Abstract

The effects of linear and two-photon absorption on bright spatial soliton propagation are studied. A spatial soliton switch that achieves gain through the novel mechanism of colliding, dragging, or trapping of two fundamental solitons of different widths is proposed. Figures of merit for use in evaluating the suitability of absorbing nonlinear media for soliton switching applications are presented. The main effect of linear absorption is to limit the propagation distance, which places an upper bound on the width of the soliton in order to fit sufficient characteristic soliton propagation lengths within the device. The optical limiting nature of two-photon absorption places an upper bound on the gain that an interaction can achieve. The combined effects of linear and two-photon absorption are to reduce the gain upper bound imposed by two-photon absorption alone with the addition of the soliton width constraint. A maximized gain upper bound is determined solely by material parameters and is compared among three promising nonlinear materials. It is shown numerically that the spatial soliton dragging interaction requires shorter propagation distances and achieves greater gain than the collision interaction and that both are tolerant to the presence of absorption and can provide, with high contrast, gains of three or greater using measured material parameters. These results warrant pursuing the implementation of spatial soliton-based logic gates.

© 1996 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  21. A. Barthelemy, C. Froehly, S. Maneuf, and F. Reynaud, “Experimental observation of beams’ self-deflection appearing with two-dimensional spatial soliton propagation in bulk Kerr material,” Opt. Lett. 17, 844–846 (1992).
    [CrossRef]
  22. J.-R. Bian and A. K. Chan, “A nonlinear all-optical switch using spatial soliton interactions,” Microwave Opt. Technol. Lett. 4, 575–580 (1991).
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    [CrossRef]
  29. A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147 (1992).
    [CrossRef]
  30. K. Al-hemyari, A. Villeneuve, J. U. Kang, J. S. Aitchison, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in GaAlAs directional couplers at 1.55 µm without multiphoton absorption,” Appl. Phys. Lett. 63, 3562–3564 (1993).
    [CrossRef]
  31. C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, “Effects of three-photon absorption on nonlinear directional coupling,” Opt. Lett. 17, 710–712 (1992).
    [CrossRef] [PubMed]
  32. M. Thakur, R. C. Frye, and B. I. Greene, “Nonresonant absorption of single-crystal films of polydiacetylene measured by photothermal deflection spectroscopy,” Appl. Phys. Lett. 56, 1187–1188 (1990).
    [CrossRef]
  33. M. D. Dvorak, W. A. Schroeder, D. R. Anderson, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
    [CrossRef]

1995 (2)

V. V. Afanasjev, J. S. Aitchison, and Y. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116, 331–338 (1995).
[CrossRef]

R. McLeod, K. Wagner, and S. Blair, “(3 + 1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

1994 (5)

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal p-toluene sulfonate (PTS) at 1600 nm,” Electron. Lett. 30, 447 (1994).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Anderson, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

X. Yang, Y. S. Kivshar, and B. Luther-Davies, “Is two-photon absorption a limitation to dark soliton switching?” Opt. Lett. 19, 344–346 (1994).
[CrossRef] [PubMed]

X. D. Cao and D. D. Meyerhofer, “All-optical switching by means of collisions of spatial vector solitons,” Opt. Lett. 19, 1711–1713 (1994).
[CrossRef] [PubMed]

S. Blair, K. Wagner, and R. McLeod, “Asymmetric spatial soliton dragging,” Opt. Lett. 19, 1943–1945 (1994).
[CrossRef] [PubMed]

1993 (1)

K. Al-hemyari, A. Villeneuve, J. U. Kang, J. S. Aitchison, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in GaAlAs directional couplers at 1.55 µm without multiphoton absorption,” Appl. Phys. Lett. 63, 3562–3564 (1993).
[CrossRef]

1992 (6)

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

J. P. Robinson and D. R. Anderson, “Soliton logic,” Opt. Comput. Process. 2, 57–61 (1992).

J. Bian and A. K. Chan, “The design of an all-optical spatial soliton switch in a lossy nonlinear medium,” Microwave Opt. Technol. Lett. 5, 433–439 (1992).
[CrossRef]

