Abstract

A generalized interaction geometry between orthogonally polarized optical spatial solitons is presented in which a weak signal soliton induces a small angular deflection of a stronger power supply, or pump, soliton, resulting in a spatially resolved shift of the pump at the gate output. This geometry allows for the all-optical realization of true three-terminal, inverting and restoring logic devices with gain, which can serve as building blocks for more complex logic operations. In addition, the effects of linear and nonlinear material absorption, which degrades the performance of the angular deflection gates, are considered. Even in the presence of realistic absorption, the angular deflection logic gates can still produce large-signal gain (>2) sufficient for general logic. Finally, by use of a modified gate transfer function approach, these optical logic gates are shown to possess large noise margins for robust operation.

© 1999 Optical Society of America

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    [CrossRef]
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    [CrossRef]

1999 (1)

R. McLeod, K. Wagner, S. Blair, “Variational approach to orthogonally-polarized optical soliton interaction with cubic and quintic nonlinearities,” Phys. Scr. 59, 365–373 (1999).
[CrossRef]

1998 (1)

S. Blair, K. Wagner, “(2 + 1)-D propagation of spatio-temporal solitary waves including higher-order corrections,” Opt. Quantum Electron. 30, 697–737 (1998).
[CrossRef]

1997 (1)

L. Lefort, A. Barthelemy, “All-optical demultiplexing of a signal using collision and waveguiding of spatial solitons,” IEEE Photonics Technol. Lett. 9, 1364–1366 (1997).
[CrossRef]

1996 (4)

1995 (5)

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

A. Villeneuve, J. U. Kang, J. S. Aitchison, G. I. Stegeman, “Unity ratio of cross- to self-phase modulation in bulk AlGaAs and AlGaAs/GaAs MQW waveguides at half the band gap,” Appl. Phys. Lett. 67, 760–762 (1995).
[CrossRef]

S. Chakravarty, M. J. Ablowitz, J. R. Sauer, R. B. Jenkins, “Multisoliton interactions and wavelength-division multiplexing,” Opt. Lett. 20, 136–138 (1995).
[CrossRef] [PubMed]

R. B. Jenkins, J. R. Sauer, S. Chakravarty, M. J. Ablowitz, “Data-dependent timing jitter in wavelength-division-multiplexing soliton systems,” Opt. Lett. 20, 1964–1966 (1995).
[CrossRef] [PubMed]

R. J. Manning, G. Sherlock, “Recovery of a π phase shift in ∼12.5 ps in a semiconductor laser amplifier,” Electron. Lett. 31, 307–308 (1995).
[CrossRef]

1994 (3)

1993 (3)

1992 (4)

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

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

Q. Wang, P. K. A. Wai, C.-J. Chen, C. R. Menyuk, “Soliton shadows in birefringent optical fibers,” Opt. Lett. 17, 1265–1267 (1992).
[CrossRef] [PubMed]

A. Barthelemy, C. Froehly, S. Maneuf, 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 (8)

1990 (7)

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, P. C. Becker, K. W. Wecht, “Soliton collision interaction force dependence on wavelength separation in fibre amplifier based systems,” Electron. Lett. 26, 1499–1501 (1990).
[CrossRef]

F. Reynaud, A. Barthelemy, “Optically controlled interaction between two fundamental soliton beams,” Europhys. Lett. 12, 401–405 (1990).
[CrossRef]

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

P. A. Andrekson, N. A. Olsson, P. C. Becker, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “Observation of multiple wavelength soliton collisions in optical systems with fiber amplifiers,” Appl. Phys. Lett. 57, 1715–1717 (1990).
[CrossRef]

D. R. Andersen, D. E. Hooten, J. G. A. Swartzlander, A. E. Kaplan, “Direct measurement of the transverse velocity of dark spatial solitons,” Opt. Lett. 15, 783–785 (1990).
[CrossRef] [PubMed]

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

M. N. Islam, C. E. Soccolich, D. A. B. Miller, “Low-energy ultrafast fiber soliton logic gates,” Opt. Lett. 15, 909–911 (1990).
[CrossRef] [PubMed]

1989 (3)

1988 (3)

1987 (5)

Y. Kodama, “On solitary-wave interaction,” Phys. Lett. A 123, 276–282 (1987).
[CrossRef]

F. M. Mitschke, L. F. Mollenauer, “Experimental observation of the interaction forces between solitons in optical fibers,” Opt. Lett. 12, 355–357 (1987).
[CrossRef] [PubMed]

T. Morioka, M. Saruwatari, A. Takada, “Ultrafast optical multi/demultiplexer utilising optical Kerr effect in polarisation-maintaining single-mode fibers,” Electron. Lett. 23, 453–454 (1987).
[CrossRef]

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I. Equal propagation amplitudes,” Opt. Lett. 12, 614–616 (1987).
[CrossRef] [PubMed]

C. R. Menyuk, “Nonlinear pulse propagation in birefringent fibers,” IEEE J. Quantum Electron. QE-23, 174–176 (1987).
[CrossRef]

1985 (1)

K.-I. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, “Optical sampling using an all-fiber optical Kerr shutter,” Appl. Phys. Lett. 46, 623–625 (1985).
[CrossRef]

1983 (2)

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, “An ultrafast all-optical gate,” IEEE J. Quantum Electron. QE-19, 1718–1723 (1983).
[CrossRef]

J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (1983).
[CrossRef] [PubMed]

1982 (2)

1979 (1)

D. A. B. Miller, S. D. Smith, A. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low-power nonlinear effects in InSb,” Appl. Phys. Lett. 35, 658–660 (1979).
[CrossRef]

1976 (1)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

1974 (1)

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

1969 (1)

M. A. Duguay, J. W. Hansen, “An ultrafast light gate,” Appl. Phys. Lett. 15, 192–194 (1969).
[CrossRef]

Aakjer, T.

