Cellular automaton model for the simulation of laser dynamics

Abstract

The classical modeling approach for laser study relies on the differential equations. In this paper, a cellular automaton model is proposed as an alternative for the simulation of population dynamics. Even though the model is simplified it captures the essence of laser phenomenology: (i) there is a threshold pumping rate that depends inversely on the decaying lifetime of the atoms and the photons; and (ii) depending on these lifetimes and on the pumping rate, a constant or an oscillatory behavior can be observed. More complex behaviors such as spiking and pattern formation can also be studied with the cellular automaton model.

Parallel Implementation of a Cellular Automaton Model for the Simulation of Laser Dynamics

“…The results of the simulations carried out with a sequential implementation of the 2D CA laser model (previously presented in references [9,10]) are reproduced with the present parallel implementation. An example is shown in Fig.…”

“…The ratio of noise photons (introduced in every time step) to total number of cells in the system has been maintained constant (0.03% of the cells) for the experiments with different system sizes. The typical laser behaviour known as relaxation oscillations or laser spiking (correlated large amplitude damping oscillations) [9] is reproduced. The differences between both results are that the populations are scaled and that the shape of the oscillations is smoother in (b) due to having used a much larger system size, thus reproducing more accurately the relaxation oscillations obtained in real lasers or from the integration of macroscopic differential equations.…”

“…This communication is carried out directly between the slave programs. In addition, in the last part of each time iteration, each slave program computes the total number of electrons a i (t) and laser photons c i (t) in its CA partition and sends this information to the master, which can record it and make some calculations with it, such as computing the Shannon's entropy as described in [9].…”

“…A laser system is modeled by a cellular automaton [9,10] defined on a twodimensional square lattice of N c = L × L cells with periodic boundary conditions. Two variables a i (t) and c i (t) are associated with each node of the CA.…”

“…In this work, we present a parallel implementation in two dimensions of a discrete model of laser dynamics based on CA, introduced in references [9,10,11]. This implementation will allow us to run large size 2D simulations of the model on clusters of workstations.…”