The theory of stability, bistability, and instability in three-mode class-A lasers

Abstract

Instability is an inevitable and common problem in all different kinds of lasers when they are oscillating in both single-and multi-mode states. Here, the stability conditions are investigated for a three-mode class-A laser. A set of linear equations is derived for the stable oscillation of the cavity central mode together with its left and right adjacent longitudinal modes. The coefficient determinant of stability equations is Hermitian and equal to zero for the roots of two diagonal arrays. In other words, the novelty of our work is to expand the stability coefficient determinant in terms of main diagonal arrays rather than for one row or one column. These diagonal roots lead to two lower and upper boundary curves in the form of a bifurcation. The lower boundary curve mimics the single-mode laser and delimits the instability region (with no above-threshold oscillating mode) from the bistability region (with two above-threshold oscillating modes). The upper boundary curve mimics the two-mode laser and delimits the bistability region from the stability region, in which all three-longitudinal modes are simultaneously oscillating in the above-threshold state.

Detuning Effect Between the Cavity Resonance and Atomic Transition Frequencies on Noise Flux Profiles of Class-C Lasers

“…Finally, we have recently described the general features of a three-mode class-A laser including stability, bistability, instability and forming the bifurcation [22]. It is demonstrated that the bifurcation curve separates the bistability region with the two oscillating modes from the stability and instability regions with the respective three and no oscillating modes.…”

The stability conditions of diatomic molecules via analogy with the stability theory of lasers

“…We have already exploited the stability theory for evaluating the stability ranges of an electromagnetic wave inside the laser cavity as an optical oscillator [15,16]. The application of stability theory is here extended to determine the stability ranges of an oscillating diatomic molecule as a microscopic material oscillator.…”

A simple method for precisely evaluating the stability regions of a multi-mode laser

“…Instability [1][2][3][4] and noise [5,6] are two important inherent characteristics of lasers that commonly depend on the damping rates of the cavity electric field γ C , atomic population inversion γ , and the atomic dipole moment γ ⊥ . Therefore, all lasers have been divided into the three important categories of class A, class B, and class C according to the damping con- and γ γ γ ≈ ≈ ⊥ C , respectively [7].…”

“…Similarly, the coefficient determinant expansion of a three-mode class A laser with three freedom degrees has produced a third-order characteristic equation [1]. The stability boundaries are then determined by looking for three simultaneous negative roots using Hurwitz's criteria [2,10,12].…”

“…These problems can be easily avoided by exploiting our stability procedure. The main diagonal arrays of the coefficient determinant (3 × 3) are taken equal to zero until its expansion is nullified [1]. The roots of the diagonal arrays then lead to the upper and lower boundaries of a single bifurcation that separates the states of below threshold, with no oscillating mode, and above threshold, with three simultaneous oscillating modes.…”