Abstract
The long-established approach to study laser dynamics uses a set of differential equations known as the laser rate equations. In this work we present an overview of an alternative model based on a cellular automaton (CA). We also present a panorama of different variants of the model: the original one, designed to simulate general laser dynamics; an additional one, that was proposed to simulate pulsed pumped lasers; and finally a new model to simulate lasers that exhibit antiphase dynamics, which is proposed here. Despite its simplicity, the CA model reproduces qualitatively the phenomenology encountered in many real laser systems: (i) the existence of a threshold value of the pumping rate \(R_t\); (ii) the exact dependence of \(R_t\) on the life times of the photons and the inversion population; (iii) the two main laser regimes: a steady state and an oscillatory one.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bandini, S., Pavesi, G.: Simulation of vegetable populations dynamics based on cellular automata (2002)
Brydon, D., Pearson, J., Marder, M.: Solving stiff differential equations with the method of patches. J. Comput. Phys. 144, 280–298 (1998)
Byrne, G.D., Hindmarsh, A.C.: Stiff ODE solvers: a review of current and coming attractions. J. Comput. Phys. 70, 1–62 (1987)
Cabrera, E., Calderón, O.G., Guerra, J.: Experimental evidence of antiphase population dynamics in lasers. Phys. Rev. A 72, 043824 (2005)
Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press (1998)
Chopard, B., Luthi, P., Droz, M.: Reaction-diffusion cellular automata model for the formation of liesegang patterns. Phys. Rev. Lett. 72, 1284–1387 (1994)
Creutz, M.: Deterministic Ising dynamics (1986)
Dinand, M., Schuette, C.: Theoretical modeling of relaxation oscillations in Er-doped waveguide lasers. J. Lightwave Technol. 13(1), 14–23 (1995)
Guisado, J.L., Jiménez-Morales, F., Guerra, J.M.: Cellular automaton model for the simulation of laser dynamics. Phys. Rev. E 67(6), 066708 (2003)
Guisado, J.L., Jiménez-Morales, F., Guerra, J.M.: Simulation of the Dynamics of Pulsed Pumped. In: Lecture Notes in Computer Science, vol. 3305, pp. 278–285 (2004)
Guisado, J.L., Jiménez-Morales, F., Guerra, J.M.: Application of Shannon’s entropy to classify emergent behaviors in a simulation of laser dynamics. Math. Comput. Model. 42(7–8), 847–854 (2005)
Ilachinski, A.: Cellular Automata: a discrete universe. World Scientific (2001)
Lega, J., Moloney, J.V., Newell, A.C.: Universal description of laser dynamics near threshold. Phys. D 83(4), 478–498 (1995)
Miranker, W.L.: Numerical Methods for Stiff Equations and Singular Perturbation Problems: and singular perturbation problems. D. Reidel—Springer, Dordrecht, The Netherlands (1981)
von Neumann, J.: Theory of Self-Reproducing Automata. University of Illinois Press, Urbana (1966)
Qiu, G., Kandhai, D., Sloot, P.M.A.: Understanding the complex dynamics of stock markets through cellular automata. Phys. Rev. E—Stat. Nonlinear Soft Matter Phys. 75(4) (2007)
Siegman, A.: Lasers. Unversity Science Books (1986)
Sloot, P., Chen, F., Boucher, C.: Cellular Automata Model of Drug Therapy for HIV Infection (2002)
Subrata, R., Zomaya, A.Y.: Evolving cellular automata for location management in mobile computing networks. IEEE Trans. Parallel Distrib. Syst. 14(1), 13–26 (2003)
Svelto, O.: Principles of Lasers. Plenum Press (1989)
Veasey, D.L., Gary, J.M., Amin, J., Aust, J.A.: Time-dependent modeling of erbium-doped waveguide lasers in lithiumniobate pumped at 980 and 1480 nm. IEEE J. Quantum Electron. 33(10), 1647–1662 (1997)
Wolfram, S.: Cellular Automata and Complexity: collected papers. Addison-Wesley (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Jiménez-Morales, F., Guisado, J.L., Guerra, J.M. (2018). Simulating Laser Dynamics with Cellular Automata. In: Carmona, V., Cuevas-Maraver, J., Fernández-Sánchez, F., García- Medina, E. (eds) Nonlinear Systems, Vol. 1. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-66766-9_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-66766-9_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66765-2
Online ISBN: 978-3-319-66766-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)