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Journal of Physics B Atomic Molecular and Optical Physics

Lasing without inversion and optimal pumping conditions for a diode pumped alkali laser

Joe Watson Jr, M. S. Shahriar, Yuri V. Rostovtsev

Published May 29, 2026• 0 citations
Publisher

Abstract

Abstract Diode-pumped alkali lasers (DPALs) exhibit remarkable efficiency. The modeling of these lasers has been limited by rate equations that neglect quantum coherence. In this paper, we introduce a semiclassical approach based on the density matrix formalism, which accurately accounts for relaxation processes and coherent effects. This framework enables us to reveal several previously unreported coherent effects in DPALs. Some of these effects, such as gain saturation due to power broadening, are expected. However, others are entirely unexpected and counterintuitive. Notably, we demonstrate the existence of laser gain even in the absence of population inversion, with a significantly broad lasing without inversion (LWI) regime extending beyond just the laser threshold. Even more surprising are the optimal pumping conditions, which reveal that a counterintuitive mix of coherent and incoherent pumping yields the highest efficiency. Our simulations highlight the crucial role of coherence, even in scenarios with high relaxation rates.

DOI
10.1088/1361-6455/ae751e

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Abstract Diode-pumped alkali lasers (DPALs) exhibit remarkable efficiency. The modeling of these lasers has been limited by rate equations that neglect quantum coherence. In this paper, we introduce a semiclassical approach based on the density matrix formalism, which accurately accounts for relaxation processes and coherent effects. This framework enables us to reveal several previously unreported coherent effects in DPALs. Some of these effects, such as gain saturation due to power broadening, are expected. However, others are entirely unexpected and counterintuitive. Notably, we demonstrate the existence of laser gain even in the absence of population inversion, with a significantly broad lasing without inversion (LWI) regime extending beyond just the laser threshold. Even more surprising are the optimal pumping conditions, which reveal that a counterintuitive mix of coherent and incoherent pumping yields the highest efficiency. Our simulations highlight the crucial role of coherence, even in scenarios with high relaxation rates.
The most commonly used lasers operate with population inversion. This requires an incoherent pumping power (from lamps, electrical discharges, etc.) that rapidly scales with the frequency of the generated laser radiation. In practice, this is the main obstacle for the operation in the continuous-wave regime of short-wavelength lasers in the UV, X-rays, etc. But lasers can also operate without population inversion using atomic coherences excited in the laser medium by coherent pumping with another laser. We present in this paper a short review of the field of lasing without inversion (LWI). In particular, we summarize the basic physics of LWI in the framework of both semiclassical theory and quantumjump formalism to describe light-matter interaction. We also review the experimental state-of-the-art in LWI. Most proof-of-principle demonstrations of LWI have used atomic vapours, so far. But recently gain without inversion (a pre-requisite for lasing) has been observed also in a technologically relevant medium: semiconductor nanostructures that can be tailored to have “artificial atom” electron states.
A rigorous density-matrix-based theory of lasing based on optically induced or autoionization-induced coherence between the levels is developed. The balance equations are obtained, and the conditions for lasing threshold are derived as a function of pumping strength and relaxation rates. Connection between the lasing without inversion and Raman and parametric processes is established. The main conclusion is that true CW lasing without inversion can indeed be obtained but only in a system where pumping and relaxation rates are favorable for attaining conventional lasing with population inversion. Practical implications of it, especially for the intersubband lasers, are discussed.
The importance of lasing without inversion (LWI) in comparison with the use of nonlinear optical techniques and techniques based on high-intensity femtosecond light pulses to generate high-frequency coherent radiation is outlined. The original development and utilization of an experimental facility based on semiconductor diode lasers to study the fundamental aspects of LWI on the D1 line of the Cs atom, which is rarely attempted, is described. This experimental facility is used to observe inversionless amplification on the D1 line of the Cs atom by use of a Λ atomic scheme. A combination of EIT and broadband pumping of atoms from the lower to the upper level of the probe transition allowed the observation of the inversionless gain. Justification for the absence of inversion in the probe transition is provided. We report a single-pass inversionless gain of ≈11% with relatively weak incoherent pumping. The results show improvement over the previously reported inversionless gain observed in Na, Rb, and Cs, illustrating the potential advantage of using the D1 line of Cs.
A three level model for optically pumped alkali metal vapor lasers is developed by considering the steady state rate equations for the longitudinally averaged number densities of the ground 2 S1/2 and first excited 2 P3/2, and 2 P1/2 states. For efficient operation, the collisional relaxation between the two upper levels should be fast relative to stimulated emission. By assuming a statistical distribution between the upper two levels, the limiting analytic solution for the quasi-two level system is achieved. A second limiting solution is identified for strongly bleached conditions where the atom recycle rate, limited by spin-orbit relaxation, fully specifies the output power. Performance in the intermediate regime depends significantly on pump laser bandwidth and requires numerical simulation. The ratio of populations for the two excited, 2 P3/2,1/2 states completes an analytic solution and depends primarily on pump laser bandwidth, threshold and alkali concentration.
An analytic model for the cw diode pumped alkali laser is developed by considering the longitudinally averaged number densities of the ground 2S1/2 and first excited 2P3/2, and 2P1/2 states. The pump intensity to reach threshold requires fully bleaching the pump transition and exceeding optical losses, typically about 200 Watts/cm2. Slope efficiency depends critically on the fraction of incident photons absorbed and the overlap of pump and resonator modes, approaching the quantum efficiency of 0.95 - 0.98. For marginal cavity transmission losses, peak performance is achieved for low output coupling. For efficient operation, the collisional relaxation between the two upper levels should be fast to prevent bottlenecking. By assuming a statistical distribution between the upper two levels, the limiting analytic solution for the quasitwo level system is achieved. For properly designed gain conditions, the quasi two level solution is usually achievable and represents ideal performance.
The LWI operation condition for an open Λ-type three level atomic system is obtained by solving the steady-state density-matrix equation with the system being driven by a strong coherent field while the inherent pumping rate and decay rate being arbitrary.It is shown that the inversions of inherent pumping rate and spontaneous decay rate replace the inversion of population,and together help to realize lasing without population inversion.Furthermore,the LWI can be realized if just either one of the two inversions is fulfilled.A schrodinger equation of three-level atomic system with appropriate conditions is analytically solved to explain the quantum interference process that leads to LWI.