Ablowitz, M. J.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Agrawal, N.

E. Jahn, N. Agrawal, W. Pieper, H.-J. Ehrke, D. Franke, W. Fürst, C. M. Weinert, “Monolithically integrated nonlinear Sagnac interferometer and its application as a 20 Gbit/s all-optical demultiplexor,” Electron. Lett. 32, 782–784 (1996).
[CrossRef]

Aitchison, J. S.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, “One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides,” Opt. Lett. 21, 189–191 (1996).
[CrossRef] [PubMed]

A. Villeneuve, J. U. Kang, J. S. Aitchison, G. I. Stegeman, “Unity ratio of cross- to self-phase modulation in bulk AlGaAs and AlGaAs/GaAs MQW waveguides at half the band gap,” Appl. Phys. Lett. 67, 760–762 (1995).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, P. W. E. Smith, “Experimental observation of spatial soliton interactions,” Opt. Lett. 16, 15–17 (1991).
[CrossRef] [PubMed]

Allan, G. R.

S. R. Skinner, G. R. Allan, D. R. Anderson, A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

Andersen, D. R.

Anderson, D. R.

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

S. R. Skinner, G. R. Allan, D. R. Anderson, A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

Andrekson, P. A.

P. A. Andrekson, N. A. Olsson, P. C. Becker, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “Observation of multiple wavelength soliton collisions in optical systems with fiber amplifiers,” Appl. Phys. Lett. 57, 1715–1717 (1990).
[CrossRef]

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, P. C. Becker, K. W. Wecht, “Soliton collision interaction force dependence on wavelength separation in fibre amplifier based systems,” Electron. Lett. 26, 1499–1501 (1990).
[CrossRef]

Barthelemy, A.

L. Lefort, A. Barthelemy, “All-optical demultiplexing of a signal using collision and waveguiding of spatial solitons,” IEEE Photonics Technol. Lett. 9, 1364–1366 (1997).
[CrossRef]

A. Barthelemy, C. Froehly, S. Maneuf, 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]

M. Shalaby, A. Barthelemy, “Experimental spatial soliton trapping and switching,” Opt. Lett. 16, 1472–1474 (1991).
[CrossRef] [PubMed]

F. Reynaud, A. Barthelemy, “Optically controlled interaction between two fundamental soliton beams,” Europhys. Lett. 12, 401–405 (1990).
[CrossRef]

Becker, P. C.

P. A. Andrekson, N. A. Olsson, P. C. Becker, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “Observation of multiple wavelength soliton collisions in optical systems with fiber amplifiers,” Appl. Phys. Lett. 57, 1715–1717 (1990).
[CrossRef]

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, P. C. Becker, K. W. Wecht, “Soliton collision interaction force dependence on wavelength separation in fibre amplifier based systems,” Electron. Lett. 26, 1499–1501 (1990).
[CrossRef]

Bian, J.-R.

J.-R. Bian, 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, S. Blair, “Variational approach to orthogonally-polarized optical soliton interaction with cubic and quintic nonlinearities,” Phys. Scr. 59, 365–373 (1999).
[CrossRef]

S. Blair, K. Wagner, “(2 + 1)-D propagation of spatio-temporal solitary waves including higher-order corrections,” Opt. Quantum Electron. 30, 697–737 (1998).
[CrossRef]

S. Blair, K. Wagner, R. McLeod, “Material figures of merit for spatial soliton interactions in the presence of absorption,” J. Opt. Soc. Am. B 13, 2141–2153 (1996).
[CrossRef]

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

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

S. Blair, K. Wagner are preparing a manuscript to be called “Cascadable spatial soliton gates.”

S. Blair, “Optical soliton-based logic gates,” Ph.D. dissertation (University of Colorado, Boulder, Boulder, 1998).

Cao, X. D.

Chakravarty, S.

Chan, A. K.

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

Chen, C.-J.

Chi, S.

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

S. Chi, S. Wen, “Optical soliton near zero-dispersion regime in Raman pump fiber,” Opt. Commun. 69, 334–338 (1989).
[CrossRef]

Crosignani, B.

Cutolo, A.

DiPorto, P.

Doran, N. J.

N. J. Doran, D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13, 311–313 (1988).
[CrossRef]

Duguay, M. A.

M. A. Duguay, J. W. Hansen, “An ultrafast light gate,” Appl. Phys. Lett. 15, 192–194 (1969).
[CrossRef]

Ehrke, H.-J.

E. Jahn, N. Agrawal, W. Pieper, H.-J. Ehrke, D. Franke, W. Fürst, C. M. Weinert, “Monolithically integrated nonlinear Sagnac interferometer and its application as a 20 Gbit/s all-optical demultiplexor,” Electron. Lett. 32, 782–784 (1996).
[CrossRef]

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362–367 (1991).
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J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Fleck, J. J. A.

Franke, D.

E. Jahn, N. Agrawal, W. Pieper, H.-J. Ehrke, D. Franke, W. Fürst, C. M. Weinert, “Monolithically integrated nonlinear Sagnac interferometer and its application as a 20 Gbit/s all-optical demultiplexor,” Electron. Lett. 32, 782–784 (1996).
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Friberg, S. R.