A. B. Aceves and J. V. Moloney, “Effect of two-photon absorption on bright spatial soliton switches,” Opt. Lett. 17, 1488–1490 (1992).
[CrossRef] [PubMed]

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, “Effects of three-photon absorption on nonlinear directional coupling,” Opt. Lett. 17, 710–712 (1992).
[CrossRef] [PubMed]

A. Barthelemy, C. Froehly, S. Maneuf, and F. Reynaud, “Experimental observation of beams’ self-deflection appearing with two-dimensional spatial soliton propagation in bulk Kerr material,” Opt. Lett. 17, 844–846 (1992).
[CrossRef]

1991 (5)

J. S. Aitchison, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jackel, E. M. Vogel, and P. W. E. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B 8, 1290–1297 (1991).
[CrossRef]

B. A. Malomed and S. Wabnitz, “Soliton annihilation and fusion from resonant inelastic collisions in birefringent optical fibers,” Opt. Lett. 16, 1388–1390 (1991).
[CrossRef] [PubMed]

Y. Chen and J. Atai, “Absorption and amplification of dark solitons,” Opt. Lett. 16, 1933–1935 (1991).
[CrossRef] [PubMed]

J.-R. Bian and A. K. Chan, “A nonlinear all-optical switch using spatial soliton interactions,” Microwave Opt. Technol. Lett. 4, 575–580 (1991).

S. T. Ho, C. E. Soccolich, M. N. Islam, W. S. Hobson, A. F. J. Levi, and R. E. Slusher, “Nonlinear spectroscopy near half-gap in bulk and quantum well GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 59, 2558–2560 (1991).
[CrossRef]

1990 (7)

1989 (2)

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
[CrossRef] [PubMed]

K. W. DeLong, K. B. Rochford, and G. I. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55, 1823–1825 (1989).
[CrossRef]

1988 (2)

1981 (2)

A. Hasegawa and Y. Kodama, “Signal transmission by optical solitons in monomode fiber,” Proc. IEEE 69, 1145–1150 (1981).
[CrossRef]

D. A. B. Miller, “Refractive Fabry–Perot bistability with linear absorption: theory of operation and cavity optimization,” IEEE J. Quantum Electron. QE-17, 306–311 (1981).
[CrossRef]

Aceves, A. B.

Afanasjev, V. V.

V. V. Afanasjev, J. S. Aitchison, and Y. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116, 331–338 (1995).
[CrossRef]

Aitchison, J. S.

V. V. Afanasjev, J. S. Aitchison, and Y. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116, 331–338 (1995).
[CrossRef]

K. Al-hemyari, A. Villeneuve, J. U. Kang, J. S. Aitchison, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in GaAlAs directional couplers at 1.55 µm without multiphoton absorption,” Appl. Phys. Lett. 63, 3562–3564 (1993).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, “Effects of three-photon absorption on nonlinear directional coupling,” Opt. Lett. 17, 710–712 (1992).
[CrossRef] [PubMed]

J. S. Aitchison, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jackel, E. M. Vogel, and P. W. E. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B 8, 1290–1297 (1991).
[CrossRef]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471–473 (1990).
[CrossRef] [PubMed]

Al-hemyari, K.

K. Al-hemyari, A. Villeneuve, J. U. Kang, J. S. Aitchison, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in GaAlAs directional couplers at 1.55 µm without multiphoton absorption,” Appl. Phys. Lett. 63, 3562–3564 (1993).
[CrossRef]

Anderson, D. R.

M. D. Dvorak, W. A. Schroeder, D. R. Anderson, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

J. P. Robinson and D. R. Anderson, “Soliton logic,” Opt. Comput. Process. 2, 57–61 (1992).

Andrejco, M. J.

Atai, J.

Baker, G.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal p-toluene sulfonate (PTS) at 1600 nm,” Electron. Lett. 30, 447 (1994).
[CrossRef]

Barthelemy, A.

Bian, J.

J. Bian and A. K. Chan, “The design of an all-optical spatial soliton switch in a lossy nonlinear medium,” Microwave Opt. Technol. Lett. 5, 433–439 (1992).
[CrossRef]

Bian, J.-R.

