Effects of phase fluctuation in an open four-level inversionless lasing system

A steady analytical solution of an open four-level inversionless lasing system with a driving field having the phase fluctuation has been given, and the effects of the finite width due to the phase fluctuation on the gain, dispersion, and population difference have been analyzed by using the numerical simulation from the steady analytical solution. It is found that: with the linewidth increasing, the gain decreases and the absolute value of population difference between levels coupled by the probe field increases, but the variation of the linewidth cannot change the properties of the inversionless lasing and refractive index increase of the system; when the linewidth does not equal to zero, the system can still get a high refractive index with zero absorption, and these conclusions have very obvious difference from those obtained in other inversionless lasing systems.     

Master-slave synchronization from the point of view of global dynamics

We present a mathematical framework for the theory of a synchronization phenomenon for dynamical systems discovered by Pecora and Carroll [Phys. Rev. Lett. 64, 821-824 (1990)]. From this perspective, we can synchronize, using a single coordinate, an open dense set of linear systems. We use our insights to synchronize nonlinear systems which were not previously recognized as being synchronizable. (c) 1995 American Institute of Physics.     

Heavy-ion dynamics from the point of view of classical mean-field theory

A simple classical force model, based on mean-field dynamics, is applied to fusion phenomena and other processes in heavy-ion collisions. We find reasonable agreement with trends in the fusion cross section going to heavy nuclei, including the barrier to fusion at high Z²/A. Collision times are calculated for a variety of reactions; recent evidence for non-equilibration of energy suggests that the equilibration time for energy is smaller than 300 fm/c and larger than 50 fm/c.     

Effect of Doppler broadening on gain in an open V-type inversionless lasing system

Our study shows that for the copropagating probing and driving fields, the gain without inversion doesn't monotonously decrease or increase with the increasement of Doppler width. When the driving field is resonant, at a suitable Doppler width, we can get a maximum value of the gain without inversion, which is much larger than that obtained when Doppler broadening is absent.     

Fronts between rhythms: spatiotemporal dynamics of extended polyrhythmic media

We study the propagation of fronts in extended oscillatory reaction-diffusion systems that contain several coexisting limit cycles. In contrast with the variational behavior, fronts between regions oscillating in two different limit cycles are found to propagate not necessarily towards the region of the less stable limit cycle, but towards the regions of the largest amplitudes, provided that the frequency mismatch between the cycles is sufficiently large. In other words, the smaller oscillations can always be made to control the whole system.     

About the regime of unidirectional propagation of radiation in nonlinear media

The generation of counterpropagating waves with low frequencies by pump copropagating waves in a weakly nonlinear medium is analyzed. The generation is shown to be efficient in the presence of intervals with anomalous and normal dispersion in the spectrum. Under these conditions, the approximation of unidirectional propagation, which is widely used in the literature, is incorrect and the nonlinear propagation of radiation should be described by the full wave equation.     

Statistical theory of the propagation of optical radiation in turbulent media

The problem of the propagation of a plane light wave in a turbulent medium is studied on the basis of the ideas of statistical topography. A cluster (caustic) structure of the intensity of the wave field in a plane perpendicular to the direction of propagation of the wave is analyzed both in the region of weak intensity fluctuations and in the region of saturated fluctuations. The specific (per unit area) values of the total area of the regions where the intensity is greater than a fixed level, the fraction of the power confined in these regions, and the total perimeter and average number of such regions are estimated. It is shown that estimates of this kind can be made on the basis of a knowledge of the joint one-point probability distribution of the intensity and transverse gradient of the wave field. Zh. éksp. Teor. Fiz. 111, 2044–2058 (June 1997)     

Ray dynamics of the propagation of sound in nonuniform moving media

This paper presents a new ray theory for the propagation of sound waves in nonuniformly moving media. It is found that the ray equations in weakly inhomogeneous and slowly moving media are analogous to the equations of motion of charged particles in nonuniform electric and magnetic fields. The adiabatic approximation is used to study the problem of the propagation of sound rays in a model of near-ocean-bottom waveguide with horizontal flow and slowly varying parameters along the direction of propagation of the wave. A general formula is derived that describes the transverse displacement of the trajectory of the ray relative to the direction of propagation of the wave.     

Effect of spontaneously generated coherence on inversionless lasing gain in an atomic system with Doppler broadening

We have studied the effect of the spontaneously generated coherence (SGC) on gain of lasing without inversion (LWI) in a closed three-level $\Lambda $-type atomic system with Doppler broadening. It is shown that, regardless of the driving and probe fields being co- or counter-propagating, at a suitable value of the Doppler width, we can obtain a much larger LWI gain with SGC than that without SGC; and the region of the LWI gain spectrum with SGC is obviously larger than that without SGC. When the Doppler width takes a constant value, the gain does not monotonically decrease or increase with increasing strength of SGC, the largest LWI gain can be obtained by adjusting strength of SGC. Generally speaking, the co-propagating probe and driving fields is favourable to obtain a larger LWI gain.     

