X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

Balyan, M. K.

doi:10.1134/s106377451607004x

Cited by 5 publications

(10 citation statements)

References 9 publications

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“…In a non-absorbing crystal (weak absorption) one can put = 0. Two integrals of motion of the system (9) can be found in non-absorbing crystals (Balyan, 2015a(Balyan, , 2016b,…”

Section: Theorymentioning

confidence: 99%

“…Our purpose is to find the exact solution of the system (9) using the boundary conditions (10) and the integrals of motion (11). The exact solution has been found by Balyan (2016b) for the case p = 0 (exact Bragg orientation, i.e. Á = 0) and for a forbidden 2h reflection, when 2h;2 " h h = 0, 2h;2 " h h = 0.…”

Section: Exact Solutionmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

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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“…In a non-absorbing crystal (weak absorption) one can put = 0. Two integrals of motion of the system (9) can be found in non-absorbing crystals (Balyan, 2015a(Balyan, , 2016b,…”

Section: Theorymentioning

confidence: 99%

Section: Exact Solutionmentioning

confidence: 99%

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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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“…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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“…X-ray dynamical diffraction is described by Takagi's equations [1]. In the wave equation, replacing the linear susceptibility by the third-order nonlinear one, the stationary and time dependent nonlinear Takagi's equations (NTE) are established [2][3][4][5][6] and third-order nonlinear stationary and time-dependent effects are investigated. In [7], using cold plasma model, the linear dynamical diffraction of the formed X-ray second-order harmonic in a perfect crystal under two wave diffraction conditions has been studied.…”

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confidence: 99%

X-Ray Third-Order Nonlinear Renninger Effect and Rocking Curves

Balyan

2017

Proc. YSU A: Phys. Math. Sci.

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In the work third-order nonlinear Takagi’s equations for X-ray monochromatic waves are investigated for the forbidden reflection case. The forbidden dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations of the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third-order nonlinear susceptibility. As a consequence, in the third-order nonlinear Bragg diffraction case, a nonlinear analogue of the well known Renninger effect takes place, which is considered theoretically and numerically. The numerical calculations show that in the Bragg geometry the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves are by several orders more sensitive to the input intensity value.

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X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

Cited by 5 publications

References 9 publications

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

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

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

X-Ray Third-Order Nonlinear Renninger Effect and Rocking Curves

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