Abstract

Analytical soliton solutions of the nonlinear three-wave-interaction (TWI) equations are generalized to include phase mismatch Δk. These solutions describe the interaction of so-called TWI solitons. The TWI-soliton and near-TWI-soliton regimes show high-second-harmonic and sum-frequency compression with insignificant satellite pulses for a wide range of nonlinear crystals. Analysis of the solutions shows large time and phase shifts of the fundamentals after the interaction. These shifts are fairly insensitive to the phase mismatch (the dependence is second order in Δk), which may make them useful in all-optical switching devices.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Wang and R. Dragila, “Efficient conversion of picosecond laser pulses into second-harmonic frequency using group-velocity dispersion,” Phys. Rev. A 41, 5645 (1990).
    [CrossRef] [PubMed]
  2. A. Stabinis, G. Valiulis, and E. A. Ibragimov, “Effective sum frequency pulse compression in nonlinear crystals,” Opt. Commun. 86, 301 (1991).
    [CrossRef]
  3. Y. Wang, B. Luther-Davies, Y.-H. Chuang, R. S. Craxton, and D. D. Meyerhofer, “Highly efficient conversion of picosecond Nd laser pulses with the use of group-velocity-mismatched frequency doubling in KDP,” Opt. Lett. 16, 1862 (1991).
    [CrossRef] [PubMed]
  4. Y. Wang and B. Luther-Davies, “Frequency-doubling pulse compressor for picosecond high-power neodymium laser pulses,” Opt. Lett. 17, 1459 (1992).
    [CrossRef] [PubMed]
  5. C. Y. Chien, G. Korn, J. S. Coe, J. Squier, G. Mourou, and R. S. Craxton, “Highly efficient second harmonic generation of ultraintense Nd:glass laser pulses,” Opt. Lett. 20, 353 (1994).
    [CrossRef]
  6. A. U. Umbrasas, J. C. Diels, J. Jacob, G. Valiulis, and A. Piskarskas, “Generation of femtosecond pulses through second-harmonic compression of the output of a Nd:YAG laser,” Opt. Lett. 20, 2228 (1995).
    [CrossRef] [PubMed]
  7. R. Danelius, A. Dubietis, G. Valiulis, and A. Piskarskas, “Generation of compressed 600–720-nm tunable femtosecond pulses by transient frequency mixing in β-barium borate crystal,” Opt. Lett. 20, 2225 (1995).
  8. T. Zhang, Y. Kato, and H. Daido, “Efficient third-harmonic generation of a picosecond laser pulse with time delay,” IEEE J. Quantum Electron. 32, 137 (1996).
    [CrossRef]
  9. E. Ibragimov and A. Struthers, “Soliton regime for second-harmonic generation by ultrashort laser pulses in dispersive media,” in Conference on Lasers & Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, DC, 1996), p. 276.
  10. E. Ibragimov and A. Struthers, “Second-harmonic pulse compression in the soliton regime,” Opt. Lett. 21, 1582 (1996).
    [CrossRef] [PubMed]
  11. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Equations and Inverse Scattering (Cambridge U. Press, London, 1991), p. 19.
  12. V. E. Zakharov and S. V. Manakov, “The theory of resonance interaction of wave packets in nonlinear media,” Sov. Phys. JETP 42, 842 (1976).
  13. D. J. Kaup, “The three-wave interaction—a nondispersive phenomenon,” Studies Appl. Math. 55, 9 (1976).
  14. For the SHG the compression coefficient can be defined as a ratio of the intensity of the SH to the average intensity of two fundamental pulses: I3max/(Io, 02+ Ie, 02)1/2. However, in the case of SFG it is more natural to use the ratio between I3max and the intensity of the signal wave. Here we use the first definition.
  15. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 117, 1918 (1962).
    [CrossRef]
  16. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).

1996 (2)

T. Zhang, Y. Kato, and H. Daido, “Efficient third-harmonic generation of a picosecond laser pulse with time delay,” IEEE J. Quantum Electron. 32, 137 (1996).
[CrossRef]

E. Ibragimov and A. Struthers, “Second-harmonic pulse compression in the soliton regime,” Opt. Lett. 21, 1582 (1996).
[CrossRef] [PubMed]

1995 (2)

1994 (1)

1992 (1)

1991 (2)

1990 (1)

Y. Wang and R. Dragila, “Efficient conversion of picosecond laser pulses into second-harmonic frequency using group-velocity dispersion,” Phys. Rev. A 41, 5645 (1990).
[CrossRef] [PubMed]

1976 (1)

V. E. Zakharov and S. V. Manakov, “The theory of resonance interaction of wave packets in nonlinear media,” Sov. Phys. JETP 42, 842 (1976).

