Transport equations of amplitudes in the eikonal approximation of dynamical diffraction equations

Balyan, M. K.

doi:10.3103/s1068337213010088

Cited by 3 publications

(9 citation statements)

References 3 publications

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“…Work [10] gives the eikonal approximation to dynamical diffraction equations where the second yderivatives are preserved. In work [11] the retarded Green function was found for dynamical diffraction equations with second y-derivatives of amplitudes in a perfect crystal. Solutions for amplitudes inside the perfect crystal is represented via convolution of amplitudes with Green function on the crystal surface.…”

Section: Introductionmentioning

confidence: 99%

“…It should be noted that here the existence of a single carrier wave with divergence in both mutually-perpendicular planes is assumed, which is distinct from the dynamical diffraction of a strongly divergent beam considered in [4,5]. In [12] the representation obtained in [11] was employed for revealing the influence of second derivatives of amplitudes on Laue diffraction in a perfect crystal with plane entrance and exit surfaces, as well as for estimations of spatial and temporal coherence of beams in considered case.…”

Section: Introductionmentioning

confidence: 99%

“…In the present work, the solution representation of [11] is applied to study the influence of second derivatives of amplitudes on Bragg diffraction in a perfect crystal with plane entrance surface, as well as for estimations of spatial and temporal coherence of beams in considered case. Beam divergence is taken into account in both the diffraction plane and the perpendicular direction and the source-crystal distance is allowed for.…”

Section: Introductionmentioning

confidence: 99%

“…In a perfect crystal, in conditions of two-wave dynamical diffraction, amplitudes, E 0 and E h , of transmitted and diffracted waves may, with preserving the second y-derivative of amplitudes, represented, according to [11], in the form…”

Section: Introductionmentioning

confidence: 99%

“…It is suitable now to pass in these integrals to the coordinate system Os h ys 0 , where s 0 and s h are coordinates along the transmitted and diffracted waves respectively. For this purpose, we note [11] that these integrals were obtained by integration over the volume element dX 'dy 'dX ' with subsequent use of Gauss theorem. These volume elements will pass into sin2θds' 0 ds' h dy'.…”

Section: Introductionmentioning

confidence: 99%

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X-ray Bragg diffraction with allowance for the second derivatives of amplitudes in dynamical diffraction equations

Balyan

2014

J. Contemp. Phys.

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Abstract⎯Asymmetrical Bragg diffraction in a perfect crystal with plane entrance surface is considered theoretically. In the dynamical diffraction equations the second derivatives of amplitudes in the direction, perpendicular to the diffraction plane are taken into account. Using the corresponding Green function, a general form for the amplitudes of waves in the crystal is presented. The sizes of the source in both directions as well as the source-crystal distance and non-monochromaticity of the radiation incident on the crystal are taken into account. On the basis of obtained formulas, the coherent properties of the field depending on the sizes of the source and on the width of spectrum of the incident radiation, are analized.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

X-ray Bragg diffraction with allowance for the second derivatives of amplitudes in dynamical diffraction equations

Balyan

2014

J. Contemp. Phys.

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Relativistically exact eikonal equation for optical fibers with application to adiabatically deforming ring interferometers

Avron

Kenneth

2016

Phys. Rev. A

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We derive the relativistically exact Eikonal equation for ring interferometers undergoing deformations. For ring interferometers that undergo slow deformation we describe the two leading terms in the adiabatic expansion of the phase shift. The leading term is independent of the refraction index n and is given by a line integral generalizing results going back to Sagnac [21,28,18] for non-deforming interferometers to all orders in β = |v|/c. In the non-relativistic limit this term is O(β). The next term in the adiabaticity has the form of a double integral, it is of order β 0 and depends on the refractive index n. It accounts for non-reciprocity due to changing circumstances in the fiber. The adiabatic correction is often comparable to the Sagnac term. In particular, this is the case in Fizeau's interferometer. Besides providing a mathematical framework that puts all ring interferometers under a single umbrella, our results generalize and strengthen results of [18,24] to fibers with chromatic dispersion.

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Theoretical consideration of an X-ray Bragg-reflection lens using the eikonal approximation

Balyan

2014

J Synchrotron Radiat

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On the basis of the eikonal approximation, X-ray Bragg-case focusing by a perfect crystal with parabolic-shaped entrance surface is considered theoretically. Expressions for focal distances, intensity gain and distribution around the focus spot as well as for the focus spot sizes are obtained. The condition of point focusing is presented. The experiment can be performed using X-ray synchrotron radiation sources (particularly free-electron lasers).

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Transport equations of amplitudes in the eikonal approximation of dynamical diffraction equations

Cited by 3 publications

References 3 publications

X-ray Bragg diffraction with allowance for the second derivatives of amplitudes in dynamical diffraction equations

X-ray Bragg diffraction with allowance for the second derivatives of amplitudes in dynamical diffraction equations

Relativistically exact eikonal equation for optical fibers with application to adiabatically deforming ring interferometers

Theoretical consideration of an X-ray Bragg-reflection lens using the eikonal approximation

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