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Simulating Laser Dynamics with Cellular Automata

  • Francisco Jiménez-Morales
  • José Luis Guisado
  • José Manuel Guerra
Chapter
Part of the Understanding Complex Systems book series (UCS)

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.

References

  1. 1.
    Bandini, S., Pavesi, G.: Simulation of vegetable populations dynamics based on cellular automata (2002)Google Scholar
  2. 2.
    Brydon, D., Pearson, J., Marder, M.: Solving stiff differential equations with the method of patches. J. Comput. Phys. 144, 280–298 (1998)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Byrne, G.D., Hindmarsh, A.C.: Stiff ODE solvers: a review of current and coming attractions. J. Comput. Phys. 70, 1–62 (1987)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Cabrera, E., Calderón, O.G., Guerra, J.: Experimental evidence of antiphase population dynamics in lasers. Phys. Rev. A 72, 043824 (2005)Google Scholar
  5. 5.
    Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press (1998)Google Scholar
  6. 6.
    Chopard, B., Luthi, P., Droz, M.: Reaction-diffusion cellular automata model for the formation of liesegang patterns. Phys. Rev. Lett. 72, 1284–1387 (1994)ADSCrossRefGoogle Scholar
  7. 7.
    Creutz, M.: Deterministic Ising dynamics (1986)ADSCrossRefGoogle Scholar
  8. 8.
    Dinand, M., Schuette, C.: Theoretical modeling of relaxation oscillations in Er-doped waveguide lasers. J. Lightwave Technol. 13(1), 14–23 (1995)ADSCrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Ilachinski, A.: Cellular Automata: a discrete universe. World Scientific (2001)Google Scholar
  13. 13.
    Lega, J., Moloney, J.V., Newell, A.C.: Universal description of laser dynamics near threshold. Phys. D 83(4), 478–498 (1995)CrossRefGoogle Scholar
  14. 14.
    Miranker, W.L.: Numerical Methods for Stiff Equations and Singular Perturbation Problems: and singular perturbation problems. D. Reidel—Springer, Dordrecht, The Netherlands (1981)Google Scholar
  15. 15.
    von Neumann, J.: Theory of Self-Reproducing Automata. University of Illinois Press, Urbana (1966)Google Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    Siegman, A.: Lasers. Unversity Science Books (1986)Google Scholar
  18. 18.
    Sloot, P., Chen, F., Boucher, C.: Cellular Automata Model of Drug Therapy for HIV Infection (2002)Google Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Svelto, O.: Principles of Lasers. Plenum Press (1989)Google Scholar
  21. 21.
    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)ADSCrossRefGoogle Scholar
  22. 22.
    Wolfram, S.: Cellular Automata and Complexity: collected papers. Addison-Wesley (1994)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Francisco Jiménez-Morales
    • 1
  • José Luis Guisado
    • 2
  • José Manuel Guerra
    • 3
  1. 1.Departamento de Física de la Materia CondensadaUniversidad de SevillaSevillaSpain
  2. 2.Departamento de Arquitectura y Tecnología de ComputadoresUniversidad de SevillaSevillaSpain
  3. 3.Departamento de ÓpticaFacultad de CC. Físicas, Universidad Complutense de MadridMadridSpain

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