Froehly, C.

Fürst, W.

E. Jahn, N. Agrawal, W. Pieper, H.-J. Ehrke, D. Franke, W. Fürst, C. M. Weinert, “Monolithically integrated nonlinear Sagnac interferometer and its application as a 20 Gbit/s all-optical demultiplexor,” Electron. Lett. 32, 782–784 (1996).
[CrossRef]

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J. P. Sokoloff, P. R. Prucnal, I. Glesk, M. Kane, “A terahertz optical asymmetric demultiplexor (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362–367 (1991).
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Haus, H. A.

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, “An ultrafast all-optical gate,” IEEE J. Quantum Electron. QE-19, 1718–1723 (1983).
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E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

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A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, “An ultrafast all-optical gate,” IEEE J. Quantum Electron. QE-19, 1718–1723 (1983).
[CrossRef]

Ironside, C. N.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Islam, M. N.

Jackel, J. L.

Jahn, E.

E. Jahn, N. Agrawal, W. Pieper, H.-J. Ehrke, D. Franke, W. Fürst, C. M. Weinert, “Monolithically integrated nonlinear Sagnac interferometer and its application as a 20 Gbit/s all-optical demultiplexor,” Electron. Lett. 32, 782–784 (1996).
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Jenkins, R. B.

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
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D. A. B. Miller, S. D. Smith, A. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low-power nonlinear effects in InSb,” Appl. Phys. Lett. 35, 658–660 (1979).
[CrossRef]

Kane, M.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, M. Kane, “A terahertz optical asymmetric demultiplexor (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).
[CrossRef]

Kang, J. U.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, “One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides,” Opt. Lett. 21, 189–191 (1996).
[CrossRef] [PubMed]

A. Villeneuve, J. U. Kang, J. S. Aitchison, G. I. Stegeman, “Unity ratio of cross- to self-phase modulation in bulk AlGaAs and AlGaAs/GaAs MQW waveguides at half the band gap,” Appl. Phys. Lett. 67, 760–762 (1995).
[CrossRef]

Kaplan, A. E.

Kimura, Y.

K.-I. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, “Optical sampling using an all-fiber optical Kerr shutter,” Appl. Phys. Lett. 46, 623–625 (1985).
[CrossRef]

Kitayama, K.-I.

K.-I. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, “Optical sampling using an all-fiber optical Kerr shutter,” Appl. Phys. Lett. 46, 623–625 (1985).
[CrossRef]

Kodama, Y.

Lattes, A.

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, “An ultrafast all-optical gate,” IEEE J. Quantum Electron. QE-19, 1718–1723 (1983).
[CrossRef]

Leaird, D. E.

Lefort, L.

L. Lefort, A. Barthelemy, “All-optical demultiplexing of a signal using collision and waveguiding of spatial solitons,” IEEE Photonics Technol. Lett. 9, 1364–1366 (1997).
[CrossRef]

Leonberger, F. J.

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, “An ultrafast all-optical gate,” IEEE J. Quantum Electron. QE-19, 1718–1723 (1983).
[CrossRef]

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P. A. Andrekson, N. A. Olsson, P. C. Becker, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “Observation of multiple wavelength soliton collisions in optical systems with fiber amplifiers,” Appl. Phys. Lett. 57, 1715–1717 (1990).
[CrossRef]

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, P. C. Becker, K. W. Wecht, “Soliton collision interaction force dependence on wavelength separation in fibre amplifier based systems,” Electron. Lett. 26, 1499–1501 (1990).
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[CrossRef]

McLeod, R.

R. McLeod, K. Wagner, S. Blair, “Variational approach to orthogonally-polarized optical soliton interaction with cubic and quintic nonlinearities,” Phys. Scr. 59, 365–373 (1999).
[CrossRef]

S. Blair, K. Wagner, R. McLeod, “Material figures of merit for spatial soliton interactions in the presence of absorption,” J. Opt. Soc. Am. B 13, 2141–2153 (1996).
[CrossRef]

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

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

K. Wagner, R. McLeod, “Spatial soliton dragging gates and light bullets,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 305–307.

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Meyerhofer, D. D.

Miller, D. A. B.

M. N. Islam, C. E. Soccolich, D. A. B. Miller, “Low-energy ultrafast fiber soliton logic gates,” Opt. Lett. 15, 909–911 (1990).
[CrossRef] [PubMed]

D. A. B. Miller, S. D. Smith, A. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low-power nonlinear effects in InSb,” Appl. Phys. Lett. 35, 658–660 (1979).
[CrossRef]

D. A. B. Miller, “Device requirements for digital optical processing,” in Digital Optical Computing, Vol. CR35 of SPIE Critical Reviews (Society of Photo-Optical and Instrumentation Engineers, Bellingham, Wash., 1990), pp. 68–76.

Millman, J.

J. Millman, A. Grabel, Microelectronics, 2nd ed. (McGraw-Hill, New York, 1987).

Mitschke, F. M.

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362–367 (1991).
[CrossRef]

F. M. Mitschke, L. F. Mollenauer, “Experimental observation of the interaction forces between solitons in optical fibers,” Opt. Lett. 12, 355–357 (1987).
[CrossRef] [PubMed]

Morioka, T.

T. Morioka, M. Saruwatari, A. Takada, “Ultrafast optical multi/demultiplexer utilising optical Kerr effect in polarisation-maintaining single-mode fibers,” Electron. Lett. 23, 453–454 (1987).
[CrossRef]

Morris, J. R.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Okamoto, K.

