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Telecommunications and Radio Engineering

Bistability and Transient Processes in a Three-Level Phaser System Saturated by a Standing Pumping Field and a Signal Traveling Wave

D. N. Makovetskii

Published Jan 1, 2005• 0 citations
Publisher

Abstract

Nonstationary processes in a three-level active paramagnetic phaser system have been investigated in case of the inversion state branching (bistability) which takes place below the threshold of self-excitation of the phonon generation. It has been shown that the nature of the branching of inversion states and transient processes in such a system depends significantly not only on a hypersound signal intensity, that was determined before, but also on a signal modulation frequency. Narrow nonlinear resonances and a critical slowing-down of transient processes have been found at simultaneous saturation of a spin-system by a standing electromagnetic pumping field and a hypersound-signal traveling wave.

DOI
10.1615/telecomradeng.v64.i9.40

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Soviet Journal of Quantum Electronics•Feb 28, 1986•1 citation
Nonstationary processes in a three-level active paramagnetic phaser system have been investigated in case of the inversion state branching (bistability) which takes place below the threshold of self-excitation of the phonon generation. It has been shown that the nature of the branching of inversion states and transient processes in such a system depends significantly not only on a hypersound signal intensity, that was determined before, but also on a signal modulation frequency. Narrow nonlinear resonances and a critical slowing-down of transient processes have been found at simultaneous saturation of a spin-system by a standing electromagnetic pumping field and a hypersound-signal traveling wave.
The inversion states of a saturated traveling-wave three-level quantum paramagnetic amplifier have been investigated under conditions of bistable resonator pumping. The equations of motion for the vectorial order parameter have been obtained using adiabatic elimination of fast variables. The exact solutions for stationary inversion states have been found from these equations. For high-quality pump resonators, the isolated and the semi-isolated branches of the inversion ratio have been revealed in stationary solutions. The existence of the semi-isolated branches means a possibility of collapse of the inversion state under influence of a saturating signal. Revival of inversion is possible in this case only by the hard excitation of the pump system. This nonlinear phenomenon is of a qualitatively another nature than one described by us in arXiv:0901.0449v1 [nlin.AO], and may be observed at moderate Q-factor of pump resonator.
The inversion states of a saturated three-level traveling-wave quantum paramagnetic amplifier have been investigated under conditions of bistable resonator pumping. The equations of motion for the vectorial order parameter have been obtained using adiabatic elimination of fast variables. These equations are a generalization of the scalar two-level Drummond model for the case of a three-level quantum active system. Isolated branches of the constant of inversion have been found from stationary solutions of equations for the vectorial order parameter. A analysis of bifurcations in the saturated quantum amplifier with bistable pumping has been represented with full details.
The nonlinear dynamics in a paramagnetic maser amplifier is investigated experimentally and theoretically under conditions such that the active medium exerts a sufficiently strong feedback influence on the pump field to induce population inversion of the spin levels. Branching of the inversion ratio due to the onset of bistability in the nonlinear microwave cavity of the pump at a frequency of 150 GHz is observed experimentally. Conditions are determined for the possible excitation of new nonlinear resonances when the spin system is inverted by a standing-wave field, and the stability of the resulting stationary nonequilibrium states of the paramagnet is analyzed.
Investigation of dynamical processes in microwave laser-like quantum devices is of great interest because of extremely low level of intrinsic noises (spontaneous emission) in their active media. One of the most interesting features of laser dynamics is branching of nonequilibrium states in dissipative system, which includes active medium and resonators, tuned to the frequencies of pumping and signal fields. The pointed branching leads to coexistence of various, sometimes very complex forms of regular, chaotic and transient inversion states. Understanding of the nature of inversion formation and evolution is of vital importance to the quantum electronics. In this report, we present results of investigations of microwave power spectra (MPS) and spatiotemporal dynamics (STD) concerning on the relationship between complex fine structure of MPS and corresponding evolution of patterns in STD.
We present a theoretical study of phase-conjugate (PC) emission by backward degenerate four-wave mixing (DFWM) processes in a resonant gas medium. In this study, high-intensity (pump) saturation and Doppler broadening are simultaneously taken into account. We develop a general formalism to deal with the saturation effects in the case of a three-level atom (with degenerate frequencies) and obtain analytical expressions of the PC field amplitude (after integration over the velocity distribution) under the following conditions: (1) the probe beam and one of the pump beams have intensities weak enough to be treated at the lowest perturbation order, whereas the other pump intensity is arbitrarily high; (2) the probe crosses the standing pump wave at grazing incidence. It is shown that the saturation induced by the forward pump (copropagating with the probe beam) leads to entirely different behavior of the nonlinear susceptibility from that induced by the backward pump (counterpropagating with the probe beam). This saturation anisotropy is specific to the inhomogeneous broadening of the gas medium, which is also responsible for the frequency splitting experimentally observed in the intensity line shape of the PC emission for large pump intensities. At saturation, this splitting is theoretically shown to be proportional to the Rabi frequency, with a proportionality coefficient critically dependent on the relaxation processes; in the case of a single-relaxation model, the splitting is equal to 1.5 times the Rabi frequency. The PC intensity line shape is demonstrated to be of dispersive origin in the case of backward saturation, whereas for forward saturation, narrow structures are predicted in both real and imaginary parts of the nonlinear susceptibility, also leading to the intensity line-shape splitting. One also finds that the reflectivity of PC mirrors based on resonant DFWM strongly depends on the origin of the saturation. For a saturating forward pump, the PC emission intensity tends toward zero with increasing pump intensities, and it reaches a finite (nonzero) limit in the case of backward saturation. Most of these predictions have been observed experimentally [ BlochD., Phys. Rev. Lett.49, 719 ( 1982)].
A theoretical study is made of the influence of changes in the relaxation of a three-level system in a resonance field on the dispersion, absorption, and difference between the populations of levels activated by noncoherent pumping. This change in the relaxation is due to a tendency of a thermal reservoir to create an additional difference between the populations of quasienergy states that appear under the influence of the resonance field. It is shown that as a consequence there is a considerable change in the nature of the interaction with the radiation field in laser crystals with three-level active centers when the pump power is close to the threshold. The lasing conditions are found subject to such changes. It is shown that the threshold pump power can be reduced in this case to a value at which the difference between the populations of the active levels vanishes and lasing appears because of an inversion of the populations in a system of quasienergy levels. Under transient conditions the lasing frequency near the threshold should then depend on the pump