J.-R. Bian and A. K. Chan, “A nonlinear all-optical switch using spatial soliton interactions,” Microwave Opt. Technol. Lett. 4, 575–580 (1991).

Blair, S.

R. McLeod, K. Wagner, and S. Blair, “(3 + 1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

S. Blair, K. Wagner, and R. McLeod, “Asymmetric spatial soliton dragging,” Opt. Lett. 19, 1943–1945 (1994).
[CrossRef] [PubMed]

Caglioti, E.

Cao, X. D.

Cha, M.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal p-toluene sulfonate (PTS) at 1600 nm,” Electron. Lett. 30, 447 (1994).
[CrossRef]

Chan, A. K.

J. Bian and A. K. Chan, “The design of an all-optical spatial soliton switch in a lossy nonlinear medium,” Microwave Opt. Technol. Lett. 5, 433–439 (1992).
[CrossRef]

J.-R. Bian and A. K. Chan, “A nonlinear all-optical switch using spatial soliton interactions,” Microwave Opt. Technol. Lett. 4, 575–580 (1991).

Chen, Y.

Chi, S.

DeLong, K. W.

K. W. DeLong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

K. W. DeLong, K. B. Rochford, and G. I. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55, 1823–1825 (1989).
[CrossRef]

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
[CrossRef] [PubMed]

Dvorak, M. D.

M. D. Dvorak, W. A. Schroeder, D. R. Anderson, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

Etemad, S.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal p-toluene sulfonate (PTS) at 1600 nm,” Electron. Lett. 30, 447 (1994).
[CrossRef]

Finlayson, N.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Froehly, C.

Frye, R. C.

M. Thakur, R. C. Frye, and B. I. Greene, “Nonresonant absorption of single-crystal films of polydiacetylene measured by photothermal deflection spectroscopy,” Appl. Phys. Lett. 56, 1187–1188 (1990).
[CrossRef]

Greene, B. I.

M. Thakur, R. C. Frye, and B. I. Greene, “Nonresonant absorption of single-crystal films of polydiacetylene measured by photothermal deflection spectroscopy,” Appl. Phys. Lett. 56, 1187–1188 (1990).
[CrossRef]

Hall, D. W.

Hasegawa, A.

A. Hasegawa and Y. Kodama, “Signal transmission by optical solitons in monomode fiber,” Proc. IEEE 69, 1145–1150 (1981).
[CrossRef]

Ho, S. T.

S. T. Ho, C. E. Soccolich, M. N. Islam, W. S. Hobson, A. F. J. Levi, and R. E. Slusher, “Nonlinear spectroscopy near half-gap in bulk and quantum well GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 59, 2558–2560 (1991).
[CrossRef]

Hobson, W. S.

S. T. Ho, C. E. Soccolich, M. N. Islam, W. S. Hobson, A. F. J. Levi, and R. E. Slusher, “Nonlinear spectroscopy near half-gap in bulk and quantum well GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 59, 2558–2560 (1991).
[CrossRef]

Ironside, C. N.

K. Al-hemyari, A. Villeneuve, J. U. Kang, J. S. Aitchison, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in GaAlAs directional couplers at 1.55 µm without multiphoton absorption,” Appl. Phys. Lett. 63, 3562–3564 (1993).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

Islam, M. N.

S. T. Ho, C. E. Soccolich, M. N. Islam, W. S. Hobson, A. F. J. Levi, and R. E. Slusher, “Nonlinear spectroscopy near half-gap in bulk and quantum well GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 59, 2558–2560 (1991).
[CrossRef]

M. N. Islam, “All-optical cascadable nor gate with gain,” Opt. Lett. 15, 417–419 (1990).
[CrossRef] [PubMed]

Jackel, J. L.

Kang, J. U.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal p-toluene sulfonate (PTS) at 1600 nm,” Electron. Lett. 30, 447 (1994).
[CrossRef]

K. Al-hemyari, A. Villeneuve, J. U. Kang, J. S. Aitchison, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in GaAlAs directional couplers at 1.55 µm without multiphoton absorption,” Appl. Phys. Lett. 63, 3562–3564 (1993).
[CrossRef]

Kivshar, Y.

