Nonlinear effects in random lasers

Abstract

Recent numerical and theoretical studies have demonstrated that the modes at threshold of a random laser are in direct correspondence with the resonances of the same system without gain, a feature which is well known in a conventional laser but which was not known until recently for a random laser. This paper presents numerical results, which extend such studies to the multimode regime that takes place when the pumping rate is progressively increased above threshold. Behavior that is already known in standard lasers, such as mode competition and nonlinear wave-mixing, are shown to also take place in random lasers thus reinforcing their recent modal description. However, due to the complexity of the laser modes and to the openness of such lasers, which requires large external pumping to compensate for strong loss, one observes that these effects are more pronounced than in a conventional laser.

A random laser as a dynamical network

“…In contrast, the 10 ns pump ramp of our experiment can be regarded as quasi-stationary excitation. The resultant data represents the first experimental evidence of co-lasing of multiple modes in this regime, as theoretically derived for static pump levels [17,18,20].…”

“…The design of the sample used in the experiment (top panel in figure 1) is similar to that sketched in figure 1 of reference [14]. It is grown on a-plane sapphire (11)(12)(13)(14)(15)(16)(17)(18)(19)(20) is grown on top. This layer structure produces a planar waveguide structure, wave propagation can be regarded thus as two-dimensional.…”

HIGH ORDER SPLITTING METHODS FOR FORWARD PDEs AND PIDEs

“…Recently, this problem has come under attention for local stochastic volatility (LSV) models. For instance, Andreasen & Huge (2011) present a numerical solution that achieves full consistency between calibration, option pricing using finite-difference solutions and Monte Carlo simulation. The method is based on a fully implicit finite-difference scheme of first-order in time, which was motivated by the fact that Monte Carlo simulation, even with the use of the Milstein scheme, is also of first-order in time, see Glasserman (2003) and references therein.…”

“…As mentioned in Andreasen & Huge (2011), if special care is not taken, then the different numerical schemes will generally be fully consistent with each other only in the limit when the number of Fourier steps for FFT, the number of time and spatial steps in the finitedifference grid, and the number of time steps in the Monte Carlo all tend to infinity and the numerical schemes converge to the continuous time and space solution. Furthermore, setting appropriate boundary conditions to guarantee this consistency could be a nontrivial task.…”

“…The method was then alluded to in Lipton (2001Lipton ( , 2002. Later, the same idea was rediscovered in Andreasen & Huge (2011) and used to construct a consistent implicit finite-difference scheme that is first-order in time. See Andersen & Andreasen (2000) for the forward and backward equations.…”