Steady-state ab initio laser theory for N-level lasers

Abstract

We show that Steady-state Ab initio Laser Theory (SALT) can be applied to find the stationary multimode lasing properties of an N-level laser. This is achieved by mapping the N-level rate equations to an effective two-level model of the type solved by the SALT algorithm. This mapping yields excellent agreement with more computationally demanding N-level time domain solutions for the steady state.

Steady-stateab initiolaser theory for fully or nearly degenerate cavity modes

“…As long as the presence of this second lasing mode does not violate the SIA, the corresponding two-mode lasing solution is considered stable (as was previously verified using FDTD simulations [18,34,35]). As we will demonstrate through a comparison to timedependent solutions of the MB equations, this simple criterion can not be applied for nearly degenerate modes.…”

“…This is the case described by SALT, in which the MB equations are simplified to a set of time-independent, non-Hermitian, nonlinear and coupled Helmholtz equations. The solutions of these SALT equations are much more efficiently calculated than those of the MB equations [18,25,34,35].…”

“…Hence, the stability of the solutions obtained from our extended SALT approach has to be verified. Up to now such additional stability checks were always done using direct time-dependent simulations of the MB equations [18,25,34,35]. One of the reasons for using SALT, however, is exactly to avoid this kind of computationally very demanding numerics.…”

Scalable numerical approach for the steady-stateab initiolaser theory

“…II) simplify the general MB equations by removing the time dependence for steady-state modes, which allows SALT solvers to be potentially far more efficient than previous timedomain approaches [13,14], while providing comparable accuracy [15,16]. However, all earlier approaches to SALT required the intermediate construction of a specialized constant-flux (CF) basis for the laser modes.…”

“…It makes no a priori assumptions about the geometry of the laser system, treats the open (non-Hermitian) character of the laser system exactly, and the nonlinear hole-burning interactions between the laser modes to infinite order. More realistic and quantitative laser modeling typically requires treating a gain medium with three, four, or more relevant atomic levels, but it has been shown that for the steady-state properties, under the same assumptions as SALT, the semiclassical equations can be reduced to an effective two-level (MB) system with renormalized parameters and solved with essentially the same efficiency as two-level SALT [16,27]. SALT can also be used to describe quantum properties of lasers by combining the nonlinear scattering matrix of SALT with input-output theory, leading specifically to a general formula for the linewidth of each mode in the nonlinear steady state [28].…”