V. V. Afanasjev, J. S. Aitchison, and Y. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116, 331–338 (1995).
[CrossRef]

Kivshar, Y. S.

Kodama, Y.

A. Hasegawa and Y. Kodama, “Signal transmission by optical solitons in monomode fiber,” Proc. IEEE 69, 1145–1150 (1981).
[CrossRef]

Lawrence, B. L.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal p-toluene sulfonate (PTS) at 1600 nm,” Electron. Lett. 30, 447 (1994).
[CrossRef]

Leaird, D. E.

Lee, D. L.

D. L. Lee, Electromagnetic Principals of Integrated Optics (Wiley, New York, 1986), Chap. 7.

Levi, A. F. J.

S. T. Ho, C. E. Soccolich, M. N. Islam, W. S. Hobson, A. F. J. Levi, and R. E. Slusher, “Nonlinear spectroscopy near half-gap in bulk and quantum well GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 59, 2558–2560 (1991).
[CrossRef]

Luther-Davies, B.

Malomed, B. A.

Maneuf, S.

McLeod, R.

R. McLeod, K. Wagner, and S. Blair, “(3 + 1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

S. Blair, K. Wagner, and R. McLeod, “Asymmetric spatial soliton dragging,” Opt. Lett. 19, 1943–1945 (1994).
[CrossRef] [PubMed]

Meth, J.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal p-toluene sulfonate (PTS) at 1600 nm,” Electron. Lett. 30, 447 (1994).
[CrossRef]

Meyerhofer, D. D.

Miller, D. A. B.

D. A. B. Miller, “Refractive Fabry–Perot bistability with linear absorption: theory of operation and cavity optimization,” IEEE J. Quantum Electron. QE-17, 306–311 (1981).
[CrossRef]

Mizrahi, V.

Moloney, J. V.

Newhouse, M. A.

Oliver, M. K.

Reynaud, F.

Robinson, J. P.

J. P. Robinson and D. R. Anderson, “Soliton logic,” Opt. Comput. Process. 2, 57–61 (1992).

Rochford, K. B.

K. W. DeLong, K. B. Rochford, and G. I. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55, 1823–1825 (1989).
[CrossRef]

Saifi, M. A.

Schroeder, W. A.

M. D. Dvorak, W. A. Schroeder, D. R. Anderson, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

Seaton, C. T.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Shi, T.-T.

Silberberg, Y.

Slusher, R. E.

S. T. Ho, C. E. Soccolich, M. N. Islam, W. S. Hobson, A. F. J. Levi, and R. E. Slusher, “Nonlinear spectroscopy near half-gap in bulk and quantum well GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 59, 2558–2560 (1991).
[CrossRef]

Smirl, A. L.

M. D. Dvorak, W. A. Schroeder, D. R. Anderson, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

Smith, P. W. E.

Soccolich, C. E.

S. T. Ho, C. E. Soccolich, M. N. Islam, W. S. Hobson, A. F. J. Levi, and R. E. Slusher, “Nonlinear spectroscopy near half-gap in bulk and quantum well GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 59, 2558–2560 (1991).
[CrossRef]

Stegeman, G.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal p-toluene sulfonate (PTS) at 1600 nm,” Electron. Lett. 30, 447 (1994).
[CrossRef]

Stegeman, G. I.

K. Al-hemyari, A. Villeneuve, J. U. Kang, J. S. Aitchison, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in GaAlAs directional couplers at 1.55 µm without multiphoton absorption,” Appl. Phys. Lett. 63, 3562–3564 (1993).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, “Effects of three-photon absorption on nonlinear directional coupling,” Opt. Lett. 17, 710–712 (1992).
[CrossRef] [PubMed]

K. W. DeLong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

K. W. DeLong, K. B. Rochford, and G. I. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55, 1823–1825 (1989).
[CrossRef]

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
[CrossRef] [PubMed]

E. Caglioti, S. Trillo, S. Wabnitz, and G. I. Stegeman, “Limitations to all-optical switching using nonlinear couplers in the presence of linear and nonlinear absorption and saturation,” J. Opt. Soc. Am. B 5, 472–482 (1988).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Thakur, M.

