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Quantum Optics Journal of the European Optical Society Part B

Basic models of lasing without inversion: general form of amplification condition and problem of self-consistency

Olga A. Kocharovskaya, Paul Mandel

Published Aug 1, 1994• 31 citations
Publisher

Abstract

We derive an amplification condition which generalizes the traditional population inversion requirement for the basic schemes of inversionless amplification. We develop a self-consistent quantum approach for the description of such schemes and demonstrate the limitations of the traditional phenomenological approach.
DOI
10.1088/0954-8998/6/4/002

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This review paper is devoted to amplification and lasing without population inversion involving atomic transitions in gas media. We start by discussing the main motivation in inversionless lasing research, namely, the generation of short-wavelength laser light. Then, we review the basic physics of inversionless lasing in two-level and, eventually, in three- and multilevel atomic configurations. Finally, we summarize the current state of the art of LWI experiments and indicate the main difficulties with respect to short-wavelength laser generation.
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Abstract Starting from a quantum description of multiple Λ-type three-level atoms driven with a coherent microwave field and incoherent optical pumping, we derive a microscopic model of lasing from which we move towards a consistent macroscopic picture. Our analysis applies across the range of system sizes from nanolasers to the thermodynamic limit of conventional lasing. We explore the necessary conditions to achieve lasing without inversion in certain regimes by calculating the non-equilibrium steady state solutions of the model at, and between, its microscopic and macroscopic limits. For the macroscopic picture, we use mean-field theory to present a thorough analysis of the lasing phase transition. In the microscopic case, we exploit the underlying permutation symmetry of the density matrix to calculate exact solutions for N three-level systems. This allows us to show that the steady state solutions approach the thermodynamic limit as N increases, restoring the sharp non-equilibrium phase transition in this limit. We demonstrate how the lasing phase transition and degree of population inversion can be adjusted by simply varying the phase of the coherent driving field. The high level of quantum control presented by this microscopic model and the framework outlined here have applications to further understanding and developing nanophotonic technology.
The author demonstrate that lasing without inversion can be achieved through a self-pulsing instability. This is shown for the resonant coherently driven three-level media proposed by Kocharovskaya, Mandel and Radeonychev (1992) as inversionless amplifiers of a monochromatic field. A usual instability giving rise to CW lasing is also found. Both instabilities are mutually exclusive, since they are primarily determined by opposite signs of the population difference between the two levels coupled by the driving field. The general necessary conditions for inversionless lasing are given and it is found that the two instabilities require a good quality cavity and are produced in a limited range of driving field intensity.