Abstract

The three-terminal spatial-soliton angular-deflection geometry provides the characteristics of an inverting logic gate with gain, and phase-insensitive implementations can be realized by a number of specific nonlinear interactions between orthogonally polarized waves. In particular, numerical simulations of spatial-soliton dragging and collision are used to calculate the transfer functions of inverter and multiple configurations of two-input nor gates and to address their cascadability. These transfer functions converge in cascaded operation and suggest that fan-out greater than 2 with a large noise margin is attainable in a system with standardized signal levels. These results are obtained with the material properties of fused silica and are representative of low-loss Kerr media.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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1999 (3)

1997 (2)

1996 (4)

1995 (3)

D. A. Pattison, W. Forysiak, P. N. Kean, I. Bennion, N. J. Doran, “Soliton switching using cascaded nonlinear-optical loop mirrors,” Opt. Lett. 20, 19–21 (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 bandgap,” Appl. Phys. Lett. 67, 760–762 (1995).
[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]

1994 (2)

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, “Subpicosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

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

1993 (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]

1992 (1)

M. Eiselt, W. Pieper, H. G. Weber, “slalom as a high speed multiplexor/demultiplexor,” Electron. Lett. 28, 1505–1507 (1992).
[CrossRef]

1990 (1)

1989 (1)

1988 (2)

1985 (3)

S. D. Smith, I. Janossy, H. A. MacKenzie, J. G. H. Mathew, J. J. E. Reid, M. R. Taghizadeh, F. A. P. Tooley, A. C. Walker, “Nonlinear optical circuit elements as logic gates for optical computers: the first digital optical circuits,” Opt. Eng. 24, 569–574 (1985).

R. W. Keyes, “What makes a good computer device?” Science 230, 138–144 (1985).
[CrossRef] [PubMed]

R. W. Keyes, “Optical logic—in the light of computer technology,” Opt. Acta 32, 525–535 (1985).
[CrossRef]

1982 (1)

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

1976 (1)

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
[CrossRef]

Ahn, K. H.

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 bandgap,” Appl. Phys. Lett. 67, 760–762 (1995).
[CrossRef]

Andrejco, M. J.

Barnett, B. C.

Bennion, I.

Bertolotti, M.

Blair, S.

Blow, K. J.

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).

R. J. Manning, A. D. Ellis, A. J. Poustie, K. J. Blow, “Semiconductor laser amplifiers for ultrafast all-optical signal processing,” J. Opt. Soc. Am. B 14, 3204–3216 (1997).
[CrossRef]

Caglioti, E.

Cao, X. D.

Darwish, A. M.

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, “Subpicosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

DeLong, K. W.

Doran, N. J.

Eiselt, M.

M. Eiselt, W. Pieper, H. G. Weber, “slalom as a high speed multiplexor/demultiplexor,” Electron. Lett. 28, 1505–1507 (1992).
[CrossRef]

Ellis, A. D.

Fazio, E.

Forysiak, W.

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
[CrossRef]

Glesk, I.

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]

Hall, K. L.

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]

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, “Subpicosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

Ippen, E. P.

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, “Subpicosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

Islam, M. N.

Janossy, I.

S. D. Smith, I. Janossy, H. A. MacKenzie, J. G. H. Mathew, J. J. E. Reid, M. R. Taghizadeh, F. A. P. Tooley, A. C. Walker, “Nonlinear optical circuit elements as logic gates for optical computers: the first digital optical circuits,” Opt. Eng. 24, 569–574 (1985).

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
[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 bandgap,” Appl. Phys. Lett. 67, 760–762 (1995).
[CrossRef]

Kean, P. N.

Kelly, A. E.

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).

Keyes, R. W.

R. W. Keyes, “Optical logic—in the light of computer technology,” Opt. Acta 32, 525–535 (1985).
[CrossRef]

R. W. Keyes, “What makes a good computer device?” Science 230, 138–144 (1985).
[CrossRef] [PubMed]

Lenz, G.

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, “Subpicosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

Liang, Y.

MacKenzie, H. A.