K.-I. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, “Optical sampling using an all-fiber optical Kerr shutter,” Appl. Phys. Lett. 46, 623–625 (1985).
[CrossRef]

Oliver, M. K.

Olsson, N. A.

P. A. Andrekson, N. A. Olsson, P. C. Becker, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “Observation of multiple wavelength soliton collisions in optical systems with fiber amplifiers,” Appl. Phys. Lett. 57, 1715–1717 (1990).
[CrossRef]

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, P. C. Becker, K. W. Wecht, “Soliton collision interaction force dependence on wavelength separation in fibre amplifier based systems,” Electron. Lett. 26, 1499–1501 (1990).
[CrossRef]

Patel, N. S.

Pieper, W.

E. Jahn, N. Agrawal, W. Pieper, H.-J. Ehrke, D. Franke, W. Fürst, C. M. Weinert, “Monolithically integrated nonlinear Sagnac interferometer and its application as a 20 Gbit/s all-optical demultiplexor,” Electron. Lett. 32, 782–784 (1996).
[CrossRef]

Poole, C. D.

Povlsen, J. H.

Prucnal, P. R.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, M. Kane, “A terahertz optical asymmetric demultiplexor (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).
[CrossRef]

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Reynaud, F.

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

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Saruwatari, M.

T. Morioka, M. Saruwatari, A. Takada, “Ultrafast optical multi/demultiplexer utilising optical Kerr effect in polarisation-maintaining single-mode fibers,” Electron. Lett. 23, 453–454 (1987).
[CrossRef]

Sauer, J. R.

Seikai, S.

K.-I. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, “Optical sampling using an all-fiber optical Kerr shutter,” Appl. Phys. Lett. 46, 623–625 (1985).
[CrossRef]

Shalaby, M.

Sherlock, G.

R. J. Manning, G. Sherlock, “Recovery of a π phase shift in ∼12.5 ps in a semiconductor laser amplifier,” Electron. Lett. 31, 307–308 (1995).
[CrossRef]

Shi, T.-T.

Silberberg, Y.

Simpson, J. R.

P. A. Andrekson, N. A. Olsson, P. C. Becker, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “Observation of multiple wavelength soliton collisions in optical systems with fiber amplifiers,” Appl. Phys. Lett. 57, 1715–1717 (1990).
[CrossRef]

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, P. C. Becker, K. W. Wecht, “Soliton collision interaction force dependence on wavelength separation in fibre amplifier based systems,” Electron. Lett. 26, 1499–1501 (1990).
[CrossRef]

Skinner, S. R.

S. R. Skinner, G. R. Allan, D. R. Anderson, A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

Smirl, A. L.

S. R. Skinner, G. R. Allan, D. R. Anderson, A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

Smith, P. W. E.

Smith, S. D.

D. A. B. Miller, S. D. Smith, A. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low-power nonlinear effects in InSb,” Appl. Phys. Lett. 35, 658–660 (1979).
[CrossRef]

Soccolich, C. E.

Sokoloff, J. P.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, M. Kane, “A terahertz optical asymmetric demultiplexor (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).
[CrossRef]

Stegeman, G. I.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, “One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides,” Opt. Lett. 21, 189–191 (1996).
[CrossRef] [PubMed]

A. Villeneuve, J. U. Kang, J. S. Aitchison, G. I. Stegeman, “Unity ratio of cross- to self-phase modulation in bulk AlGaAs and AlGaAs/GaAs MQW waveguides at half the band gap,” Appl. Phys. Lett. 67, 760–762 (1995).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Swartzlander, J. G. A.

Takada, A.

T. Morioka, M. Saruwatari, A. Takada, “Ultrafast optical multi/demultiplexer utilising optical Kerr effect in polarisation-maintaining single-mode fibers,” Electron. Lett. 23, 453–454 (1987).
[CrossRef]

Tanbun-Ek, T.

P. A. Andrekson, N. A. Olsson, P. C. Becker, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “Observation of multiple wavelength soliton collisions in optical systems with fiber amplifiers,” Appl. Phys. Lett. 57, 1715–1717 (1990).
[CrossRef]

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, P. C. Becker, K. W. Wecht, “Soliton collision interaction force dependence on wavelength separation in fibre amplifier based systems,” Electron. Lett. 26, 1499–1501 (1990).
[CrossRef]

Villeneuve, A.

A. Villeneuve, J. U. Kang, J. S. Aitchison, G. I. Stegeman, “Unity ratio of cross- to self-phase modulation in bulk AlGaAs and AlGaAs/GaAs MQW waveguides at half the band gap,” Appl. Phys. Lett. 67, 760–762 (1995).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Wabnitz, S.

Wagner, K.

R. McLeod, K. Wagner, S. Blair, “Variational approach to orthogonally-polarized optical soliton interaction with cubic and quintic nonlinearities,” Phys. Scr. 59, 365–373 (1999).
[CrossRef]

S. Blair, K. Wagner, “(2 + 1)-D propagation of spatio-temporal solitary waves including higher-order corrections,” Opt. Quantum Electron. 30, 697–737 (1998).
[CrossRef]

S. Blair, K. Wagner, R. McLeod, “Material figures of merit for spatial soliton interactions in the presence of absorption,” J. Opt. Soc. Am. B 13, 2141–2153 (1996).
[CrossRef]

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

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

K. Wagner, R. McLeod, “Spatial soliton dragging gates and light bullets,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 305–307.

S. Blair, K. Wagner are preparing a manuscript to be called “Cascadable spatial soliton gates.”

Wai, P.

