Remarks on dispersionless KP,KdV, and 2D gravity

Summary We use the SDiff(2) framework of Takasaki and Takebe and the (L, M) program (L is the Lax operator andMω=ω_λ) to show that =semiclassical limit ofM is , where ( ) are action angle variables in the Gibbons-Kodama theory of Hamilton-Jacobi type for dispersionless KP. We also show is the semiclassical limit ofWxW ⁻¹ (W is the gauge operator), whereG=WxW ⁻¹ is a quantity studied by the author in an earlier paper in connection with symmetries. We give then a semiclassical version of the Jevicki-Yoneya action principle for 2D gravity, where again arises in calculations, and this yields directly the Landau-Ginsburg equation that corresponds to the semiclassical limit of an integrated string equation. For KdV we also show how inverse scattering data are connected to Hamiltonians for dispersionless KdV. We also discuss Hirota bilinear formulas relative to the dispersionless hierarchies and establish various limiting formulas.     

Detailed large-signal dynamic modelling of DFB laser structures and comparison with experiment

This paper describes the first general large-signal dynamic multiple-mode laser model that incorporates all the main mechanisms known to influence the dynamic behaviour of DFB laser structures with the exception of thermal effects: longitudinal mode spatial hole burning, carrier transport effects, nonlinear gain, and laser and submount parasitics. The time evolution of the output power and wavelength of all modes is predicted, and full spectra can be plotted as a function of time. The model has been extended to include an approximation to the effects of propagation down dispersive fibre, thereby allowing the simulation of filtered received eye diagrams. Detailed comparison of the model with the experimental performance of 2×/8 DFB lasers has shown good agreement, allowing the performance to be optimized, particularly with respect to longitudinal hole burning and carrier transport. The model is also applied to gain-switched operation of 2×/8 DFB structures, fast pulsing of three-section /4 DFB lasers, and the dynamic behaviour of complex coupling coefficient DFB laser structures.     

An exact numerical analysis of coupled planar electron waveguides with asymmetric rectangular potential profiles

An exact numerical analysis is given of electron waves in a pair of coupled semiconductor heterojunction electron waveguides modelled by a rectangular potential distribution. The waveguide lengths required for electron current transfer between the guides agree asymptotically with estimates from Yariv's coupled mode theory and are usefully more accurate. Moreover the electron wave coupling due to an ideal launcher can be worked out, leading to estimates of the off/on current ratio occurring in the waveguides when regarded as an ultrafast switch. For a Poisson probability distribution of the number of electrons N making up a bit-pulse, we have calculated the minimum average N, dependent upon , which would be required to keep the switching bit-error rate below prescribed limits. Pulse rise times and switching delays are derived from the explicit forms for the longitudinal electron wave group velocity. Combining the bit-error and switching-time calculations leads to estimates of the waveguide current densities which would be required in practice. Some normalized sets of curves relating to our analysis are given and used to predict the performance of particular examples of recently proposed AlGaAs/GaAs heterojunction electron waveguide switch/couplers.