peak input intensity of each fundamental field was 10 GW/cm2. (b) The 0.4-GW/cm2 input fundamental beams for conventional SHG were focused to 100 μm at the center of the crystal.

Equations (6)

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A1z+12ik1 2A1x2+2A1y2
=iΓA2*A3 exp(-iΔkz),
A2z-ρω A2x+12ik2 2A2x2+2A2y2
=iΓA1*A3 exp(-iΔkz),
A3z-ρ2ω A3x+12ik3 2A3x2+2A3y2
=2iΓA1A2 exp(iΔkz),

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