Geometry from the spectral point of view

In this Letter, we develop geometry from a spectral point of view, the geometric data being encoded by a triple (A. H. D.) of an algebraA represented in a Hilbert spaceH with selfadjoint operatorD. This point of view is dictated by the general framework of noncommutative geometry and allows us to use geometric ideas in many situations beyond Riemannian geometry.

This paper is dedicated to the memory of J. Schwinger     

Spatial evolutions of inversionless gain and lasing field intensity in an open V-type system with SGC

This paper studies manly spatial evolution of gain without inversion (GWI) and the Rabi frequency E (intensity ?_p) of the probe field in an open V-type three-level inversionless lasing system with spontaneously generated coherence (SGC) for both cases with and without Doppler broadening. We found that: (1) Varying sizes of SGC strength (measured by angle θ), atomic exit rate (r₀) and ratio (S) of the atomic injection rates has remarkable effect on spatial evolutions of GWI and E (?_p). This effect in the case with Doppler broadening is similar to but weaker than that in the case without Doppler broadening. (2) Regardless of that Doppler broadening is present or not, GWI and E (?_p) increase with increase of θ, r₀ and S in certain value ranges of θ, r₀ and S; in the case with SGC we can obtain GWI and E (?_p) much larger than those in the case without SGC, while by choosing values of γ₀ and S, in the open system we can obtain LWI gain and E (?_p) much larger than those in the corresponding closed system. (3) The propagation distance in which GWI exists in the case with Doppler broadening is longer than that in the case without Doppler broadening; in the case without Doppler broadening, we can obtain larger GWI than that in the case with Doppler broadening; but in the case with Doppler broadening, we can obtain larger E (?_p) than that in the case without Doppler broadening.     

Waveguide propagation of intense electromagnetic radiation in slightly inhomogeneous nonlinear media

The propagation of self-localizing beams of electromagnetic waves in the form of nonlinear waveguides in a slightly inhomogeneous medium is studied analytically and numerically. The trajectories of the axial ray are studied as a function of its direction and the field strength at the initial point on the basis of a nonlinear scalar Helmholtz equation. Analytic expressions are derived. The longitudinal refractive index, the field intensity, and the waveguide radius are plotted as functions of the instantaneous position of the point on the axial ray. Deep penetration of the beam into the opaque region and the position of the screening surface are studied as functions of the parameters of the beam and the medium. A steady-state 3D problem is analyzed for a power-law nonlinearity with an arbitrary power. A 2D problem is analyzed for the case of a ponderomotive nonlinearity with saturation.     

Master equation approach to propagation of radiation through random media

Master and Fokker-Planck equations are obtained for radiation propagating through a random medium using the q-c-number correspondence of the coherent state technique. The corresponding equation for the antinormal characteristic function is solved by means of the method of characteristics. The master equation method and the recently developed method based on the Heisenberg equations and quantum characteristic function are shown to be equivalent. Some existence problems for the Glauber-Sudarshan weighting function are discussed. New light is thrown on approximations in the photocounting statistics used earlier.     

Features of propagation of laser radiation in media with small-scale periodic inhomogeneities

The problem of laser-radiation propagation in media with small-scale periodic phase inhomogeneities is considered analytically. Relying on our analytical treatment and numerical calculations performed in the diffraction approximation, we demonstrate the effect of periodic self-reproduction of the field structure of radiation during its propagation in media with small-scale periodic inhomogeneities, which is similar to the Talbot effect in a homogeneous medium.     

Evolution of the angular power spectrum of scattered radiation from a point source upon propagation in a turbid medium

The propagation of radiation from a point source through a plane layer of an absorbing medium with smooth random permittivity inhomogeneities is considered for the case in which the source and a receiver are spaced by different distances from the layer boundaries. The angular power spectra of the scattered radiation are calculated by the method of statistical modeling for different values of the layer thickness, positions of the source and the receiver relative to the layer, and absorption in the layer. The results for the moments of the angular power distribution obtained earlier in the small-angle approximation are fully confirmed. The transformation of the angular power spectrum upon variation of the source or receiver position with respect to the layer is analyzed for the first time.     

The dynamics of the two-level system in glasses

The self-consistent system of equations for longitudinal and transversal dynamical susceptabilities of the two-level system (TLS) in metallic glasses is obtained by using the method of irreducible relaxation functions. The dynamics of TLS interacting with acoustic phonons and electrons is discussed in the weak coupling limit and in the slow-fluctuation regime.     

Control of lasing filament arrays in nonlinear liquid media

Multiple filamentation in a high concentration solution of coumarin 153 in ethanol is studied. It is shown that the output filament pattern may be controlled by placing diffractive elements (circular aperture, edge) in the input beam path. These filaments are formed in highly reproducible arrays along diffraction maxima corresponding to the element used. Experimental results are supported by numerical simulations. They confirm that diffraction-induced intensity gradients swamp modulational instability on the wavefront, forcing filaments to form along diffraction maxima. The effect of two-photon absorption by coumarin molecules on filament patterns is also investigated over a range of dye concentrations. Control results are finally exploited in the production of arrays of localized lasing filaments, which should open novel applications. The resultant lasing sources are mutually coherent and highly repeatable from shot-to-shot, as is shown by their far-field interference patterns. PACS 42.65.Tg; 52.38.Hb; 42.68.Ay