Phase compensation for refractive distortions of partially coherent beams

Колосов, В. В.; Kuzikovskii, A. V.

doi:10.1070/qe1981v011n03abeh006302

Cited by 3 publications

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“…For this case, in eqns (19) and (21) Eqn (18) describing evolution of the mutual coherence function is difficult to analyze because it represents the second order partial differential equation (PDE) for a complex function that depends on two vector (p and R) and two scalar (t and z) variables. The equation (18) can be simplified by considering propagation of a returned wave in a medium with relatively smooth refractive index fluctuations, so that the characteristic scale l (z)for MCF falloff over the difference coordinate (coherence length) p in eqn (18) is smaller than the characteristic spatial scales 4, for refractive index fluctuations -the smooth-refractive-index (SRI) approximation16'9. in this case refractive index fluctuations can be approximated in (18) by the first two terms ofthe Taylor series expansion: n(z,R+p/2)-n(z,R-p/2)n pVRn(z,R).…”

Section: Evolution Of Returned Wave Mutual Coherence Functionmentioning

confidence: 99%

“…The equation (18) can be simplified by considering propagation of a returned wave in a medium with relatively smooth refractive index fluctuations, so that the characteristic scale l (z)for MCF falloff over the difference coordinate (coherence length) p in eqn (18) is smaller than the characteristic spatial scales 4, for refractive index fluctuations -the smooth-refractive-index (SRI) approximation16'9. in this case refractive index fluctuations can be approximated in (18) by the first two terms ofthe Taylor series expansion: n(z,R+p/2)-n(z,R-p/2)n pVRn(z,R).…”

Section: Evolution Of Returned Wave Mutual Coherence Functionmentioning

confidence: 99%

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<title>Adaptive focusing of laser radiation onto a rough reflecting surface through the turbulent and nonlinear atmosphere</title>

Vorontsov

Колосов

2004

SPIE Proceedings

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Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related with maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing outgoing wave propagation, and the equation describing evolution of the mutual coherence function (MCF) for the backscattered (returned) wave. The resulting evolution equation for the MCF is further simplified by the use of the smooth refractive index approximation. This approximation enables derivation ofthe transport equation for the returned wave brightness function, analyzed here using method characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wavefront sensors that perform sensing of speckle-averaged characteristics of the wavefront phase (TIL sensors). Analysis of the wavefront phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (targetinduced phase) that cannot be easily separated from the atmospheric turbulence-related phase aberrations. We also show that wavefront sensing results depend on the extended target shape, surface roughness, and the outgoing beam intensity distribution on the target surface.

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Section: Evolution Of Returned Wave Mutual Coherence Functionmentioning

confidence: 99%

Section: Evolution Of Returned Wave Mutual Coherence Functionmentioning

confidence: 99%

<title>Adaptive focusing of laser radiation onto a rough reflecting surface through the turbulent and nonlinear atmosphere</title>

Vorontsov

Колосов

2004

SPIE Proceedings

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“…But for the case of r 0.5 and 1 .0 these differences are not large for the more important region p < ap. 6. We now discuss several qualitative features of the derived formulae and the application to existing x-ray lasers.…”

Section: Introductionmentioning

confidence: 98%

<title>X-ray laser coherence in the presence of density fluctuations</title>

et al. 1996

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A ray-tracing technique based on the radiation transfer equation is used to describe the spontaneous emission gain in active media. Using this approach analytical solutions for the intensity distribution and coherence function in the output plane of an active medium with parabolic transverse profiles of dielectric constant and gain coefficient are presented. Applicability of the approximation when contribution into output emission is made by only spontaneous sources adjacent to the far face region of an active medium is analyzed. This approximation is seen not to be applicable for many real situations and it is necessary take into account the sources in the whole active medium. The effect of dielectric constant fluctuations on output coherence is treated by using the phase approximation of Huygens-Kirchhoff method.Keywords: x-ray laser, inhomogeneous active media, fluctuations, degree of coherence, ray-tracing technique. INTRODUCTIONThere are several approaches for theoretical description of the output emission of the lasers of interest. All of them are based on paraxial version of the wave equation. The approach based on expansion of the wave field into infmite series over transverse modes"2 is widely used. This approach is similar to conventional methods used in the laser optics. However, it can be practically used for a limited number of dielectric constant and gain coefficient profiles in an active medium for which transverse modes can be obtained analytically.The second approach3 is based on the numerical solution of the paraxial wave equation using the fast Fourier-transform split-operator method. The spontaneous emission is treated with the random-phase Monte-Carlo method. The coherence function is calculated by averaging over 1 00-200 temporal steps.The third approach is based on solving the equation for the transverse coherence function.4'5 Using this approach authors succeeded in analytical solving for a number of profiles of dielectric constant distribution (but for homogeneous distribution of gain coefficient) and for the case of saturation of emission gain.In this paper, we present an approach based on the solution of radiation transfer equation. This equation is an approximating the equation for transverse coherence function and allows not only to realize effective numerical algorithms for solution of the given problem but also obtain analytical solutions for inhomogeneous distribution of dielectric constant and gain coefficient in an active medium.3. Our starting point is the paraxial wave equationwhere k is the wave number, ic is the relative perturbation of the complex dielectric constant, P, is the spontaneous polarization , and r (z, p). Let us consider an active medium with relative dielectric constant distribution As(z, p) = s(z, p) + ioz,p) ,where s is the real component and is the imaginary part of the dielectric constant which is connected with the gain coefficient of the medium g by a(z,p) = -k'g(z,p).The form of the functions and c is determined by the spatial distribution of inverse pop...

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Adaptive laser beam projection on an extended target: phase- and field-conjugate precompensation

Vorontsov

Колосов²,

Kohnle³

2007

J. Opt. Soc. Am. A

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The problem of adaptive laser beam projection onto an extended object (target) having a randomly rough surface in an optically inhomogeneous medium (atmosphere) is analyzed. Outgoing beam precompensation is considered through conjugation of either the target-return wave phase or the complex field. It is shown that in the presence of "frozen" turbulence, both phase-conjugate (PC) and field-conjugate (FC) precompensation can result in a superfocusing effect, which suggests the possibility of achieving a brighter target hit spot in volume turbulence than in vacuum. This superfocusing effect is significantly more distinct for FC precompensation. In the quasi-stationary case (slowly moving turbulence or target), PC and FC beam control lead to enhanced intensity fluctuations at the target surface associated with intermittent formation and disintegration of bright target hit spots that sporadically attach to the extended target surface. This intensity fluctuation level exceeds intensity fluctuations in the absence of beam control and is higher for FC precompensation. In the nonstationary case, both PC and FC lead to an increase of beam width and centroid wander at the extended target surface compared with conventional projection of a collimated or focused beam.

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Phase compensation for refractive distortions of partially coherent beams

Cited by 3 publications

References 0 publications

<title>Adaptive focusing of laser radiation onto a rough reflecting surface through the turbulent and nonlinear atmosphere</title>

<title>Adaptive focusing of laser radiation onto a rough reflecting surface through the turbulent and nonlinear atmosphere</title>

<title>X-ray laser coherence in the presence of density fluctuations</title>

Adaptive laser beam projection on an extended target: phase- and field-conjugate precompensation

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