X-ray third-order nonlinear plane-wave Bragg-case dynamical diffraction effects in a perfect crystal

Balyan, M. K.

doi:10.1107/s1600577515017804

Cited by 10 publications

(14 citation statements)

References 11 publications

(16 reference statements)

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“…À k(3!). As already shown (Balyan, 2015b), due to this phase mismatch the intensity of the third-harmonic is small and can be neglected. The second essential effect is connected to the tensor…”

Section: Introductionmentioning

confidence: 79%

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Investigation of third-order nonlinear dynamical X-ray diffraction based on a new exact solution

Balyan

2020

J Synchrotron Radiat

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Third-order nonlinear two-wave dynamical X-ray diffraction in a crystal is considered. For the Laue symmetrical case of diffraction a new exact solution is obtained. The solution is presented via Jacobi elliptic functions. Two input free parameters are essential: the deviation parameter from the Bragg exact angle and the intensity of the incident wave. It is shown that the behavior of the field inside the crystal is determined by the sign of a certain combination of these parameters. For negative and positive signs of this combination, the wavefield is periodic and the nonlinear Pendellösung effect takes place. For the nonlinear Pendellösung distance the appropriate expressions are obtained. When the above-mentioned combination is zero, the behavior of the field can be periodic as well as non-periodic and the solution is presented by elementary functions. In the nonperiodic case, the nonlinear case Pendellösung distance tends to infinity. The wavefield diffracts and propagates in a medium, whose susceptibility is modulated by the amplitudes of the wavefields. The behavior of the wavefield can be described also by an effective deviation from the Bragg exact angle. This deviation is also a function of the wavefields.

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Section: Introductionmentioning

confidence: 79%

“…the third-order nonlinear dynamical diffraction of hard X-rays in crystals, has been considered by Balyan (2015aBalyan ( ,b, 2016a. An exact solution in a nonabsorbing crystal and for the exact Bragg angle was obtained for the symmetrical Laue case by Balyan (2016b), and for the symmetrical Bragg case by Balyan (2015b).…”

Section: Introductionmentioning

confidence: 99%

Investigation of third-order nonlinear dynamical X-ray diffraction based on a new exact solution

Balyan

2020

J Synchrotron Radiat

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“…DOI:10.54503/0002-3035-2022-57. Для случая симметричного отражения по Брэггу точное решение найдено в работе [4]. Точное решение в случае Лауэ, учитывающее отклонение от угла Брэгга, а так же асимметричность дифракции, найдено в работе [5].…”

Section: Introductionunclassified

Кривые Качания Рентгеновской Асимметричной Лауэ Дифракции В Кристалле С Кубически-Нелинейным Откликом

Балян¹

2022

Proceedings of NAS RA. Physics

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Рассмотрена рентгеновская асимметричная Лауэ дифракция в идеальном кристалле с плоской входной поверхностью с учетом кубически-нелинейного отклика кристалла. С использованием точных решений изучены кривые качания в зависимости от угла отклонения от точного направления Брэгга и от интенсивности падающей волны. Исследована зависимость кривых качаний от степени асимметричности геометрии дифракции. Полученные результаты, являясь одним из важных характеристик нелинейной динамической дифракции, могут быть использованы для получения интенсивных рентгеновских пучков с заданными параметрами, а так же для исследования объектов и кристаллических деформаций.

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“…The formulae (2) and (4) in the paper Balyan (2015) have the same essential typographical error. The correct forms of these equations are…”

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confidence: 97%