Wai, P. K. A.

Wang, Q.

Wecht, K. W.

P. A. Andrekson, N. A. Olsson, P. C. Becker, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “Observation of multiple wavelength soliton collisions in optical systems with fiber amplifiers,” Appl. Phys. Lett. 57, 1715–1717 (1990).
[CrossRef]

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, P. C. Becker, K. W. Wecht, “Soliton collision interaction force dependence on wavelength separation in fibre amplifier based systems,” Electron. Lett. 26, 1499–1501 (1990).
[CrossRef]

Weiner, A. M.

Weinert, C. M.

E. Jahn, N. Agrawal, W. Pieper, H.-J. Ehrke, D. Franke, W. Fürst, C. M. Weinert, “Monolithically integrated nonlinear Sagnac interferometer and its application as a 20 Gbit/s all-optical demultiplexor,” Electron. Lett. 32, 782–784 (1996).
[CrossRef]

Wen, S.

S. Chi, S. Wen, “Optical soliton near zero-dispersion regime in Raman pump fiber,” Opt. Commun. 69, 334–338 (1989).
[CrossRef]

Wigley, P. G. J.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Wood, D.

N. J. Doran, D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13, 311–313 (1988).
[CrossRef]

Yang, C. C.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Appl. Phys. Lett. (6)

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

A. Villeneuve, J. U. Kang, J. S. Aitchison, G. I. Stegeman, “Unity ratio of cross- to self-phase modulation in bulk AlGaAs and AlGaAs/GaAs MQW waveguides at half the band gap,” Appl. Phys. Lett. 67, 760–762 (1995).
[CrossRef]

P. A. Andrekson, N. A. Olsson, P. C. Becker, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “Observation of multiple wavelength soliton collisions in optical systems with fiber amplifiers,” Appl. Phys. Lett. 57, 1715–1717 (1990).
[CrossRef]

M. A. Duguay, J. W. Hansen, “An ultrafast light gate,” Appl. Phys. Lett. 15, 192–194 (1969).
[CrossRef]

K.-I. Kitayama, Y. Kimura, K. Okamoto, S. Seikai, “Optical sampling using an all-fiber optical Kerr shutter,” Appl. Phys. Lett. 46, 623–625 (1985).
[CrossRef]

D. A. B. Miller, S. D. Smith, A. Johnston, “Optical bistability and signal amplification in a semiconductor crystal: applications of new low-power nonlinear effects in InSb,” Appl. Phys. Lett. 35, 658–660 (1979).
[CrossRef]

Electron. Lett. (4)

E. Jahn, N. Agrawal, W. Pieper, H.-J. Ehrke, D. Franke, W. Fürst, C. M. Weinert, “Monolithically integrated nonlinear Sagnac interferometer and its application as a 20 Gbit/s all-optical demultiplexor,” Electron. Lett. 32, 782–784 (1996).
[CrossRef]

T. Morioka, M. Saruwatari, A. Takada, “Ultrafast optical multi/demultiplexer utilising optical Kerr effect in polarisation-maintaining single-mode fibers,” Electron. Lett. 23, 453–454 (1987).
[CrossRef]

R. J. Manning, G. Sherlock, “Recovery of a π phase shift in ∼12.5 ps in a semiconductor laser amplifier,” Electron. Lett. 31, 307–308 (1995).
[CrossRef]

P. A. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, P. C. Becker, K. W. Wecht, “Soliton collision interaction force dependence on wavelength separation in fibre amplifier based systems,” Electron. Lett. 26, 1499–1501 (1990).
[CrossRef]

Europhys. Lett. (1)

F. Reynaud, A. Barthelemy, “Optically controlled interaction between two fundamental soliton beams,” Europhys. Lett. 12, 401–405 (1990).
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IEEE J. Quantum Electron. (4)

S. R. Skinner, G. R. Allan, D. R. Anderson, A. L. Smirl, “Dark spatial soliton propagation in bulk ZnSe,” IEEE J. Quantum Electron. 27, 2211–2219 (1991).
[CrossRef]

C. R. Menyuk, “Nonlinear pulse propagation in birefringent fibers,” IEEE J. Quantum Electron. QE-23, 174–176 (1987).
[CrossRef]

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
[CrossRef]

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, “An ultrafast all-optical gate,” IEEE J. Quantum Electron. QE-19, 1718–1723 (1983).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. P. Sokoloff, P. R. Prucnal, I. Glesk, M. Kane, “A terahertz optical asymmetric demultiplexor (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

L. Lefort, A. Barthelemy, “All-optical demultiplexing of a signal using collision and waveguiding of spatial solitons,” IEEE Photonics Technol. Lett. 9, 1364–1366 (1997).
[CrossRef]

J. Lightwave Technol. (1)

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 362–367 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (5)

Microwave Opt. Technol. Lett. (1)

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

Opt. Commun. (1)

S. Chi, S. Wen, “Optical soliton near zero-dispersion regime in Raman pump fiber,” Opt. Commun. 69, 334–338 (1989).
[CrossRef]

Opt. Comput. Process. (1)

