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Soviet Journal of Quantum Electronics

Spatial statistics of pulsed partly coherent radiation in a medium with a thermal nonlinearity

Sergey M. Babichenko, Valeriy P. Kandidov

Published Jul 31, 1984• 0 citations
Publisher

Abstract

The approximation of small fluctuations of the optical field is used to solve the transient problem of conversion of the spatial statistics of partly coherent radiation in a randomly inhomogeneous weakly absorbing medium. Pulsed radiation is considered and it is assumed that the pulse duration does not exceed the lifetime of inhomogeneities. Equations derived for the coherence functions of field perturbations are used to study in detail the dynamics of the statistical characteristics of radiation, such as the correlation radius, variance of the fluctuations, correlation functions of the amplitudes, and phase of the field perturbations.

DOI
10.1070/qe1984v014n07abeh005278

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The approximation of small fluctuations of the optical field is used to solve the transient problem of conversion of the spatial statistics of partly coherent radiation in a randomly inhomogeneous weakly absorbing medium. Pulsed radiation is considered and it is assumed that the pulse duration does not exceed the lifetime of inhomogeneities. Equations derived for the coherence functions of field perturbations are used to study in detail the dynamics of the statistical characteristics of radiation, such as the correlation radius, variance of the fluctuations, correlation functions of the amplitudes, and phase of the field perturbations.
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Based on the equation for the second-order coherence function, the propagation of partially coherent radiation is studied under the combined action of diffraction and refraction caused by the inhomogeneous distribution of the real and imaginary parts of the perturbation of the permittivity of a medium in the case of inhomogeneous absorption (amplification). The limits of application of the method of geometrical optics for inhomogeneously absorbing (amplifying) media are studied, as well as of the methods that neglect refraction caused by the inhomogeneous distribution of the imaginary part of the permittivity of the medium.
A study is made of the excitation of inhomogeneous holographic gratings by ultrashort light pulses with an arbitrary amplitude and phase modulation in a cubic nonlinear medium. The relaxation and diffusion of a pulse-induced grating is considered. The problem of diffraction of probe radiation by an inhomogeneous grating is solved using an electrodynamic theory of perturbations and also using the coupled wave approximation. It is shown that a cubic nonlinear medium may be used to store and then to retrieve uniquely a complete complex coherence function of a pulse. A simple method is proposed for the determination of the area under an exciting pulse, which makes it possible to introduce integral parameters of such a pulse (including a generalized amplitude and duration) that can serve as satisfactory estimates of the corresponding real quantities.
Coherent backscattering of pulsed radiation emitted by optically dense atomic ensembles is considered. The diagrammatic technique is used for deriving analytic expressions for correlation functions of scattered light, which make it possible to take into account all main factors affecting the dynamics of the process, including the hyperfine and Zeeman structure of the ground and first excited states of atoms, polarization of probe radiation, the actual shape and size of an atomic cloud, its spatial inhomogeneity, motion of atoms, and angular-momentum polarization of atoms. On the basis of these relations, the time dependence of the total intensity and the dependence of enhancement factor of backscattered light on the pulse duration, type of polarization of the polarization system of observation, optical thickness of the scattering medium, and the carrier frequency of the pulse are investigated. The calculations are performed for an ensemble of rubidium-85 atoms cooled in magnetooptical traps.
It is shown that the absorbtion of a weak field in a thick resonant absorber is a reversible process even in the case of the homogeneous broadening of the absorption line. As an example, the propagation of a long rectangular pulse with sharp edges in an optically dense resonant medium is studied theoretically in the linear response approximation. Transient nutation (TN), free induction decay (FID), and transients, induced by the phase switch of the incident pulse, are considered. It is shown that in exact resonance the amplitude of FID increases with the length of the medium. FID arises due to the scattered radiation field (dipoles ringing). In a thick medium the scattered field is almost of the same amplitude but opposite in phase with the incident radiation field. Both fields interfere destructively to produce what is seen as radiation damping at the output of the medium. The scattered field needs time to develop. Therefore, the leading edge of the pulse is not absorbed, demonstrating temporal transparency followed by TN. Phase shift (180${}^{\ensuremath{\circ}}$) of the pulse brings the incident pulse in phase with the scattered radiation. Constructive interference of the pulse with the scattered radiation field produces a short pulse with an amplitude that is two times larger than the amplitude of the incident pulse. If the input pulse is detuned from resonance, for a particular detuning and optical thickness of the medium the amplitude of the transient pulse, induced by the phase shift, is nearly three times larger than the amplitude of the incident pulse. This is explained by the interference of the scattered field, the phase-shifted input field, and the slowly propagating part of the pulse, developed before the phase shift.
An analytic method of decoupling of physical factors is used to investigate the relationship between the temporal and spatial coherence of a randomly modulated light pulse representing a superposition of a signal and noise in a medium with a local nonlinearity. An analysis is made of the factors that influence the transformation of the spatial and temporal characteristics of a diffracted and spreading light pulse in a nonlinear medium. The relationships governing the mutual influence of the signal and noise, resulting in changes in the regular envelopes and statistical characteristics, are determined.