Spectral Output and Spiking Behavior of Solid-State Lasers

Abstract

Experiments show that conventional solid-state lasers can go into oscillation simultaneously in many modes. This is somewhat surprising since it appears impossible to ``eat holes'' in temperature-broadened lines and thus only one or, at most, a few modes should be able to oscillate. However, the spatial variation in the field intensity of the various modes produces nonuniform distributions in the inverted population and one can show that there is little tendency for these distributions to smooth out due to spatial cross relaxation. Such nonuniform distributions could lead to simultaneous oscillation in many modes. Formulas which relate the number of unstable modes to the pump power and various other maser parameters are obtained. The results show that it is exceedingly difficult to obtain single mode operation in conventional masers at high pumping levels. Ways to avoid a nonuniform distribution density and methods to achieve high-power single-mode operation in practice are discussed. It is also possible to show the effect of slow spatial cross relaxation on the spiking behavior.

Global rate equation description of a laser

“…This leads to an infinite hierarchy of equations which is truncated without much justification to yield a finite set of purely differential equations. The most popular truncation scheme, leading to the simplest rate equations, was proposed by Tang, Statz, and deMars [2]. The TSD rate equations couple the modal intensities to the population inversion averaged over the cavity length and to the population gratings at the optical frequencies.…”

“…Up to now, most studies of equations (1,2) have been based on modal expansions of the population inversion. This leads to an infinite hierarchy of equations which is truncated without much justification to yield a finite set of purely differential equations.…”

Stability of two loss-coupled lasers

“…The two lasers are coupled by a loss mechanism which depends on the intensity of the other laser. The evolution equations for such a pair of lasers are derived from the equations of Tang et al [7] by adding intensity-dependent losses. We shall use the formulation of these equations in terms of reduced variables [8].…”

Two-mode threshold of a solid-state Fabry-Perot laser

“…It was shown recently [2] that for a laser in a Fabry-Perot resonator with a constant intracavity pump profile, the spurious divergences resulting from the TSD rate equations, such as in (1), disappear if the full integro-differential rate equations are used, leading to the implicit equation for w th : 4w th − 1 − 8w th + 1 (γ +2−2γ w th ) 2 = 16γ (γ w th −1).…”

“…The single-mode regime, for instance, is bounded from below by the laser first oscillation threshold and from above by the two-mode threshold. Tang, Statz and deMars [1] (TSD) have introduced a widely used theory for Fabry-Perot lasers based on the rate equations approximation. Using this theory for homogeneously broadened lasers, the single-mode intensity I = w 2 −2+ 2 + w 2 /4 where w is the optical pump parameter normalized to unity at the lasing first threshold, is found to be the stable steady-state solution above the laser first threshold and below the two-mode laser threshold given by…”