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

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F. M. Mitschke, L. F. Mollenauer, “Experimental observation of the interaction forces between solitons in optical fibers,” Opt. Lett. 12, 355–357 (1987).
[CrossRef] [PubMed]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, P. W. E. Smith, “Experimental observation of spatial soliton interactions,” Opt. Lett. 16, 15–17 (1991).
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B. A. Malomed, S. Wabnitz, “Soliton annihilation and fusion from resonant inelastic collisions in birefringent optical fibers,” Opt. Lett. 16, 1388–1390 (1991).
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J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (1983).
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S. Chakravarty, M. J. Ablowitz, J. R. Sauer, R. B. Jenkins, “Multisoliton interactions and wavelength-division multiplexing,” Opt. Lett. 20, 136–138 (1995).
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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Y. Kodama, A. Hasegawa, “Effects of initial overlap on the propagation of optical solitons at different wavelengths,” Opt. Lett. 16, 208–210 (1991).
[CrossRef] [PubMed]

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

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

M. N. Islam, “Ultrafast all-optical logic gates based on soliton trapping in fibers,” Opt. Lett. 14, 1257–1259 (1989).
[CrossRef] [PubMed]

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I. Equal propagation amplitudes,” Opt. Lett. 12, 614–616 (1987).
[CrossRef] [PubMed]

N. S. Patel, K. L. Hall, K. A. Rauschenbach, “40-Gbit/s cascadable all-optical logic with an ultrafast nonlinear interferometer,” Opt. Lett. 21, 1466–1468 (1996).
[CrossRef] [PubMed]

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[CrossRef]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, “One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides,” Opt. Lett. 21, 189–191 (1996).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

M. N. Islam, C. D. Poole, J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett. 14, 1011–1013 (1989).
[CrossRef] [PubMed]

Q. Wang, P. K. A. Wai, C.-J. Chen, C. R. Menyuk, “Soliton shadows in birefringent optical fibers,” Opt. Lett. 17, 1265–1267 (1992).
[CrossRef] [PubMed]

Opt. Quantum Electron. (1)

S. Blair, K. Wagner, “(2 + 1)-D propagation of spatio-temporal solitary waves including higher-order corrections,” Opt. Quantum Electron. 30, 697–737 (1998).
[CrossRef]

Phys. Lett. A (1)

Y. Kodama, “On solitary-wave interaction,” Phys. Lett. A 123, 276–282 (1987).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Scr. (1)

R. McLeod, K. Wagner, S. Blair, “Variational approach to orthogonally-polarized optical soliton interaction with cubic and quintic nonlinearities,” Phys. Scr. 59, 365–373 (1999).
[CrossRef]

Sov. Phys. JETP (1)

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

Other (10)

D. A. B. Miller, “Device requirements for digital optical processing,” in Digital Optical Computing, Vol. CR35 of SPIE Critical Reviews (Society of Photo-Optical and Instrumentation Engineers, Bellingham, Wash., 1990), pp. 68–76.

J. Millman, A. Grabel, Microelectronics, 2nd ed. (McGraw-Hill, New York, 1987).

K. Wagner, R. McLeod, “Spatial soliton dragging gates and light bullets,” in Optical Computing, Vol. 7 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 305–307.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

M. Fogiel, ed., Handbook of Mathematical, Scientific, and Engineering Formulas, Tables, Functions, Graphs, Transforms (Research and Education Association, New York, 1986).

The actual numerically obtained coefficient is not exactly π2. This coefficient is used instead for simplicity.

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

S. Blair, K. Wagner are preparing a manuscript to be called “Cascadable spatial soliton gates.”

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

S. Blair, “Optical soliton-based logic gates,” Ph.D. dissertation (University of Colorado, Boulder, Boulder, 1998).

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Figures (19)

Fig. 1
Fig. 1

Temporal soliton trapping–dragging gate. Soliton pump pulses (always present) initially overlap in time with data (or signal) pulses of different wavelength, polarization, or both. Cross-induced chirp causes the pump and the signal to copropagate with the same group velocity. This frequency shift must be resolvable for the trapping gate. The change in frequency is manifest as an arbitrarily large timing shift after propagation through a dispersive fiber, delay line. For the dragging gate, this timing shift must be resolvable. WDM, wavelength-division multiplexer; PBS, polarizing beam splitter.

Fig. 2
Fig. 2

Illustration of the normalized interaction angle κ as given by the spatial frequency separation between two beams divided by the sum of the individual power spectral HWHM. Left, the κ = 1 condition in linear real-space propagation where the beam on the left is propagating down the optical axis and the beam on the right is propagating with normalized angle κ = 1. The heavy lines indicate the spatial FWHM of the respective beams, and the contours are spaced at 3-dB intervals relative to the initial peak intensity. Right, the spatial frequency power spectra of two beams for different values of κ. When κ = 1, the beams are at the angular resolvability condition (i.e., the somewhat arbitrary condition that the spatial frequency spectra overlap at their half-power points). The normalized distance Z 0 = π2 w 0 2/λ.

Fig. 3
Fig. 3

Logic gate geometry based on the light-induced deflection of an optical pump beam away from a spatial aperture placed at the output. At one extreme the pump can propagate nonlinearly as a spatial soliton (left); at the other extreme the pump can propagate linearly and diffract (right). Deflection is induced by the cross-nonlinear interaction with a signal beam that is tilted with respect to the pump. The dashed contours represent the deflected pump.

Fig. 4
Fig. 4

Transfer function for the r = 1 dragging gate of length 10Z 0 with normalized angle κ = 0.8 and separation r s = 0. Absorption is included, with s opt = 0.2627, and the threshold contrast is 131. This gate provides large-signal gain G = 1.4 with NM L = 0.13 and NM H = 0.07. The high noise margin represents 14% deviation about I H , and the filled diamonds denote the operating points and threshold. The transfer function characteristics are defined in Subsection 4.A below.