S. D. Smith, I. Janossy, H. A. MacKenzie, J. G. H. Mathew, J. J. E. Reid, M. R. Taghizadeh, F. A. P. Tooley, A. C. Walker, “Nonlinear optical circuit elements as logic gates for optical computers: the first digital optical circuits,” Opt. Eng. 24, 569–574 (1985).

Manning, R. J.

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).

R. J. Manning, A. D. Ellis, A. J. Poustie, K. J. Blow, “Semiconductor laser amplifiers for ultrafast all-optical signal processing,” J. Opt. Soc. Am. B 14, 3204–3216 (1997).
[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]

Mathew, J. G. H.

S. D. Smith, I. Janossy, H. A. MacKenzie, J. G. H. Mathew, J. J. E. Reid, M. R. Taghizadeh, F. A. P. Tooley, A. C. Walker, “Nonlinear optical circuit elements as logic gates for optical computers: the first digital optical circuits,” Opt. Eng. 24, 569–574 (1985).

McCall, S. L.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
[CrossRef]

McLeod, R.

Miller, D. A. B.

D. A. B. Miller, “Device requirements for digital optical processing,” Digital Optical Computing, SPIE Crit. Rev.CR35, 68–76 (1990).

Mizrahi, V.

Patel, N. S.

Pattison, D. A.

Pieper, W.

M. Eiselt, W. Pieper, H. G. Weber, “slalom as a high speed multiplexor/demultiplexor,” Electron. Lett. 28, 1505–1507 (1992).
[CrossRef]

Poustie, A. J.

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).

R. J. Manning, A. D. Ellis, A. J. Poustie, K. J. Blow, “Semiconductor laser amplifiers for ultrafast all-optical signal processing,” J. Opt. Soc. Am. B 14, 3204–3216 (1997).
[CrossRef]

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]

Rauschenbach, K. A.

Reid, J. J. E.

S. D. Smith, I. Janossy, H. A. MacKenzie, J. G. H. Mathew, J. J. E. Reid, M. R. Taghizadeh, F. A. P. Tooley, A. C. Walker, “Nonlinear optical circuit elements as logic gates for optical computers: the first digital optical circuits,” Opt. Eng. 24, 569–574 (1985).

Saifi, M. A.

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]

Smith, S. D.

S. D. Smith, I. Janossy, H. A. MacKenzie, J. G. H. Mathew, J. J. E. Reid, M. R. Taghizadeh, F. A. P. Tooley, A. C. Walker, “Nonlinear optical circuit elements as logic gates for optical computers: the first digital optical circuits,” Opt. Eng. 24, 569–574 (1985).

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.

Taghizadeh, M. R.

S. D. Smith, I. Janossy, H. A. MacKenzie, J. G. H. Mathew, J. J. E. Reid, M. R. Taghizadeh, F. A. P. Tooley, A. C. Walker, “Nonlinear optical circuit elements as logic gates for optical computers: the first digital optical circuits,” Opt. Eng. 24, 569–574 (1985).

Tooley, F. A. P.

S. D. Smith, I. Janossy, H. A. MacKenzie, J. G. H. Mathew, J. J. E. Reid, M. R. Taghizadeh, F. A. P. Tooley, A. C. Walker, “Nonlinear optical circuit elements as logic gates for optical computers: the first digital optical circuits,” Opt. Eng. 24, 569–574 (1985).

Trillo, S.

Vaziri, M.

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
[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 bandgap,” Appl. Phys. Lett. 67, 760–762 (1995).
[CrossRef]

Wabnitz, S.

Wagner, K.

Walker, A. C.

S. D. Smith, I. Janossy, H. A. MacKenzie, J. G. H. Mathew, J. J. E. Reid, M. R. Taghizadeh, F. A. P. Tooley, A. C. Walker, “Nonlinear optical circuit elements as logic gates for optical computers: the first digital optical circuits,” Opt. Eng. 24, 569–574 (1985).

Weber, H. G.

M. Eiselt, W. Pieper, H. G. Weber, “slalom as a high speed multiplexor/demultiplexor,” Electron. Lett. 28, 1505–1507 (1992).
[CrossRef]

Williams, G. R.

Willner, A. E.