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 117, 1918 (1962).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 117, 1918 (1962).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 117, 1918 (1962).
[CrossRef]

Chien, C. Y.

Chuang, Y.-H.

Coe, J. S.

Craxton, R. S.

Daido, H.

T. Zhang, Y. Kato, and H. Daido, “Efficient third-harmonic generation of a picosecond laser pulse with time delay,” IEEE J. Quantum Electron. 32, 137 (1996).
[CrossRef]

Danelius, R.

Diels, J. C.

Dragila, R.

Y. Wang and R. Dragila, “Efficient conversion of picosecond laser pulses into second-harmonic frequency using group-velocity dispersion,” Phys. Rev. A 41, 5645 (1990).
[CrossRef] [PubMed]

Dubietis, A.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 117, 1918 (1962).
[CrossRef]

Ibragimov, E.

Ibragimov, E. A.

A. Stabinis, G. Valiulis, and E. A. Ibragimov, “Effective sum frequency pulse compression in nonlinear crystals,” Opt. Commun. 86, 301 (1991).
[CrossRef]

Jacob, J.

Kato, Y.

T. Zhang, Y. Kato, and H. Daido, “Efficient third-harmonic generation of a picosecond laser pulse with time delay,” IEEE J. Quantum Electron. 32, 137 (1996).
[CrossRef]

Korn, G.

Luther-Davies, B.

Manakov, S. V.

V. E. Zakharov and S. V. Manakov, “The theory of resonance interaction of wave packets in nonlinear media,” Sov. Phys. JETP 42, 842 (1976).

Meyerhofer, D. D.

Mourou, G.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 117, 1918 (1962).
[CrossRef]

Piskarskas, A.

Squier, J.

Stabinis, A.

A. Stabinis, G. Valiulis, and E. A. Ibragimov, “Effective sum frequency pulse compression in nonlinear crystals,” Opt. Commun. 86, 301 (1991).
[CrossRef]

Struthers, A.

Umbrasas, A. U.

Valiulis, G.

Wang, Y.

Zakharov, V. E.

V. E. Zakharov and S. V. Manakov, “The theory of resonance interaction of wave packets in nonlinear media,” Sov. Phys. JETP 42, 842 (1976).

Zhang, T.

T. Zhang, Y. Kato, and H. Daido, “Efficient third-harmonic generation of a picosecond laser pulse with time delay,” IEEE J. Quantum Electron. 32, 137 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Zhang, Y. Kato, and H. Daido, “Efficient third-harmonic generation of a picosecond laser pulse with time delay,” IEEE J. Quantum Electron. 32, 137 (1996).
[CrossRef]

Opt. Commun. (1)

A. Stabinis, G. Valiulis, and E. A. Ibragimov, “Effective sum frequency pulse compression in nonlinear crystals,” Opt. Commun. 86, 301 (1991).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 117, 1918 (1962).
[CrossRef]

Phys. Rev. A (1)

Y. Wang and R. Dragila, “Efficient conversion of picosecond laser pulses into second-harmonic frequency using group-velocity dispersion,” Phys. Rev. A 41, 5645 (1990).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. E. Zakharov and S. V. Manakov, “The theory of resonance interaction of wave packets in nonlinear media,” Sov. Phys. JETP 42, 842 (1976).

Other (5)

D. J. Kaup, “The three-wave interaction—a nondispersive phenomenon,” Studies Appl. Math. 55, 9 (1976).

For the SHG the compression coefficient can be defined as a ratio of the intensity of the SH to the average intensity of two fundamental pulses: I3max/(Io, 02+ Ie, 02)1/2. However, in the case of SFG it is more natural to use the ratio between I3max and the intensity of the signal wave. Here we use the first definition.

M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Equations and Inverse Scattering (Cambridge U. Press, London, 1991), p. 19.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).

E. Ibragimov and A. Struthers, “Soliton regime for second-harmonic generation by ultrashort laser pulses in dispersive media,” in Conference on Lasers & Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, DC, 1996), p. 276.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Interaction in a frame moving with the speed of the third wave: ωi, frequencies; vi, group velocities.

Fig. 2
Fig. 2

Typical soliton interaction: Δi, time shifts.

Fig. 3
Fig. 3

Coefficient of compression for different generation regimes in KDP.