Fig. 5
Fig. 5

Collision interaction between orthogonally polarized spatial solitons with equal amplitudes r = 1 and initial separation 3.0 FWHM of the signal width, or r s = 5.29. Left, with Δ = 0, for which there is no nonlinear interaction; right, interaction with 2Δ = 2/3. The top interaction has a gate length 5.0Z 0 and achieves a threshold contrast of 1.1, and the bottom fusion interaction has a gate length of 15Z 0 and achieves a threshold contrast of 23. Each soliton propagates at an angle given by the tangent of the initial separation divided by the gate length, and the value of κ = 5.599w 0 sin θ/λ in each plot corresponds to the total angle of propagation θ between the solitons.

Fig. 6
Fig. 6

Collision interaction between orthogonally polarized spatial solitons with unequal amplitudes r = 3 and initial separation 1.5 FWHM(1 + 1/r), or r s = 5.29. The top interaction has a gate length 5.0Z 0 and achieves a threshold contrast of 9.6, and the bottom deflection interaction has a gate length of 15Z 0 and achieves a threshold contrast of >1000. Each soliton propagates at an angle given by the tangent of the initial separation divided by the gate length, and the value of κ = 11.20w 0 sin θ/λ(r + 1) corresponds to the total angle of propagation θ between the solitons. The output aperture width is now given by 3.5w 0/r.

Fig. 7
Fig. 7

Attraction–repulsion interaction between parallel-propagating orthogonally polarized spatial solitons with a gate length of 20Z 0. Top, attraction between equal-amplitude solitons with initial separation of 3.0 FWHM, or r s = 5.29, achieving a threshold contrast of 9.8. Bottom, repulsion between solitons, where the pump power is r = 3 times the signal and the initial separation is 1.0 FWHM(1 + 1/r), or r s = 3.53, achieving a threshold contrast of 69.

Fig. 8
Fig. 8

Dragging interaction between orthogonally polarized spatial solitons of unequal amplitudes (r = 3). The initial total propagation angles between the solitons are given by κ, and the gate length is 5Z 0 in each case. Each soliton acquires an angle shift that is due to mutual trapping, so the final displaced positions depend on gate length. The threshold contrasts of these gates are >1000.

Fig. 9
Fig. 9

Linear (dashed curves) and spatial soliton (solid curves) minimum deflection angle as a function of linear absorption parameter for normalized gate lengths d = 5 (thin curves) and d = 10 (heavy curves). The initial power ratio r = 3 and the material parameters of fused silica at λ f = 1.55 µm are used. The minima of the soliton deflection angle curves occur at s = 0.505 and s = 0.510 for d = 5 and d = 10, respectively. The angle scale is in radians.

Fig. 10
Fig. 10

Plot of the pump throughput factor G given by Eq. (30) versus the linear absorption parameter s parameterized by normalized gate lengths d = 5 and d = 10. The material parameters for fused silica are used, and the optimum gain upper bound occurs in both cases at s opt = 0.2627, as given by Eq. (32). For these parameters, G(0.2627, 5) = 10.5 and G(0.2627, 10) = 7.42.

Fig. 11
Fig. 11

Soliton minimum deflection angle for the optimized value s opt = 0.2627 versus initial power ratio r parameterized by normalized gate lengths d = 5 and d = 10. The material parameters for fused silica are used. The angle scale is in radians.

Fig. 12
Fig. 12

Threshold contrast contours for the spatial collision interaction for r = 3, with the material parameters of fused silica with s opt = 0.2627. The contours are spaced in decades, and the heavy contours represent the minimum desired contrast of 101 and a contrast of 104. Dashed line, the value of κ that serves as a good operating point for all normalized gate lengths. In the case of the collision interaction, this value is 0.33.

Fig. 13
Fig. 13

Threshold contrast contours for the collision interaction, with the parameters of fused silica and the value s opt = 0.2627 for all normalized gate lengths. The contour levels are spaced in decades, and the heavy curves show τ = 101 and τ = 104. The normalized interaction angle is fixed at κ = 0.33. Absorption decreases the ratio of the undeflected pump at the output to the signal at the input. This final ratio G(r, d) is indicated by the dashed curves, which do not include the 5.8% power loss that is due to clipping by the output aperture. For small values of r, two-photon absorption is weak, and the dashed contours are nearly horizontal.

Fig. 14
Fig. 14

Threshold contrast contours for the spatial dragging interaction for r = 3, with the parameters of fused silica with s opt = 0.2627. The contours are spaced in decades, and the heavy contours represent the minimum desired contrast of 101 and a contrast of 104. Dashed line, the value of κ that serves as a good operating point for all normalized gate lengths. In the case of the dragging interaction, this value is 0.8.

Fig. 15
Fig. 15

Threshold contrast contours for the dragging interaction, with the parameters of fused silica and the value s opt = 0.2627 for all gate lengths. The contour levels are spaced in decades, and the heavy contours show τ = 101 and τ = 104. The normalized interaction angle is fixed at κ = 0.8. Absorption decreases the ratio of the undeflected pump at the output to the signal at the input. This final ratio G(s, d) is indicated by the dashed curves, which do not include the 5.8% power loss that is due to clipping by the output aperture.

Fig. 16
Fig. 16

Spatial soliton collision (top) and dragging (bottom) logic gates in the presence of linear absorption and TPA. Here the gate lengths are 10Z 0 with s opt = 0.2627 and initial ratio r = 3. The normalized initial separations are r s = 5 for collision and r s = 0 for dragging, and the normalized interaction angles are κ = 0.33 and κ = 0.8, respectively. The pump soliton is represented by the heavier curves, and the intensity contours are spaced in 3-dB intervals. The threshold contrasts of these gate are 3.1 × 104 and 7.4 × 103. Note that the dominant diffracting wave in the dragging interaction collides with and reflects off the absorbing boundary conditions of the simulation, but this does not affect gate operation.

