Abstract

The property of three-wave-interaction solitons to preserve their shape upon nonlinear interaction with an arbitrary-shaped radiation is proposed for the creation of all-optical switching devices. It is shown that three-wave-interaction solitons can be used for optical switching in a polarization-gate geometry. This new all-optical logic gate combines the advantages of soliton switching devices with the short length of a second-order nonlinear interaction. Feasibility of an all-optical logic gate based on two 1.5-cm-long β-barium borate crystals and with the intensity of the control pulse 190 MW/cm2 is demonstrated.

© 1998 Optical Society of America

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References

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  1. N. M. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge University, Cambridge, 1992).
  2. L. Torner, W. E. Torruellas, C. R. Menyuk, and G. I. Stegeman, “Beam stearing by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
    [CrossRef] [PubMed]
  3. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  4. E. Ibragimov, J. D. Khaydarov, K. D. Singer, and A. Struthers, “TWI-soliton formation in a synchronously pumped optical parametric oscillator,” presented at the Conference on Laser and Electro-Optics, Baltimore, Maryland, May 18–23, 1997.
  5. E. Ibragimov and A. Struthers, “Second-harmonic pulse compression in the soliton regime,” Opt. Lett. 21, 1582 (1996).
    [CrossRef] [PubMed]
  6. E. Ibragimov and A. Struthers, “Three-wave soliton interaction of ultrashort pulses in quadratic media,” J. Opt. Soc. Am. B 14, 1472 (1997).
    [CrossRef]
  7. V. E. Zakharov and S. V. Manakov, “The theory of resonance interaction of wave packets in nonlinear media,” Sov. Phys. JETP 42, 842 (1976).
  8. D. J. Kaup, “The three-wave interaction: a nondispersive phenomenon,” Stud. Appl. Math. 55, 9 (1976).
  9. D. J. Kaup, A. Reiman, and A. Bers, “Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium,” Rev. Mod. Phys. 51, 275 (1979).
    [CrossRef]
  10. T. Morioka, M. Saruwatari, and A. Takeda, Electron. Lett. 23, 453 (1987).
    [CrossRef]
  11. M. A. Krümbugel, J. N. Sweetser, D. N. Fittinghoff, K. W. DeLong, and R. Trebino, “Ultrafast optical switching by use of fully phase-matched cascaded second-order nonlinearities in a polarization-gate geometry,” Opt. Lett. 22, 245 (1997).
    [CrossRef] [PubMed]
  12. A. Stabinis, G. Valiulis, and E. A. Ibragimov, “Effective sum frequency pulse compression in nonlinear crystals,” Opt. Commun. 86, 301 (1991).
    [CrossRef]
  13. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).

1997

1996

1995

L. Torner, W. E. Torruellas, C. R. Menyuk, and G. I. Stegeman, “Beam stearing by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

1991

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

1987

T. Morioka, M. Saruwatari, and A. Takeda, Electron. Lett. 23, 453 (1987).
[CrossRef]

1979

D. J. Kaup, A. Reiman, and A. Bers, “Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium,” Rev. Mod. Phys. 51, 275 (1979).
[CrossRef]

1976

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

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

Bers, A.

D. J. Kaup, A. Reiman, and A. Bers, “Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium,” Rev. Mod. Phys. 51, 275 (1979).
[CrossRef]

DeLong, K. W.

Fittinghoff, D. N.

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

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]

Kaup, D. J.

D. J. Kaup, A. Reiman, and A. Bers, “Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium,” Rev. Mod. Phys. 51, 275 (1979).
[CrossRef]

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

Krümbugel, M. A.

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).

Menyuk, C.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Menyuk, C. R.

Morioka, T.

T. Morioka, M. Saruwatari, and A. Takeda, Electron. Lett. 23, 453 (1987).
[CrossRef]

Reiman, A.

D. J. Kaup, A. Reiman, and A. Bers, “Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium,” Rev. Mod. Phys. 51, 275 (1979).
[CrossRef]

Saruwatari, M.

T. Morioka, M. Saruwatari, and A. Takeda, Electron. Lett. 23, 453 (1987).
[CrossRef]

Stabinis, A.

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

Stegeman, G. I.

L. Torner, W. E. Torruellas, C. R. Menyuk, and G. I. Stegeman, “Beam stearing by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Struthers, A.

Sweetser, J. N.

Takeda, A.

T. Morioka, M. Saruwatari, and A. Takeda, Electron. Lett. 23, 453 (1987).
[CrossRef]

Torner, L.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

L. Torner, W. E. Torruellas, C. R. Menyuk, and G. I. Stegeman, “Beam stearing by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
[CrossRef] [PubMed]

Torruellas, W. E.

L. Torner, W. E. Torruellas, C. R. Menyuk, and G. I. Stegeman, “Beam stearing by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Trebino, R.

Valiulis, G.

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

Van Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

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).

Electron. Lett.

T. Morioka, M. Saruwatari, and A. Takeda, Electron. Lett. 23, 453 (1987).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

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

Opt. Lett.

Phys. Rev. Lett.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Rev. Mod. Phys.

D. J. Kaup, A. Reiman, and A. Bers, “Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium,” Rev. Mod. Phys. 51, 275 (1979).
[CrossRef]

Sov. Phys. JETP

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

Stud. Appl. Math.

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

Other

E. Ibragimov, J. D. Khaydarov, K. D. Singer, and A. Struthers, “TWI-soliton formation in a synchronously pumped optical parametric oscillator,” presented at the Conference on Laser and Electro-Optics, Baltimore, Maryland, May 18–23, 1997.

N. M. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge University, Cambridge, 1992).

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

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Figures (4)

Fig. 1
Fig. 1

Elastic collision of the small TWI-soliton pulse at frequency ω1 with an intense pulse at frequency ω2. Time (horizontal axis) is given in picoseconds; the amplitudes of the waves (vertical axis) are in arbitrary units. Pictures show temporal shapes of the interacting pulses for different values of z. The profiles shown in the frame are moving with the speed of the wave at sum-frequency, which is not shown in the figure.

Fig. 2
Fig. 2

Elastic collision of the TWI soliton with a pulse with a complicated shape.

Fig. 3
Fig. 3

Schematic of a TWI-soliton logical gate. An optical pulse at ω1 changes the polarization state of a signal at ω2 in the course of a three-wave quadratic interaction.

Fig. 4
Fig. 4

Dynamic of the TWI-soliton interaction along the crystal (intensity versus time). The solid curve is the generated SF wave.

Equations (8)

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

A1z+1v1 A1t+ig1 2A1t2=iσA3A2* exp(iΔkz),
A2z+1v2 A2t+ig2 2A2t2=i ω2ω1 σA3A1* exp(iΔkz),
A3z+1v3 A3t+ig3 2A3t2=i ω3ω1 σA1A2 exp(-iΔkz),
Aj(t, z)=Ai,0 sechω2ω3σAj,0ω1ν1,2νj,3 t-zvj;
Δϕj=ψ1±ψ2,
ψj=arctanσw2w3(A2,0ν2,3±A1,0ν3,1)Δkω1ν1,2;
iβ=A2,0ν2,3-A1,0ν3,1<0
τ1=1.76ω1ν1,2ν3,1σA1,0ω2ω3.

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