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Annual Meeting Optical Society of America

Lasing without inversion—gain enhancement with a colored pump

Gautam Vemuri, G. S. Agarwal, THOMAS W. MOSSBERG

Published Jan 1, 1993• 0 citations
Publisher

Abstract

Most models of lasing without inversion utilize incoherent pumping of the upper state of the transition on which lasing occurs. We suggest replacing incoherent pumping by a color pump (i.e. laser with a finite bandwidth) for selective pumping of the upper state, where one can also take advantage of the tunability of the laser. A three-level ladder system is considered with the upper two levels providing the lasing transition. We reduce the density matrix equations for this system to a set of eight coupled Langevin equations with multiplicative noise. These equations are solved using Monte-Carlo methods to obtain the gain as a function of various atom and field parameters. The use of the color pump leads to a significant enhancement in gain. Using a dressed states formalism, an explanation of the possible physical mechanism behind this gain enhancement is provided.

DOI
10.1364/oam.1993.thq.6

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Most models of lasing without inversion utilize incoherent pumping of the upper state of the transition on which lasing occurs. We suggest replacing incoherent pumping by a color pump (i.e. laser with a finite bandwidth) for selective pumping of the upper state, where one can also take advantage of the tunability of the laser. A three-level ladder system is considered with the upper two levels providing the lasing transition. We reduce the density matrix equations for this system to a set of eight coupled Langevin equations with multiplicative noise. These equations are solved using Monte-Carlo methods to obtain the gain as a function of various atom and field parameters. The use of the color pump leads to a significant enhancement in gain. Using a dressed states formalism, an explanation of the possible physical mechanism behind this gain enhancement is provided.
We explore the possibility of enhancing the gain in lasing without inversion schemes by replacing the usual incoherent pump with a finite bandwidth (spectrally coloured) pump. Three level atoms in the ladder and lambda configuration are modelled and we find that replacing the incoherent pump with a partially coherent pump amplifies the gain by as much as a factor of 4. The results are obtained via Monte-Carlo simulations of the density matrix equations, which, for a coloured pump, have the form of Langevin equations. We find that for a given set of atom-field parameters, the gain for coherent pumping is larger than for incoherent pumping, and that maximum gain is obtained for a partially coherent pump. The frequency of the coloured pump plays an important role in determining the optimum gain that can be obtained.
Recently it was reported that replacing an incoherent pumping mechanism by a spectrally colored (partially coherent) pump can lead to significant gain enhancement in lasing without inversion schemes [Phys. Rev. A 48, R4055 (1993)]. We extend that study further by considering the effects of the noise parameters (strength and bandwidth) of the pump on the gain in two types of three-level atomic energy-level schemes---the ladder and the \ensuremath{\Lambda} models. The calculations presented in this paper show a way to continuously ``tune'' the bandwidth of the pump and make a direct comparison between the gain obtained for coherent, incoherent, and partially coherent pumping. We find that for a given set of atom-field parameters, the gain for coherent pumping is larger than for incoherent pumping, and that maximum gain is obtained for a partially coherent pump. Increasing the strength of the noise also leads to an increase in the gain. The frequency of the colored pump plays a critical role in determining the maximum gain that can be obtained.
Abstract We show that it is possible to get gain without inversion at high frequency in a three-level ladder type scheme driven by a single driving laser. The transition from the ground state to first excited state is driven by a low-frequency resonant laser field. The next excited state lies far above the first one; therefore its resonant frequency can be much higher than that of the lower transition, and hence one should go beyond the most commonly used rotating wave approximation consisting of retaining only resonant terms (slowly oscillating) in the Hamiltonian. We solve the master equation, both analytically (under proper approximations) and numerically, with the full Hamiltonian keeping counter-rotating highly non-resonant terms. We show a dressed state picture explaining spectral features of gain-absorption profiles. Also we present a kind of phase diagram in the plane γ –Λ, where γ and Λ are spontaneous emission rate and incoherent pumping rate, respectively. The whole γ –Λ plane is divided into four areas: gain-inversion, absorption-no inversion, gain without inversion and absorption with inversion. The first two are usual regimes of incoherently pumped lasers, while the last two stem from the quantum interference phenomena. We analyse the parameter areas where such quantum regimes are possible. The exact numerical solution of the time-dependent master equation shows that keeping counter-rotating terms (no rotating wave approximation) gives rise to new spectral features in the form of additional peaks at combination frequencies. Actually the considered system works as a coherent frequency up-converter.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bi-chromatic laser field in the ladder configuration is presented. In our model we allow the atom to be dressed by both of the coupling and probe fields. The system under consideration is explored both analytically and numerically within the steady-state regime. A parameter study is performed in which we explore the influence of the change of control parameters (Rabi frequencies and incoherent pump rates, etc) on the system behaviour. The parameter study also applies to situations where both coherent fields have comparable intensities. Expressions for steady-state populations and coherences are derived, from which the constraints on the system control parameters allowing gain or absorption of various types, are calculated. The system is demonstrated to possess gain without inversion (GWI), as well as regular gain with inversion, for the appropriate choice of system control parameters. Inversion without lasing (IWL) is also found. The dressed-state approach offers a different insight into the system dynamics in which Rabi oscillations and spectral features appear natural. We believe that the dressed-state approach provides a more adequate description of the system dynamics than that provided by the bare state basis.
We analyze the inversionless gain in a three-level ladder system by replacing the usual coherent coupling field with an incoherent field. Surprisingly, it is found that one can obtain inversionless amplification of a weak probe even in the absence of a coherent field in the model. We conclude that gain is determined by the ensemble average of the product of the two-photon coherence and the ``effective Rabi frequency'' of the field. Thus, even though the incoherent pump reduces the two-photon coherence, gain can be restored by choosing sufficiently high strengths of the incoherent field.