M. Thakur, R. C. Frye, and B. I. Greene, “Nonresonant absorption of single-crystal films of polydiacetylene measured by photothermal deflection spectroscopy,” Appl. Phys. Lett. 56, 1187–1188 (1990).
[CrossRef]

Toruellas, W.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal p-toluene sulfonate (PTS) at 1600 nm,” Electron. Lett. 30, 447 (1994).
[CrossRef]

Trillo, S.

Villeneuve, A.

K. Al-hemyari, A. Villeneuve, J. U. Kang, J. S. Aitchison, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in GaAlAs directional couplers at 1.55 µm without multiphoton absorption,” Appl. Phys. Lett. 63, 3562–3564 (1993).
[CrossRef]

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, “Effects of three-photon absorption on nonlinear directional coupling,” Opt. Lett. 17, 710–712 (1992).
[CrossRef] [PubMed]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

Vogel, E. M.

Wabnitz, S.

Wagner, K.

R. McLeod, K. Wagner, and S. Blair, “(3 + 1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

S. Blair, K. Wagner, and R. McLeod, “Asymmetric spatial soliton dragging,” Opt. Lett. 19, 1943–1945 (1994).
[CrossRef] [PubMed]

Weidman, D. L.

Weiner, A. M.

Wherrett, B. S.

M. D. Dvorak, W. A. Schroeder, D. R. Anderson, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

Wigley, P. G. J.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

Wright, E. M.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Yang, C. C.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, “Effects of three-photon absorption on nonlinear directional coupling,” Opt. Lett. 17, 710–712 (1992).
[CrossRef] [PubMed]

Yang, X.

Zanoni, R.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Appl. Phys. Lett. (6)

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

K. Al-hemyari, A. Villeneuve, J. U. Kang, J. S. Aitchison, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in GaAlAs directional couplers at 1.55 µm without multiphoton absorption,” Appl. Phys. Lett. 63, 3562–3564 (1993).
[CrossRef]

M. Thakur, R. C. Frye, and B. I. Greene, “Nonresonant absorption of single-crystal films of polydiacetylene measured by photothermal deflection spectroscopy,” Appl. Phys. Lett. 56, 1187–1188 (1990).
[CrossRef]

S. T. Ho, C. E. Soccolich, M. N. Islam, W. S. Hobson, A. F. J. Levi, and R. E. Slusher, “Nonlinear spectroscopy near half-gap in bulk and quantum well GaAs/AlGaAs waveguides,” Appl. Phys. Lett. 59, 2558–2560 (1991).
[CrossRef]

K. W. DeLong, K. B. Rochford, and G. I. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55, 1823–1825 (1989).
[CrossRef]

K. W. DeLong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

Electron. Lett. (1)

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal p-toluene sulfonate (PTS) at 1600 nm,” Electron. Lett. 30, 447 (1994).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. A. B. Miller, “Refractive Fabry–Perot bistability with linear absorption: theory of operation and cavity optimization,” IEEE J. Quantum Electron. QE-17, 306–311 (1981).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Anderson, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

J. Lightwave Technol. (1)

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

J. Opt. Soc. Am. B (2)

Microwave Opt. Technol. Lett. (2)

J.-R. Bian and A. K. Chan, “A nonlinear all-optical switch using spatial soliton interactions,” Microwave Opt. Technol. Lett. 4, 575–580 (1991).

J. Bian and A. K. Chan, “The design of an all-optical spatial soliton switch in a lossy nonlinear medium,” Microwave Opt. Technol. Lett. 5, 433–439 (1992).
[CrossRef]

Opt. Commun. (1)

V. V. Afanasjev, J. S. Aitchison, and Y. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116, 331–338 (1995).
[CrossRef]

Opt. Comput. Process. (1)

J. P. Robinson and D. R. Anderson, “Soliton logic,” Opt. Comput. Process. 2, 57–61 (1992).

Opt. Lett. (14)

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
[CrossRef] [PubMed]

M. N. Islam, “All-optical cascadable nor gate with gain,” Opt. Lett. 15, 417–419 (1990).
[CrossRef] [PubMed]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471–473 (1990).
[CrossRef] [PubMed]