A. E. Willner “Mining the optical bandwidth for a terabit per second,” IEEE Spectrum 34, 32–41 (1997).
[CrossRef]

Wood, D.

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

Zitelli, M.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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 bandgap,” Appl. Phys. Lett. 67, 760–762 (1995).
[CrossRef]

Electron. Lett. (2)

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]

M. Eiselt, W. Pieper, H. G. Weber, “slalom as a high speed multiplexor/demultiplexor,” Electron. Lett. 28, 1505–1507 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
[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 Spectrum (1)

A. E. Willner “Mining the optical bandwidth for a terabit per second,” IEEE Spectrum 34, 32–41 (1997).
[CrossRef]

J. Mod. Opt. (1)

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).

J. Opt. Soc. Am. B (4)

Opt. Acta (1)

R. W. Keyes, “Optical logic—in the light of computer technology,” Opt. Acta 32, 525–535 (1985).
[CrossRef]

Opt. Commun. (1)

K. L. Hall, G. Lenz, A. M. Darwish, E. P. Ippen, “Subpicosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun. 111, 589–612 (1994).
[CrossRef]

Opt. Eng. (1)

S. D. Smith, I. Janossy, H. A. MacKenzie, J. G. H. Mathew, J. J. E. Reid, M. R. Taghizadeh, F. A. P. Tooley, A. C. Walker, “Nonlinear optical circuit elements as logic gates for optical computers: the first digital optical circuits,” Opt. Eng. 24, 569–574 (1985).

Opt. Lett. (8)

Phys. Rev. Lett. (1)

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry–Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
[CrossRef]

Science (1)

R. W. Keyes, “What makes a good computer device?” Science 230, 138–144 (1985).
[CrossRef] [PubMed]

Other (1)

D. A. B. Miller, “Device requirements for digital optical processing,” Digital Optical Computing, SPIE Crit. Rev.CR35, 68–76 (1990).

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Figures (15)

Fig. 1
Fig. 1

Spatial-soliton dragging (top) and collision (bottom) angular-deflection interactions. An undeflected pump soliton passes through an aperture at the output of the gate to form the high-output state. A tilted signal wave nonlinearly induces an angle change in a strong pump soliton that results in deflection outside of a spatial aperture and a low output.

Fig. 2
Fig. 2

Logic inverting transfer function. The intersections of the normal and inverted curves locate the stable operating points, as shown for G = 1, which must lie in a region where the slope is less than unity for stable operation in the presence of noise.

Fig. 3
Fig. 3

Simulations of spatial-soliton dragging (top) and collision (bottom) interactions showing pump propagation through a spatial aperture without the signal (left) and angular deflection of the pump in the presence of the signal (right). For both simulations the gate length L = 5Z 0 and the initial pump-to-signal power ratio r = 3. The normalized interaction angle κ = 0.8 for dragging and κ = 0.35 for collision. The signal and pump solitons are separated by ρ = 5 [defined in Eq. (5)] in the collision interaction. Fused silica material parameters are used.

Fig. 4
Fig. 4

Cascaded spatial dragging inverter gates. A free-space region between nonlinear sections allows a fresh pump and signal to be brought into coincidence through a polarizing beam splitter (PBS). The pump output of the first gate is split to serve as the signal input to multiple subsequent gates.

Fig. 5
Fig. 5

Calculated transfer functions for cascaded inverter gates that use a fan-out of 3, gate length 5Z 0, and normalized interaction angle κ = 0.8. The curves for the second and the third gates converge, providing a large-signal gain G = 3 (consistent with the fan-out) with noise margins NM L = 0.20 and NM H = 0.07. Owing to absorption, the maximum output level is reduced from 3 (in normalized units) to 2.1. The high-input switching level I H = 0.71. The filled diamonds denote operating points and threshold. Absorption is included by using the parameters of fused silica.

Fig. 6
Fig. 6

Transfer functions for the cascaded r = 5 dragging gate of length 5Z 0 with normalized angle κ = 0.8. With a fan-out of 6 the operating points lie well within the saturated levels, and noise margins of NM L = 0.08 and NM H = 0.09 are obtained, where the high noise margin represents a 15% deviation about I H = 0.58.

