CONCLUSIONS

We have discussed the possibility of using the waveguide Mach--Zehnder interferometer to generate a variety of dark solitons under constant background. Under optimal operation, 30 less input power and driving voltage are required than for complete modulation. The generated solitons can have good pulse quality and stimulated Raman scattering process can be utilized to compensate for fiber loss and even to amplify and compress the dark solitons. ...

The authors thank the reviewers for their constructive comments. This research was supported by National Science Foundation grant ECS-91960-64.

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<#2029#>Figure<#2029#>: <#2030#>The dark solitons generated by the waveguide Mach-Zehnder interferometer. The amplitude of the input cw light is chosen to be #math237#a = π/2 for (a)-(c). The parameter δ is (a) 0.8, (b) 0.5, and (c) 0.2. Part (d) is the case of optimal operation when a = 1.33, and #math238#δ = 0.7. In all cases, the output pulse shapes are plotted as solid curves while the dashed curves are input pulse shapes. The pulses shown here are at a propagation distance of z = 4.<#2030#>
#figure531#
<#2042#>Figure<#2042#>: <#2043#> Dark solitons under constant gain. Pulse shapes (solid) when Γ=0.05 (a) and 1(b), after certain propagation distance, Γz=1.6, as compared to input pulse shapes (dashed). (c): The pulse duration, relative to its input, as a function of Γz at various Γ. The solid curve is the adiabatic approximation obtained by perturbation method. Three values of Γ are used: Γ = 0.05 (dotted); 0.2 (dash-dotted); and 1 (dashed). Negative Γz depicts the case of loss.<#2043#>
#figure534#
<#2059#>Figure<#2059#>: <#2060#> The pulse shapes of amplified dark solitons. (a) #math241#δ = 0.5, #math242#β = 2ln1.05, #math243#ΓpL = 2, after 8 amplifying cycles (solid); (b) #math244#δ = 0.5, #math245#β = 2ln1.02, #math246#ΓpL = 2, after 16 amplifying cycles (solid); (c) #math247#δ = 0.5, #math248#β = 2ln1.02, #math249#ΓpL = 0.5, after 16 amplifying cycles (solid); (d) The input pulse is the same as in Fig. 1(c), #math250#β = 2ln1.05, after 8 amplification periods (solid). The input pulse shapes are plotted as dashed curves.<#2060#>
#figure537#
<#2082#>Figure<#2082#>: <#2083#> (a) The shape of a fundamental dark soliton after a propagation distance of 40 (solid). The normalized time delay #math261#τd = 0.01. The dashed curve is the input pulse shape. (b) The trace of the soliton (solid) as a function of propagation distance for the situation described by (a). The dotted curve represents the case for a fundamental bright soliton under similar conditions.<#2083#>
#figure540#

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Table: Amplitudes of Secondary Even Dark Pulses
;SPMnbsp; ;SPMnbsp; Input Pulse Shape ;SPMnbsp; ;SPMnbsp; ;SPMnbsp;
ΔnValues #math263#κ0|tanht| #math264#κ0[1 - exp(- t2/τg2)]1/2 #math265#κ0[1 - sech(t/τs)] Avg. Range
Δ1 0.34 0.30 0.21 0.28 ±25%
Δ2 1.56 1.41 1.26 1.41 ±11%
Δ3 2.47 2.26 2.28 2.34 ±6%
Δ4 3.52 3.25 3.31 3.36 ±6%
Δ5 4.45 4.26 4.42 4.38 ±6%
Δ6 5.52 5.35 5.50 5.50 ±5%

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<#572#>Designing digital optical computing systems: power distribution and cross talk<#572#> <#573#>Jonathan P. Pratt and Vincent P. Heuring<#573#>

<#574#>When this work was performed, both the authors were with the Boulder Optoelectronic Computing Systems Center and Department of Electrical and Computer Engineering, University of Colorado, Campus Box 425, Boulder, Colorado 80309-0425. They are now with the Department of Radiology, University of Colorado Health Sciences Center, Box A034, 4200 East Ninth Avenue, Denver, Colorado 80262. <#574#>

<#2156#>Abstract<#2156#>:

Complex optical computer designs must implicitly or explicitly allow for power budgeting, to compensate for cross talk and loss in both devices and interconnections. We develop algorithms for calculating the system cross talk and power loss in optical systems, using a graph-theoretic model. Devices are modeled as directed graphs with nodes representing inputs and outputs, and edges are weighted with the power relationships between nodes. Systems are modeled by interconnecting the individual device graphs in a manner that reflects the connectivity of the system. A system's power budget is efficiently computed by a depth-first search of its graph. The algorithms have been incorporated into an optical computer-aided design system that is now being used to design a bit-serial optical computer containing hundreds of components.

Key words: Optical computing, optical systems, optical communications, power loss, cross talk, graphs.

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