Y. Silberberg, “Solitons and two-photon absorption,” Opt. Lett. 15, 1005–1007 (1990).
[CrossRef] [PubMed]

T.-T. Shi and S. Chi, “Nonlinear photonic switching by using the spatial soliton collision,” Opt. Lett. 15, 1123–1125 (1990).
[CrossRef] [PubMed]

M. A. Newhouse, D. L. Weidman, and D. W. Hall, “Enhanced-nonlinearity single-mode lead silicate optical fiber,” Opt. Lett. 15, 1185–1187 (1990).
[CrossRef] [PubMed]

B. A. Malomed and S. Wabnitz, “Soliton annihilation and fusion from resonant inelastic collisions in birefringent optical fibers,” Opt. Lett. 16, 1388–1390 (1991).
[CrossRef] [PubMed]

Y. Chen and J. Atai, “Absorption and amplification of dark solitons,” Opt. Lett. 16, 1933–1935 (1991).
[CrossRef] [PubMed]

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, “Effects of three-photon absorption on nonlinear directional coupling,” Opt. Lett. 17, 710–712 (1992).
[CrossRef] [PubMed]

A. Barthelemy, C. Froehly, S. Maneuf, and F. Reynaud, “Experimental observation of beams’ self-deflection appearing with two-dimensional spatial soliton propagation in bulk Kerr material,” Opt. Lett. 17, 844–846 (1992).
[CrossRef]

X. Yang, Y. S. Kivshar, and B. Luther-Davies, “Is two-photon absorption a limitation to dark soliton switching?” Opt. Lett. 19, 344–346 (1994).
[CrossRef] [PubMed]

X. D. Cao and D. D. Meyerhofer, “All-optical switching by means of collisions of spatial vector solitons,” Opt. Lett. 19, 1711–1713 (1994).
[CrossRef] [PubMed]

A. B. Aceves and J. V. Moloney, “Effect of two-photon absorption on bright spatial soliton switches,” Opt. Lett. 17, 1488–1490 (1992).
[CrossRef] [PubMed]

S. Blair, K. Wagner, and R. McLeod, “Asymmetric spatial soliton dragging,” Opt. Lett. 19, 1943–1945 (1994).
[CrossRef] [PubMed]

Phys. Rev. A (1)

R. McLeod, K. Wagner, and S. Blair, “(3 + 1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995).
[CrossRef] [PubMed]

Proc. IEEE (1)

A. Hasegawa and Y. Kodama, “Signal transmission by optical solitons in monomode fiber,” Proc. IEEE 69, 1145–1150 (1981).
[CrossRef]

Other (1)

D. L. Lee, Electromagnetic Principals of Integrated Optics (Wiley, New York, 1986), Chap. 7.

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Figures (13)

Fig. 1
Fig. 1

Spatial soliton dragging over a gate length of 10Z0 with a normalized initial relative propagation angle of κ = 1.7. The top shows the signal (thin lines) and the pump (thick lines) with no cross-phase modulation (Δ = 0). The bottom shows the dragging interaction with cross-phase modulation (Δ = 2/3, appropriate for orthogonal linear polarizations). The initial beam ratio is r = 3.0. The contrast of the gate is 6565, and the gain is 3.

Fig. 2
Fig. 2

Spatial soliton collision over a gate length of 10Z0 with a normalized initial relative propagation angle of κ = 0.7. The top shows the signal (thin lines) and the pump (thick lines) with no cross-phase modulation (Δ = 0). The bottom shows the collision interaction with cross-phase modulation (Δ = 2/3). The initial beam ratio is r = 3.0. The contrast of the gate is 79 and the gain is 3, but the reflected signal partially transmits through the aperture in this case. If a polarizer is used at the output to block the signal, the contrast of the gate rises to 4368.

Fig. 3
Fig. 3

Contour plot of the percentage error between Eq. (5) and numerical simulation results versus s = α z and K, where z = 10Z0. The range of validity of the ansatz used to derive Eq. (5) (in which the soliton maintains its sech shape but changes its width and amplitude self-consistently during propagation) is s < 1.0 and K < 0.1 to within ∼5% error of the simulation.

