Steady-state ab initio laser theory for complex gain media

Abstract

We derive and test a generalization of the steady-state ab initio laser theory (SALT) to treat complex gain media. The generalized theory (C-SALT) is able to treat atomic and molecular gain media with diffusion and multiple lasing transitions, and semiconductor gain media in the free carrier approximation including fully the effect of Pauli blocking. The key assumption of the theory is stationarity of the level populations, which leads to coupled self-consistent equations for the populations and the lasing modes that fully include the effects of openness and non-linear spatial hole-burning. These equations can be solved efficiently for the steady-state lasing properties by a similar iteration procedure as in SALT, where a static gain medium with a single transition is assumed. The theory is tested by comparison to much less efficient finite difference time domain (FDTD) methods and excellent agreement is found. Using C-SALT to analyze the effects of varying gain diffusion constant we demonstrate a cross-over between the regime of strong spatial hole burning with multimode lasing to a regime of negligible spatial hole burning, leading to gain-clamping, and single mode lasing. The effect of spatially inhomogeneous pumping combined with diffusion is also studied and a relevant length scale for spatial inhomogeneity to persist under these conditions is determined. For the semiconductor gain model, we demonstrate the frequency shift due to Pauli blocking as the pumping strength changes.

Ab initiomultimode linewidth theory for arbitrary inhomogeneous laser cavities

“…The modes E μ (x) and frequencies ω μ can be calculated using SALT, which solves the semiclassical Maxwell-Bloch equations in the absence of noise. (SALT has been generalized to include multilevel atoms [73], multiple lasing transitions, and gain diffusion [74]; any of these cases can thus be treated by N-SALT with minor modifications, but we focus on the two-level case here.) The linewidth can now be calculated by adding Langevin noise, as described below.…”

Invited Article: Acousto-optic finite-difference frequency-domain algorithm for first-principles simulations of on-chip acousto-optic devices

“…Nevertheless, one can imagine a treatment where one calculates the response of a structure to a pump at a given frequency, and then determine the effect of pump frequency fluctuation by a perturbation approach. 14,40,42,53 At the final stage of the revision, it was brought to our attention that concurrent to our work, there is another proposal for performing first-principles simulations of the SBS process using a transformation optics approach. 54 Both our work and the work in Ref.…”

“…The treatment below is similar in setup to the harmonic balance method for nonlinear circuit simulations 35,36 as well as other frequency domain algorithms developed to solve for the steady-state solutions of lasers while accounting for the nonlinear effects due to gain saturation. [37][38][39][40] To start, we first define a vector v that contains 2(M + 1) complex field elements…”

Eigenvalue dynamics in the presence of nonuniform gain and loss

“…However, lasers are an inherently non-linear system in which gain saturation both prevents any resonance from moving into the positive half of the complex plane, and also reduces the gain available for additional resonances to reach threshold when the system is lasing. We can account for the effects of gain saturation within the FDFD simulations by using the steady-state ab initio laser theory (SALT), which solves the set of self-consistent equations for each steady-state lasing mode coupled together through the saturable gain medium [31][32][33]. SALT simulations of the three coupled cavity system confirm that lasing ceases and then resumes as gain is added to the left and right cavities, as shown in Fig.…”

“…The gain medium is assumed to be homogeneously broadened, with a central frequency of ka = 9.6mm −1 , and width γ ⊥ = 0.2mm −1 . The pump level is chosen to realize the refractive indexes from (a), and n fp corresponds to D0 = 1.2 in SALT units [31][32][33].…”