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Soviet Journal of Quantum Electronics

Formation of spatial coherence of superluminescence in a dispersive medium

U A Abdullin, V A Gorshkov, Igor L Klyukach, Gennadii A Lyakhov, R. Yu. Orlov, L S Telegin

Published May 31, 1975• 4 citations
Publisher

Abstract

A theoretical and experimental investigation is reported of the formation of the spatial coherence of superluminescence in dispersive media. The theory is developed in the axial approximation for a given amplitude of a traveling population-inversion pulse. Asymptotic coherence characteristics are obtained for certain important limiting cases. The results are given of an experimental investigation of the spatial coherence of a superluminescent dye laser excited by single picosecond pulses. An analysis is made of the possibility of obtaining short-wavelength superluminescence radiation with a high degree of spatial coherence.

DOI
10.1070/qe1975v005n05abeh011168

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A theoretical and experimental investigation is reported of the formation of the spatial coherence of superluminescence in dispersive media. The theory is developed in the axial approximation for a given amplitude of a traveling population-inversion pulse. Asymptotic coherence characteristics are obtained for certain important limiting cases. The results are given of an experimental investigation of the spatial coherence of a superluminescent dye laser excited by single picosecond pulses. An analysis is made of the possibility of obtaining short-wavelength superluminescence radiation with a high degree of spatial coherence.
For pt.I see ibid., vol.10, p.425 (1977). The effect of spatial dispersion or exciton formation on the steady propagation of a coherent light pulse in a dielectric medium is studied. The optical Bloch equation for a lattice of atomic dipoles coupled to one another by an exchange-type interaction is solved simultaneously with the Maxwell equation by the method of power-series expansion developed in the preceding paper. Two kinds of pulse solutions are obtained in general: one propagating by the medium of the radiation field and the other by excitation transfer between atomic dipoles. The former solution is SIT-like in the short pulse limit, but a polariton-soliton or a standing wave of non-linear polariton if the pulse width is long. The latter is an exciton-soliton containing little photon component. When the pulse width is extremely long, there appears a polariton-soliton of a new type in which the two propagation mechanisms are mixed. It is found that the spatial dispersion prevents the polariton-soliton solutions from existing in a certain frequency range. This effect is explained on the basis of the functional behavior of the dispersion relation of the non-linear polariton.
An orderly account is given of the processes of coherent propagation, amplification, and generation of pulses in polyatomic resonant media. The characteristic features of the propagation of solitons in resonant media of finite length are considered. Comparisons are made of the exponential and lethargic amplification of pulses in resonant media. It is shown that an allowance for the reflection of the field from the boundaries of an active medium gives rise to a qualitatively different dependence of the parameters of the pulses on the reflection coefficients under superradiance and lasing conditions, which makes it possible to introduce a criterion to distinguish lasing from superradiance. An analysis is made of the characteristics of collective superradiance, which is a new case of coherent generation of pulses. Experimental and theoretical investigations of rf superradiance emitted by systems of nuclear spins are reviewed.
We have developed a self-consistent description, based on the semiclassical radiation theory of the propagation of a light pulse in a dye medium. The multilevel nature of the energy bands of a dye molecule and the solvent cage effect in a solution are taken into account. In the case of light pulses whose duration is much shorter than the solvent-solute relaxation time but much longer than the time of atomic phase memory, the latter being of the order of ${10}^{\ensuremath{-}12}$ sec for dyes, we solve the coupled system of equations for the field and the medium by the perturbation procedure. The hole-burning effect is incorporated into the solution in a natural manner. This is especially clear in the direct transition approximation where all the intermediate transitions are neglected. A recent idea of pulse superposition, consisting in storing the energy of a pulse in the form of population inversion followed by stimulated emission triggered by another pulse, is further discussed. Contrary to the orginal model developed by one of us (S.L.C.), we show that no cw pumping is required. The feasibility of the pulse superposition is supported by some experimental results obtained by sending a train of 10-psec pulses through a glycerine solution of oxazine 1 perchlorate.
A theoretical model for the propagation of coherent light pulses in resonant media where a large number of atoms cooperate in spontaneous emission (superradiance) is discussed. The medium is supposedly free of inhomogeneous broadening, and no lossy relaxation mechanisms are taken into account. The conditions for the emission of all spontaneous radiation in the direction of pulse propagation are described. A semi-classical model is used and, at each point in the medium, the propagation field and the spontaneous damping field are considered separately. The equation governing the evolution of a superradiant system in the presence of an applied pulse is derived. A mechanism of energy transfer from the traveling pulse to the medium is described which includes superradiant spontaneous emission effects. As a result of the neglect of all lossy relaxation processes, all energy stored in the medium is eventually returned to the pulse by coherent spontaneous emission. Therefore, in this theory, all pulses travel through the medium without energy loss. Numerical results for square input pulses are discussed which show two possible types of propagation behavior: (a) Low input intensities produce a negative tail to the input (positive) pulse and sharpening of the tail with the advance in the medium; (b) higher input intensities produce, after sufficient penetration, a steady-state pulse envelope somewhat similar to the $2\ensuremath{\pi}$ pulses of self-induced transparency. The steady-state solutions of the equations of motion are found numerically and the pulse shapes are computed for different degrees of superradiance. In the limit of strong superradiance, very asymmetric pulse envelopes of large area are found. For negligible superradiance, approximately $2\ensuremath{\pi}$ hyperbolic-secant pulses are obtained. The effects of inhomogeneous broadening are briefly considered, and the consequences of important superradiant damping in photon-echo experiments are qualitatively discussed.
Abstract We report an investigation of spectral and temporal properties of NV¯ centers in diamond plates fabricated from a single HPHT crystal but subjected to different electron irradiation doses during postgrowth processing. Samples 52734-1 and 52734-2, each with approximately the same nitrogen concentration of 60 ppm, are irradiated with doses of 1 and 2 × 1018 e‒/cm2, respectively. Particular attention is paid to the effect of irradiation dose on the concentration of NV¯ centers and the associated changes in the spectral and temporal properties of superluminescence under identical conditions of optical excitation with laser radiation at a wavelength of 532 nm. Analysis of the absorption spectra reveals that doubling the irradiation dose results in a 1.4-fold increase in the concentration of NV¯ centers—from 7.7 to 10.9 ppm—with a corresponding decrease in the concentration of isolated nitrogen centers (C centers)—from 49 to 43 ppm. The results demonstrate a nonlinear dependence of the increase in the concentration of NV¯ centers on the irradiation dose and make it possible to identify key characteristics of the samples and pumping conditions that determine the efficiency of superluminescence. Specifically, doubling the irradiation dose results in a threefold increase in the spectral intensity and a significant decrease in the duration of the superluminescence pulses. It is found that to achieve efficient superluminescence, it is important not only to have a significant excess of the concentration of C centers over the concentration of NV¯ centers, but also the absolute concentration of NV¯ centers and pump parameters such as the energy density of the pump pulses and the volume of the sample with a population inversion.