Fig. 4
Fig. 4

Propagation of a signal, an r = 3 fundamental pump, and an r = 4 higher-order pump in a linearly absorbing material with s = 0.5 over a distance of 10Z0. With linear absorption the signal and the pumps attenuate by the same fraction exp(−0.5) = 0.61. The contours are at constant intensity.

Fig. 5
Fig. 5

Plot of pump power Pp(d) given by either Eq. (13) for T = 0.069 or Eq. (16) for F TPA ( 10 ) = 9.3 / d versus normalized propagation distance d (where z = dZ0). The thin solid curves are the evolution of the pump power for a given initial beam ratio and the thick solid curve is the maximum (as r → ∞) given by TPA(d).

Fig. 6
Fig. 6

Propagation of a signal, an r = 3 fundamental pump, and an r = 4 higher-order pump in a two-photon-absorbing material with K = 0.005 over a distance of 15Z0. The longer distance is used to illustrate the higher-order soliton breakup more clearly. With two-photon absorption the signal and pumps attenuate by different fractions: the signal by 0.87, the r = 3 fundamental pump by 0.51, and the r = 4 higher-order pump by 0.62. The contours are at constant intensity.

Fig. 7
Fig. 7

Plot of the linear-absorption figure of merit α (thin curves) given by Eq. (9) and gain upper bound G (heavy curves) given by Eq. (20) versus the linear absorption parameter s parameterized by normalized gate lengths d = 6 and d = 10. The material is 39% lead silicate glass, and the optimum gain upper bound occurs in both cases at sopt = 0.068 as given by Eq. (21). For d = 6 the upper bound on gain is 3.5, whereas for d = 10 it is 2.7.

Fig. 8
Fig. 8

Regions exceeding contrast of 5 (thick curves) for optimized spatial soliton dragging and collision interactions superimposed with gain contours (thin dotted lines) versus gate length and initial beam ratio in a material with no absorption. The optimal normalized interaction angles are approximated by the expressions κ (r) = 2.2r/(r + 1) for dragging (heavy) and κ (r) = 0.9r/(r + 1) for collision (medium), and the aperture width is given by 3.5wp = 3.5w0/r.

Fig. 9
Fig. 9

Regions exceeding contrast of 5 (thick curves) for optimized spatial soliton dragging and collision interactions superimposed with gain contours (thin dotted lines) versus gate length and initial beam ratio in a material with no absorption. The normalized interaction angles for dragging are κ = 1.5 (heavy dashed) and κ = 2.0 (heavy solid) and for collision κ = 0.6 (medium dashed) and κ = 0.8 (medium solid), and the aperture width is fixed at 3.5w0.

Fig. 10
Fig. 10

Plot of minimum desired contrast (thick curves) and gain contours (thin dotted lines) versus gate length and initial beam ratio for spatial soliton dragging and collision in a linearly absorbing material for s = 0.5. The normalized interaction angles for dragging are κ = 1.5 (heavy dashed) and κ = 2.0 (heavy solid) and for collision κ = 0.6 (medium dashed) and κ = 0.8 (medium solid), and the aperture width is 3.5w0. The maximum gain is limited by the linear absorption material figure of merit α(0.5, d), which determines the maximum initial ratio r.

Fig. 11
Fig. 11

Spatial soliton dragging with the parameters of 39% lead-doped silicate glass, where α (0.068, 10) = 11 and TPA(10) = 2.9 with an initial relative propagation angle of κ = 1.7. The top shows the signal (thin lines) and the pump (thick lines) with Δ = 0, whereas the bottom shows the dragging interaction with Δ = 2/3. The initial beam ratio is 3.0, and the gain is 2.0 with a contrast of 6637 without the use of a polarizer at the output. The material parameters place an upper bound of 2.7 on the gain at 10Z0. Note that cross-two-photon absorption suppresses the trapped signal beam (when Δ = 2/3) in comparison with the case when Δ = 0.

