# Laser with Intracavity Absorber: Q-Switching, Multistable Nonlinear Oscillations and Chaos

• M. G. Velarde
• J. C. Antoranz
Part of the NATO ASI Series book series (NSSB, volume 116)

## Abstract

The laser problem refers to a highly simplified mathematical model obtained from a more refined description given by LUGIATO et al. |1, 2|. We have
$$dE/drt = - K + NV + \mathop N\limits^ - \mathop V\limits^ -$$
(1)
$$dV/dt - \mathop {{\gamma _ \bot }}\limits^ - V + |g{|^2}DE$$
(2)
$$d\mathop V\limits^ - /dt = - \mathop {{\gamma _ \bot }}\limits^ - \mathop v\limits^ - |g{|^2}\mathop D\limits^ - E$$
(3)
$$dD/dt = - {\gamma _{||}}D - 4VE + {\gamma _{||}}\sigma$$
(4)
$$d\mathop D\limits^ - /dt = - \mathop {{\gamma _{||}}}\limits^ - - 4\mathop V\limits^ - E + \mathop {{\gamma _{||}}}\limits^ - \mathop \sigma \limits^ -$$
(5)
where N is the number of two-level excitable (active)atoms. E is the electric field amplitude. V is the polarization of the atoms. D is the perturbed atomic inversion (population inversion) . g is the field-matter (active or passive) coupling constant, κ is the damping constant of the field in the cavity . σ is the unsaturated inversion. γll and γl are the longitudinal and transverse relaxation constants, respectively (their inverse are a measure of the population and dipole decay times, respectively), the bar over a quantity indicates the corresponding variable for the passive atoms (absorbing medium).

## Keywords

Fractal Dimension Lyapunov Exponent Strange Attractor Electric Field Amplitude Atomic Inversion
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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