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

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. γ_ll and γ_l 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).