Self-pulsing Behavior Research Articles

A simple model of the “casperson instability” for a single mode inhomogeneously broadened laser

A model consisting of four differential equations derived from the integro-differential (so-called “Maxwell-Bloch”) equations which describe the dynamics of a single mode inhomogeneously broadened unidirectional ring laser is proposed. The numerical analysis of this model shows a self-pulsing behaviour closely related to the “Casperson instability”.

Instability Properties of the Optical Field in Coherent-driving Intracavity Second-harmonic Generation

Abstract An optical instability process, which leads from intensity self-pulsing to period-doubling branching and then to an attenuating period doubling self-pulsing behaviour, is obtained for external coherent-driving intracavity second-harmonic generation. A suitable way of enhancing the self-pulsing effect of the optical field in this nonlinear process is also proposed.

Optical multistability in sodium: analysis of a theoretical model

We study a theoretical model that describes an optically pumped Fabry–Perot cavity filled with sodium vapor as a nonlinear absorptive medium. The nonlinear medium is subjected to a static magnetic field. A difference of population is built up between Zeeman sublevels of the ground state when the pump exceeds a threshold. This gives rise to a nonsymmetrical absorption of the two circularly polarized components of the incident light. The emphasis of this paper is on the derivation of analytic results. We show that the system can exhibit a self-pulsing behavior and that in a suitable domain of parameters the system has two or more steady states. This is known as optical bistability or optical multistability.

Bistability, self-pulsing and chaos in optical parametric oscillators

We consider a degenerate parametric oscillator and show that, when the cavity is detuned both with respect to the pump and with respect to its subharmonic, the system can display bistable or self-pulsing behaviour. Bistability (self-pulsing) requires that the product of the two detuning parameters is positive (negative). In the self-pulsing regime, the system exhibits period doubling and chaos. We generalize our steady-state analysis to the case in which the cavity has a poor finesse for the pump mode.

Mode-mode competition and unstable behavior in a homogeneously broadened ring laser.

We present theoretical and experimental evidence for a new type of multimode instability in a homogeneously broadened ring-laser system. The unstable behavior discussed in this paper is the result of multimode competition and can manifest itself either through self-pulsing or hysteretic behavior of the bistable type in the laser output intensity and operating frequency. We have verified some of our predictions with the help of a ${\mathrm{CO}}_{2}$ laser whose observed bistable behavior is in good qualitative agreement with the theoretical predictions.

Two-mode operation in a laser with nonlinear mirror

The operation of two modes in a multistable laser is examined. One of the modes is treated as a perturbation and the stability of the oscillating mode is analysed. We find that the perturbing mode can switch the oscillating mode from one state to the other state of lower intensity. We also find that for a certain choice of steady-state parameters the system might exhibit self-pulsing or chaotic behaviour.

An organizing center for optical bistability and self-pulsing

The problem of self-pulsing in optically bistable systems is discussed within the framework of imperfect bifurcation theory. The joint appearance of a hysteresis cycle in the cw-transmission curve and of transitions to self-pulsing is described as an interaction between steady-state and Hopf bifurcations induced by varying the incident field intensity. The bifurcation equations for the most degenerate case are shown to be determined by a corank-two and codimension-four polynomial normal form. This form can be extracted from analytical and numerical studies on the Maxwell-Bloch equations, and acts as an organizing center for bistable switching and the self-pulsing mechanism. The structurally stable unfolded bifurcation diagrams are analyzed. Besides describing correctly and in a comprehensive way all bifurcations to self-pulsing that have so far been observed, a number of new generic transitions are predicted. These include self-pulsing from the low transmission branch and transitions leading to the formation of islands with self-pulsing behavior.

Self-pulsing and chaos in a mean-field model of optical bistability

We have discovered and analyzed periodic and chaotic self-pulsing behavior in a single-mode, mean-field model of optical bistability. Our results indicate that one route to chaos taken by this system is a sequence of period doubling bifurcations. With the help of a Poincaré map we have identified the strange attractor that is responsible for the non-periodic self-pulsing.

Many-mode quantum statistical theory of optical bistability

We formulate a master equation which includes all the modes of a unidirectional ring cavity. This equation holds for small absorption and transmission, with arbitrary ratio of absorption over transmission. Within this limit, this many-mode master equation provides an ideal tool to study fluctuations in laser-type systems in general, and in optical bistability (both absorptive and dispersive) in particular. The dissipative terms for the modes are derived exactly from the boundary condition of the problem. Neglecting all the modes except the resonant one, this equation reduces to the well known quantum statistical mean field model. At a semiclassical level the master equation produces a new set of propagation equations, which are equivalent to the Maxwell-Bloch equations in the aforesaid limit. These equations are very well suitable to describe the self-pulsing behavior in laser systems, as well as the many-mode master equation is suitable to give a quantum statistical description of this phenomenon.

Analytical description of self-pulsing in absorptive optical bistability

Using Haken's theory of phase transition-like phenomena in systems far from thermal equilibrium, we give an analytical description of the self-pulsing behavior in absorptive optical bistability. The results are compared with the corresponding computer solutions. We discuss the order (first or second) of the phase transition from CW to pulsed transmission.

Self pulsing inm dispersive optical bistability

We analyze the stability of the stationary solutions of dispersive optical bistability in a ring cavity for a homogeneously broadened atomic system. The analysis is performed in the limit αL ⪡ 1, with C = αL2T fixed. It is shown that in the dispersive case one can yield instability also when bistability is absent. This feature suggests that the dispersive case is more suitable than the purely absorptive one with respect to the observation of the self-pulsing behavior.