Fig. 12
Fig. 12

Spatial soliton collision with the parameters of 39% lead-doped silicate glass, in which α (0.068, 10) = 11 and TPA(10) = 2.9 with an initial relative propagation angle of κ = 0.7. The top shows the signal (thin lines) and the pump (thick lines) with Δ = 0, whereas the bottom shows the collision interaction with Δ = 2/3. The initial beam ratio is 3.0, and the gain is 2.0 with a contrast of 12.4 without the use of a polarizer at the output and 174 with a polarizer. The material parameters place an upper bound of 2.7 on the gain at 10Z0.

Fig. 13
Fig. 13

Plot of minimum desired contrast (thick curves) and gain contours (thin dotted curves) versus gate length and initial beam ratio for spatial soliton dragging and collision with the parameters of 39% lead-doped silicate glass, including the effects of both linear and two-photon absorption. The normalized interaction angles for dragging are κ = 1.5 (heavy dashed) and κ = 2.0 (heavy solid) and for collision κ = 0.6 (medium dashed) and κ = 0.8 (medium solid), and the aperture width is 3.5w0. The material parameters place an upper bound on the gain of 3.5 at d = 6 and 2.7 at d = 10.

Tables (2)

Tables Icon

Table 1 Calculated Figures of Merit for Promising Nonlinear Materials

Tables Icon

Table 2 Summary of Soliton Dragging and Collision Performancea

Equations (24)

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2 i k E z + 2 E x 2 + 2 k 2 n 2 n 0 ( 1 + i K ) | E | 2 E + i k α E = 0 ,
z P ( z ) z | E | 2 d x = α | E | 2 d x β 2 | E | 4 d x ,
| E ( x , z ) | = 1 k w ( z ) n 0 n 2 sech x w ( z ) ,
w 2 ( z ) = 4 K 3 α k [ exp ( 2 α z ) 1 ] + w 0 2   exp ( 2 α z ) ,
P 2 ( z ) = P 0 2 ( k 3 n 2 2 K P 0 2 / 3 α n 0 2 ) [ exp ( 2 α z ) 1 ] + exp ( 2 α z ) .
w ( z ) = w 0   exp ( α z ) , P ( z ) = P 0   exp ( α z ) ,
w 0 s λ π 2 α d ,
w 0 ( s , d ) = α λ , P 0 ( s , d ) = λ 0 2 π 2 n 2 α ,
α ( s , d ) s π 2 d α λ .
w 2 ( z ) = w 0 2 + 8 K z 3 k ,
P 2 ( z ) = P 0 2 ( 2 k 3 n 2 2 K / 3 n 0 2 ) P 0 2 z + 1 ,
P 2 ( d ) = p 0 2 d T / 6 + 1 ,
P p 2 ( d ) = r 2 P 0 2 ( d T / 6 ) r 2 + 1 .
P p ( d ) max = 6 d T P 0 .
TPA ( d ) P p ( d ) max P 0 = 6 d T ,
P p ( d ) = r TPA ( d ) P 0 r 2 + TPA 2 ( d ) .
P plane ( z ) = P 0 1 + β 2 I 0 z ,
P soliton ( z ) = P 0 1 + ( 4 / 3 ) β 2 I 0 z ,
P p ( s , d ) = r 2 s TPA ( d ) P 0 r 2 [ exp ( 2 s ) 1 ] + 2 s TPA 2 ( d ) exp ( 2 s ) ,
G ( s , d ) = 2 s α ( s , d ) TPA ( d ) α 2 ( s , d ) [ exp ( 2 s ) 1 ] + 2 s TPA 2 ( d ) exp ( 2 s ) ,
exp ( 2 s opt ) 1 2 s opt = 12 π 2 α λ T + 1 ,
2 i k E x z + 2 E x x 2 + 2 k 2 n 2 n 0 ( 1 + i K ) ( | E x | 2 + Δ | E y | 2 ) E x + i k α E x = 0 ,
2 i k E y z + 2 E y x 2 + 2 k 2 n 2 n 0 ( 1 + i K ) ( | E y | 2 + Δ | E x | 2 ) E y + i k α E y = 0 ,
z P x ( z ) = α | E x | 2 d x β 2 ( | E x | 4 + Δ | E y | 2 | E x | 2 ) d x ,

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