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arXiv:0808.2915 · Optics Express

Quantitative verification of ab initio self-consistent laser theory

Li Ge, Robert J. Tandy, A. Douglas Stone, Hakan E. Türeci

Published Oct 8, 2008• 49 citations
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Abstract

We generalize and test the recent "ab initio" self-consistent (AISC) time-independent semiclassical laser theory. This self-consistent formalism generates all the stationary lasing properties in the multimode regime (frequencies, thresholds, internal and external fields, output power and emission pattern) from simple inputs: the dielectric function of the passive cavity, the atomic transition frequency, and the transverse relaxation time of the lasing transition.We find that the theory gives excellent quantitative agreement with full time-dependent simulations of the Maxwell-Bloch equations after it has been generalized to drop the slowly-varying envelope approximation. The theory is infinite order in the non-linear hole-burning interaction; the widely used third order approximation is shown to fail badly.

DOI
10.1364/oe.16.016895

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We improve the steady-state ab initio laser theory (SALT) of T\"ureci et al. by expressing its fundamental self-consistent equation in a basis set of threshold constant flux states that contains the exact threshold lasing mode. For cavities with nonuniform index and/or nonuniform gain, the new basis set allows the steady-state lasing properties to be computed with much greater efficiency. This formulation of the SALT can be solved in the single-pole approximation, which gives the intensities and thresholds, including the effects of nonlinear hole-burning interactions to all orders, with negligible computational effort. The approximation yields a number of analytic predictions, including a ``gain-clamping'' transition at which strong modal interactions suppress all higher modes. We show that the single-pole approximation agrees well with exact SALT calculations, particularly for high-QQQ cavities. Within this range of validity, it provides an extraordinarily efficient technique for modeling realistic and complex lasers.
Studying time-dependent behavior in lasers is analytically difficult due to the saturating nonlinearity inherent in the Maxwell-Bloch equations and numerically demanding because of the computational resources needed to discretize both time and space in conventional finite-difference time-domain approaches. We describe here an efficient spectral method to overcome these shortcomings in complex lasers of arbitrary shape, gain medium distribution, and pumping profile. We apply this approach to a quasidegenerate two-mode laser in different dynamical regimes and compare the results in the long-time limit to the steady-state ab initio laser theory (SALT), which is also built on a spectral method but makes a more specific ansatz about the long-time dynamical evolution of the semiclassical laser equations. Analyzing a parameter regime outside the known domain of validity of the stationary inversion approximation, we find that for only a narrow regime of pump powers the inversion is not stationary, and that this, as pump power is further increased, triggers a synchronization transition upon which the inversion becomes stationary again. We provide a detailed analysis of mode synchronization (also known as cooperative frequency locking), revealing interesting dynamical features of such a laser system in the vicinity of the synchronization threshold.
A semiclassical description for dye lasers is proposed, where the energy-level diagram of the dye molecule is assumed to consist of a continuous bandlike ground state and an excited singlet state. Unidirectional single-frequency (s.f.) operation is discussed. The linear-stability analysis for this operation reveals a very low threshold instability, which may appear generally in practical lasers. The ratio of the instability threshold to the lasing threshold may be of any value greater than 1, depending mainly on the bandwidth and the distribution of the dipole moments on the band, but it is independent of the cavity loss. This instability may account for that observed in recent experiments by Hillman, Krasinki, Boyd, and Stroud [Phys. Rev. Lett. 52, 1605 (1984)]. A general approach to analyzing the linear stability of the s.f. operation of the Maxwell-Bloch equations is also proposed, which states that only the eigenvalues of a 2\ifmmode\times\else\texttimes\fi{}2 matrix are relevant: one concerns the stability of the s.f. operation near the lasing threshold, the other determines the instability threshold of this operation.