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

Balyan, M. K.

doi:10.1107/s1600577520006724

Cited by 2 publications

(4 citation statements)

References 38 publications

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“…( ) It was shown that in the third-order nonlinear symmetrical Laue case the Pendellösung effect also takes place [30,32]. Here we will show that the Pendellösung effect also takes place in the asymmetrical nonlinear case.…”

Section: Nonlinear Pendellösung Effectmentioning

confidence: 52%

“…The exact solutions for the third-order nonlinear symmetrical Laue diffraction in non-absorbing crystals have been found for forbidden 2h reflection and for an incident plane σ-polarized wave. The deviation from the Bragg exact orientation was set zero [30] and nonzero [32]. As in both cases, here also we will search the exact solution in the form r…”

Section: Exact Solutionmentioning

confidence: 99%

“…Thus the external free parameter is only the incident wave intensity. In [32] an exact solution has been obtained for the Laue symmetrical case taking into account the deviation from the Bragg exact direction. The external free parameters are the deviation from the Bragg exact orientation and the intensity of the incident wave.…”

Section: Introductionmentioning

confidence: 99%

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X-ray third-order nonlinear asymmetric diffraction in the transmission geometry

Balyan¹

2021

Phys. Scr.

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For high intensity x-ray sources, the investigations of the nonlinear x-ray effects become essential. The x-ray third-order nonlinear asymmetric transmission case dynamical diffraction is investigated theoretically in perfect crystals. The three essential input parameters are taken into account: the deviation from the Bragg exact orientation, the asymmetry angle of reflecting atomic planes and the intensity of incident wave. The third-order nonlinear equations for the asymmetrical dynamical diffraction and two integrals of motion are presented. The exact solutions for the wave amplitudes, presented via Jacobi elliptic functions, have been found. The solutions are periodic functions of the depth. It is shown that the behavior of the waves inside the crystal is determined by the sign of a combined parameter, which includes the three input parameters, mentioned above. The regions, where this parameter is positive, negative or zero, are found. For positive values, the energy is concentrated both in the transmitted and diffracted waves while for the negative values, the energy is concentrated mainly in the transmitted beam. It is found that when this combined parameter is zero, the amplitudes are elementary periodic or non-periodic functions. For the periodic solutions, the nonlinear Pendellösung effect takes place, i.e. the transmitted and diffracted waves periodically exchange with their energies. For the period, called an extinction length, an exact expression is found. It is shown that for large values of the asymmetry factor, the observation of the nonlinear diffraction effects can be realized for sufficiently low intensities of the incident wave. The obtained results can be used for experimental investigation of the nonlinear Bragg diffraction and for preparation of high intensity x-ray beams with given parameters. The expression for the nonlinear extinction length allows to estimate the third-order nonlinear susceptibilities of crystals by measuring the extinction length in experiments. RECEIVED

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Section: Nonlinear Pendellösung Effectmentioning

confidence: 52%

Section: Exact Solutionmentioning

confidence: 99%

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X-ray third-order nonlinear asymmetric diffraction in the transmission geometry

Balyan¹

2021

Phys. Scr.

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“…The extension of the linear dynamical diffraction Takagi's equations (Takagi, 1969) for the third-order nonlinear case has been obtained (Balyan, 2015a). The behaviour of the diffracted wavefields in the third-order nonlinear case on the basis of the exact solutions has been theoretically investigated for the symmetric Bragg case (Balyan, 2015b), for the symmetric Laue case (Balyan, 2016a(Balyan, , 2020 and for the asymmetric Laue case (Balyan, 2021). The third-order nonlinear dynamical diffraction of X-ray pulses has been theoretically investigated as well (Balyan, 2016b).…”

Section: Introductionmentioning

confidence: 99%

X-ray third-order nonlinear diffraction in the asymmetric reflection geometry

Balyan¹

2022

Acta Cryst Sect A

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X-ray third-order nonlinear asymmetrical diffraction has three independent parameters: the asymmetry angle, the incident wave intensity and the deviation from the exact Bragg orientation. In contrast to the linear case, in the nonlinear case the total reflection region does not exist for all intensity values and asymmetry angles. Theoretical consideration leads to analytical conditions of the total reflection region, and the analysis can be carried out by a graphical method. An exact solution in the total reflection region is found. The numerical solutions of the third-order nonlinear diffraction allow one to find the reflection curves for a fixed asymmetry angle or for a fixed intensity. For very large or very small asymmetry factors the third-order nonlinear effects can be observed for beams with very low intensities.

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

Cited by 2 publications

References 38 publications

X-ray third-order nonlinear asymmetric diffraction in the transmission geometry

X-ray third-order nonlinear asymmetric diffraction in the transmission geometry

X-ray third-order nonlinear diffraction in the asymmetric reflection geometry

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