Fig. 7
Fig. 7

Transfer functions for the cascaded r = 3 dragging gate of length 10Z 0 with normalized angle κ = 0.8. With a fan-out of 5 the operating points lie well within the saturated levels, and noise margins of NM L = 0.07 and NM H = 0.05 are obtained, where the high noise margin represents 12% deviation about I H = 0.42.

Fig. 8
Fig. 8

Transfer functions for the cascaded r = 3 collision gate of length 5Z 0 with normalized angle κ = 0.35. With a fan-out of 1.1 the operating points lie within the saturated levels, and noise margins of NM L = 1.1 and NM H = 0.22 are obtained, where the high noise margin represents 11% deviation about I H = 2.0.

Fig. 9
Fig. 9

Transfer functions for the cascaded r = 5 collision gate of length 5Z 0 with normalized angle κ = 0.35. With a fan-out of 2.1 the operating points lie within the saturated levels, and noise margins of NM L = 0.50 and NM H = 0.18 are obtained, where the high noise margin represents 11% deviation about I H = 1.7.

Fig. 10
Fig. 10

Transfer functions for the cascaded r = 3 collision gate of length 10Z 0 with normalized angle κ = 0.35. With a fan-out of 1.6 the operating points lie well within the saturated levels, and noise margins of NM L = 0.49 and NM H = 0.18 are obtained where the high noise margin represents 14% deviation about I H = 1.3.

Fig. 11
Fig. 11

A 2-nor gate when two spatial dragging inversion stages of different lengths are used. Each stage shares a common pump, and the total material length of the gate is the same as the inverter. Because the second stage is shorter than an inverter, the switching level for this input is greater, thus reducing fan-out into the gate.

Fig. 12
Fig. 12

Calculated transfer functions for cascaded inverters and two-stage dragging 2-nor gates. The second inputs to the 2-nor gates are driven with a fan-out of 4.5 (top and bottom) and the inverter with a fan-out of 6 (top). The transfer functions of the 2-nor gates (bottom) converge, with NM L = 0.15, NM H = 0.08, and I H = 0.77.

Fig. 13
Fig. 13

Single-stage 2-nor gate when the spatial dragging interaction is used. The signals are angularly resolvable at the point of overlap with the orthogonally polarized pump at the gate input to reduce linear interference. The length of the gate is the same as an inverter.

Fig. 14
Fig. 14

Transfer functions for the single-stage dragging 2-nor gate with r = 5 and d = 5. Top (bottom), a dragging gate drives the second input to the single-stage 2-nor gate with a fan-out of 6, the output of which drives the first (second) input to another single-stage 2-nor gate with a fan-out of 6.0. Noise margins of 18% of about I H = 0.58 are obtained.

Fig. 15
Fig. 15

Transfer functions for mixed dragging and collision gates with r = 5 and d = 5. Top (bottom), a dragging gate drives the first (second) input to a single-stage 2-nor gate with a fan-out of 6 (2.1), the output of which drives the second (first) input to another single-stage 2-nor gate with a fan-out of 2.1 (6). The transfer characteristics of the single-stage 2-nor when the first (second) input are used are nearly identical with that of a single dragging (collision) inverter.

Equations (11)

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2ik0Axz+2Axx2+2k02n2n01+iK|Ax|2+2Δ|Ay|2Ax+ik0α0Ax=0,
2ik0Ayz+2Ayx2+2k02n2n01+iK|Ay|2+2Δ|Ax|2Ay+ik0α0Ay=0,
Axx, z=rk0w0n0n21/2sechrxw0expir2z2k0w02,
wp2d=4K3α0k0exp2α0dZ0-1+w0/r2 exp2α0dZ0,
PpdP0=0.942rk03n2I2Kr2P02exp2s-1/3α0n02+exp2s1/2.
rs=ρw021+1/r.
1x6+y4.5 or 6x+43 y,
κ21=r+1κ2p-κ1p2=2,
Φ=k0n2I0L Izdz,
Φ=L2k0w02
Φ=π4Z00Lexp-2αzdz=πd41-exp-2s2s,

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