Fig. 17
Fig. 17

Generic inverting logic gate transfer function. The threshold contrast τ is calculated at the unity input level (normalized by the fundamental signal soliton power), and 1/τ gives the corresponding output level. Thin solid curve, straight-line transfer function; heavy solid curve, a more-realistic transfer function, which necessarily has greater small-signal gain. These transfer functions must pass through points (0, P OH), (P IL, P OH), (1, 1/τ), and (P IH, P OL). Dashed curves represent the inverted transfer functions and are used to locate the stable operating points.

Fig. 18
Fig. 18

Transfer functions for the r = 3 collision gate of lengths 5Z 0 (top) and 10Z 0 (bottom) with normalized angle κ = 0.33 and separation r s = 5. Absorption is included using s opt = 0.2627 for each gate length. The threshold contrasts are τ = 1.2 for the 5Z 0 gate length and τ = 4.7 × 104 for the 10Z 0 gate length. These gates provide large-signal gains of G = 1.6 with NM L = 0.60 and NM H = 0.11 (top) and G = 2.8 with NM L = 0.18 and NM H = 0.07 (bottom). The high noise margins represent 8.2% and 9.7% deviation about I H , respectively, and the filled diamonds denote the operating points and threshold.

Fig. 19
Fig. 19

Transfer functions for the r = 3 dragging gate of lengths 5Z 0 (top) and 10Z 0 (bottom) with normalized angle κ = 0.8 and separation r s = 0. Absorption is included using s opt = 0.2627 for each gate length. The threshold contrasts are τ = 1.8 × 103 for the 5Z 0 gate length and τ = 7.4 × 103 for the 10Z 0 gate length. The gates provide large-signal gains of G = 3.5 with NM L = 0.05 and NM H = 0.07 (top) and G = 6.0 with NM L = 0.02 and NM H = 0.05 (bottom). The high noise margins represent 12% and 15% deviation about I H , respectively, and the filled diamonds denote the operating points and threshold.

Equations (47)

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δωk0L>τFWHM,
2ik0Az+2Ax2+2k02n2n0 |A|2 A=0.
Ax, z=1k0w0n0n2sechxw0expiz/2k0w02,
I0=n0k02w02n2I,
P0=2n0Dk02w0n2I,
sechxw1  πw12sechπw1kx2.
πw1Δkx|w12=1.7627  Δkx|w1=1.1222w1.
sechxw2expiδkxx  πw22sechπw22kx-δkx,
κ2δkxΔkx|w1+Δkx|w2=k0w1w2 sin θ0.5611w1+w2=11.20w1w2 sin θλw1+w2.
δkx=0.5611w1+w2κw1w2.
2ik0Axz+2Axx2+2k02n2n0|Ax|2+2Δ|Ay|2Ax=0,
2ik0Ayz+2Ayx2+2k02n2n0|Ay|2+2Δ|Ax|2Ay=0,
Axx, z=0=rk0w0n0n2sechx-ζ/2w0/rexp-iδkxx/2,
Ayx, z=0=1k0w0n0n2sechx+ζ/2w0expiδkxx/2,
wp2d=4K3α0k0e2s-1+w0/r2e2s,
Pp2d=r2P02k03n2I2Kr2P02e2s-1/3α0n02+e2s,
α0=-4Kr23k0w02.
wpd=w0/res,
Ppd=rP0e-s,
tan θmin=1.7627wpddZ0=1.7627πrα0λsd es.
w0=αλ,  wp=αλ/r,
α=sπ2α0dλ1/2
rmaxd=sπ2α0λ1/2,
tan θmin=1.7627α0λs es.
wpd=w0r1+4πdKr2/31/2,
Ppd=rP01+4πdKr2/31/2,
wpd=w0/TPA,
Ppd=TPAP0,
TPA=3/4πdK1/2,
tan θmin=1.7627wpddZ0=1.7627w0TPAdZ0.
wpd=λr2α2e2s-1+2sw0TPA/λ2e2s1/22srTPA,
Ppd=2srTPAP0r2e2s-1+2sTPA2e2s1/2.
sin θdiff=1.7627λrπ2w0,
e-2sopt1-2sopt=3πα0λ2K+1,
2ik0Axz+2Axx2+2k02n2n01+iK|Ax|2+2Δ|Ay|2Ax+ik0α0Ax=0,
2ik0Ayz+2Ayx2+2k02n2n01+iK|Ay|2+2Δ|Ax|2Ay+ik0α0Ay=0,
w0=soptλπ2α0d1/2=αλ
Axx, Δz=expiΔzQˆL/2expiΔzQˆIH×expiΔzQˆL/2Axx, 0,
QˆL=12k02x2+i α02k0k0+iα0+2x21/2-k0,QˆL=kz=k0k0+iα0-kx21/2-k0,
QˆIH=kfn21+iK|Ax|2+2Δ|Ay|2.
A˜xkx, Δz/2=expiQ˜LΔz/2A˜xkx, 0
m=POH-POLPIL-PIH,
mPOH-1/τ0-11τ-Gd.
NMLPIL-POL
NMHPOH-PIH,
NML=PIL-OL/G=PIL-IL,
NMH=OH/G-PIH=IH-PIH.

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