Fig. 4
Fig. 4

Coefficient of energy conversion in KDP versus normalized fundamental intensity: for BER, m=1 corresponds to a soliton interaction.

Fig. 5
Fig. 5

Compression coefficient against satellite energy in KDP.

Fig. 6
Fig. 6

Coefficient of energy conversion in a medium with asymmetric velocity relationship v2-v1=5(v3-v2).

Fig. 7
Fig. 7

Compression coefficient against satellite energy within a medium with asymmetric velocity relationship v2-v1=5(v3 -v2).

Fig. 8
Fig. 8

Energy of fundamentals within FWHM against the SH energy within FWHM in KDP.

Equations (38)

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

A3,max=σ-A2z|v2-1-v1-1|τdz=12A0lnl-A2zlνdz.
A1z+1v1A1t+ig12A1t2=iσA3A2* exp(iΔkz),
A2z+1v2A2t+ig22A2t2=iω2ω1σA3A1* exp(iΔkz),
A3z+1v3A3t+ig32A3t2=iω3ω1σA1A2 exp(-iΔkz),
A1,2(z, t)=Q1,2(z, t)exp-iμ1,2t-zv1,2,
A3(z, t)=Q3(z, t)exp-i(μ1+μ2)t-μ1v3+μ2v3z,
μ1v3+μ2v3-μ1v1-μ2v2=Δk.
A1(t, z)=2A1,0 exp(iφ1)D(ξ, η)exp(ξ)+αβexp(-ξ),
A2(t, z)=ω2ω12A2,0 exp(iφ2)D(ξ, η)×exp(η)+α*βexp(-η),
A3(t, z)=ω3ω14A1,0 exp(iφ1)A2,0 exp(iφ2)ν1,2βD(ξ, η)×exp(iΔkz),
ξ=σA2,0ω2ω3ω12ν1,2ν2,3t-zv2-T2,
η=σA1,0ω2ω3ω12ν1,2ν1,3t-zv1+T1,
D(ξ, η)=4 cosh(ξ)cosh(η)+γ exp(-ξ-η).
ν1,2=1/v2-1/v1,
α=σ-1Δkω1ν1,2/(ω2ω3)+i(A2,0ν2,3+A1,0ν1,3),
ν2,3=1/v2-1/v3,
β=σ-1Δkω1ν1,2/(ω2ω3)-i(A2,0ν2,3-A1,0ν1,3),
ν1,3=1/v3-1/v1,
γ=4A1,0A2,0ν1,3ν2,3/|β|2.
A1(t, z-v1t)αβ2A1,0 exp(iφ1)exp(η)+(1+γ)exp(-η)=α|α||β|βA1,0 exp(iφ1)cosh(η-ln|α/β|),
1+γ=αβ2,
exp(η)+αβ2 exp(-η)=2 coshη-lnαβαβ.
A1(t, z)A1,0 sechω2ω3σA1,0ω1ν1,2ν1,3t-zv1+T1-lnαβexp[i(ψ1-ψ2+φ1)]
A1(t, z)
A1,0 sechω2ω3σA1,0ω1ν1,2ν1,3t-zv1+T1-lnαβ×exp[i(φ1+ψ1-ψ2)]z, t-A1,0 sechω2ω3σA1,0ω1ν1,2ν1,3t-zv1+T1×exp(iφ1)z, t+.
A2(t, z)
ω2ω1 A2,0 sechω2ω3σA2,0ω1ν1,2ν2,3t-zv2-T2×exp(iφ2)z, t-ω2ω1 A2,0 sechω2ω3σA2,0ω1ν1,2ν2,3t-zv2-T2-lnαβexp[i(φ2-ψ1-ψ2)]z, t+.
τj=1.76ω1ν1,2νj,3σAj,0ω2ω3forj=1, 2.
Dmin=2(1+|α|/|β|).
β=σ-1Δkω1ν1,2/(ω2ω3)-i(A2,0ν2,3-A1,0ν1,3)
A2,0ν2,3=A1,0ν1,3,
A1,02v1(v1-v3)=A2,02v2(v3-v2).
|A3,max|=ω3ω12A1,0A2,0ν1,2(|β|+|α|).
|A3,max|=A1,02ω1ν1,2ω2ν2,3,
|A3,max|=2A0Δs2+Δs22+1,
ΔTi=τi ln|α||β|=τi ln1+2Δs2.
ψj=±arctanσw2w3(A2,0ν2,3±A1,0ν1,3)Δkω1ν1,2,
v=n(λ)c-λcdndλ,g=λ34πc2d2ndλ2,

Metrics