Optimizing Amplifier Placements in a Multiwavelength Optical LAN/MAN: The Unequally Powered Wavelengths Case

Optical networks based on passive-star couplers and employing WDM have been proposed for deployment in local and metropolitan areas. These networks suffer from splitting, coupling, and attenuation losses. Since there is an upper bound on transmitter power and a lower bound on receiver sensitivity, optical amplifiers are usually required to compensate for the power losses mentioned above. Due to the high cost of amplifiers, it is desirable to minimize their total number in the network. However, an optical amplifier has constraints on the maximum gain and the maximum output power it can supply; thus, optical amplifier placement becomes a challenging problem. In fact, the general problem of minimizing the total amplifier count is a mixed-integer nonlinear problem. Previous studies have attacked the amplifier-placement problem by adding the “artificial” constraint that all wavelengths, which are present at a particular point in a fiber, be at the same power level. This constraint simplifies the problem into a solvable mixed integer linear program. Unfortunately, this artificial constraint can miss feasible solutions that have a lower amplifier count but do not have the equally powered wavelengths constraint. In this paper, we present a method to solve the minimum amplifier- placement problem, while avoiding the equally powered wavelength constraint. We demonstrate that, by allowing signals to operate at different power levels, our method can reduce the number of amplifiers required.

Excitation and damping of a self-modulated laser wakefield

Spatially, temporally, and angularly resolved collinear collective Thomson scattering was used to diagnose the excitation and damping of a relativistic-phase-velocity self-modulated laser wakefield. The excitation of the electron plasma wave was observed to be driven by Raman-type instabilities. The damping is believed to originate from both electron beam loading and modulational instability. The collective Thomson scattering of a probe pulse from the ion acoustic waves, resulting from modulational instability, allows us to measure the temporal evolution of the plasma temperature. The latter was found to be consistent with the damping of the electron plasma wave.