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IEEE Journal of Quantum Electronics

Interaction of three coherent fields with Doppler broadened serial four-level systems: Application to four-level FIR lasers

G.-D. Willenberg, J. Heppner, Frank B. Foote

Published Dec 1, 1982• 28 citations
Publisher

Abstract

The semiclassical density matrix treatment is applied to serial four-level systems for the steady state. Phase and energy relaxations as well as Doppler effects andMdegeneracy are accounted for. The calculations are restricted to parallel polarized fields, avoiding problems of quantum interference. The formalism is used to calculate the gain spectra of different four-level far-infrared (FIR) laser schemes: double resonance pumped laser, Raman laser, two-photon pumped laser, and hyper-Raman-laser.

DOI
10.1109/jqe.1982.1071491

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The semiclassical density matrix treatment is applied to serial four-level systems for the steady state. Phase and energy relaxations as well as Doppler effects andMdegeneracy are accounted for. The calculations are restricted to parallel polarized fields, avoiding problems of quantum interference. The formalism is used to calculate the gain spectra of different four-level far-infrared (FIR) laser schemes: double resonance pumped laser, Raman laser, two-photon pumped laser, and hyper-Raman-laser.
Raman lasers operating in the far infrared are well described by the three- and four-level molecular systems. The theoretical analysis of these lasers is based on a density matrix treatment. Steady-state and time dynamics of these systems has been studied extensively. However, their spatial aspects involving propagation are not well understood. In this paper, we study the spatial and temporal dynamics of these lasers based on a density matrix analysis for the four-level molecular systems. The full set of Maxwell-Bloch equation consists of sixteen equations. We obtain the numerical solutions for this system and analyze regions of phase space where the laser fields show chaotic behavior.
A semiclassical density matrix treatment is developed for the parallel near-resonant interaction of three waves in a four-level atomic or molecular system. Explicit solutions are developed and contain implicit AC Stark-shift and splitting information. The role of splitting and AC Stark-shifts is discussed for a system of two competing emitted waves starting from a common optically pumped level; a situation encountered in many optically pumped lasers. Application of the results to a Raman-Raman competition situation in ammonia is illustrated.
Optically pumped FIR lasers give only discrete spectrums. This property restricts the practical use of lasers. Since 1977, many research works have been done to tune the output frequency of FIR laser, of which some are tried to find the possibility of tuning the laser lines by changing the pumping frequency continuously. But it is not easy to get an accurate result due to the complexity of theoretical calculation especially for quantum system of more than three energy levels. In this research work, two photon processes in four levels system have been studied by means of graph theory, which was developed by T. A. DeTemple et al. It was found that the output frequency of optically pumped FIR laser could be tuned with a frequency range equal to the frequency difference of two FIR transition frequencies. The tuning curves of FIR frequency and the curves of system gain coefficient vs. pump detuning frequencies were given.
The work is aimed at modeling coherence effects in a dissipative quantum system under the semi-classical density matrix formalism. A number of multiphoton coherence effects have been shown to be feasible by controlling the incoherent pumping mechanism in a generic four-level model. The specialty of the model is in finding inversionless gain without any restrictions being imposed on the decay rates of the driven transitions. Many of the coherence effects, such as absorption cancellation, inversionless gain at the line center, and sidebands of an absorptive line shape accompanied by dispersive switching, are explained using the same model under different parametric conditions. Further, it is shown that modulation in the coherence effects can effectively be controlled by the two- and three-photon excitation mechanisms with the proper choice of the rates of incoherent pumping under a stimulated Raman process. Different conditions of population inversion are found for both coherent and incoherent control of stimulated Raman resonance. In addition to Raman gain, gain without inversion in any standard state basis is found to be achieved in our present model. The proposed scheme can have potential application in controlling the properties of an optical field on propagation through rare earth ion-doped fiber material or other solid-state, as well as atomic, media.
Several polar molecules possessing strong far-infrared (FIR) transitions have been optically pumped by a mode-locked CO2TEA laser in a single-pass configuration. All the resulting FIR pulses are shorter than the sub-T2pump pulses; subnanosecond FIR pulses are observed. These short FIR pulses exhibit lethargic gain, stimulated Raman emission, and multiple-pulse superradiance. The experimental results are modeled by numerical solution of the Maxwell-density matrix equations for two fields interacting with a three-level system. Level degeneracy is included, and the pump is described by a multimode power spectrum with a parabolic envelope, resulting in a periodic train of pulses. Variation of the detuning of the pump from resonance allows simulation of the superradiant or Raman cases. This fully coherent model, which is the major contribution of this paper, explains key experimental observations such as the noncoincidence of the Raman peak with the pump modulation minimum and the enhancement of multiple-pulse superradiance due to remanent polarization.