Geodesic
$\mathrm{X}$-ray third-order nonlinear Renninger effect and rocking curves
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 1, pp. 85-88 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the work third-order nonlinear Takagi’s equations for $\mathrm{X}$-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.
Keywords: third-order nonlinearity, Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, rocking curves. 
@article{UZERU_2017_51_1_a14,
     author = {M. K. Balyan},
     title = {$\mathrm{X}$-ray third-order nonlinear {Renninger} effect and rocking curves},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {85--88},
     year = {2017},
     volume = {51},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a14/}
}
TY  - JOUR
AU  - M. K. Balyan
TI  - $\mathrm{X}$-ray third-order nonlinear Renninger effect and rocking curves
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2017
SP  - 85
EP  - 88
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a14/
LA  - en
ID  - UZERU_2017_51_1_a14
ER  - 
%0 Journal Article
%A M. K. Balyan
%T $\mathrm{X}$-ray third-order nonlinear Renninger effect and rocking curves
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2017
%P 85-88
%V 51
%N 1
%U http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a14/
%G en
%F UZERU_2017_51_1_a14
M. K. Balyan. $\mathrm{X}$-ray third-order nonlinear Renninger effect and rocking curves. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 1, pp. 85-88. http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a14/

[1] S. Takagi, “A Dynamical Theory of Diffraction for a Distorted Crystal”, J. Phys. Soc. Jpn., 26 (1969), 1239–1253 | DOI

[2] M.K. Balyan, “$\mathrm{X}$-ray Third-Order Nonlinear Dynamical Diffraction in a Crystal”, Crystallography Reports, 60 (2015), 993–1000 | DOI

[3] M.K.Balyan, “$\mathrm{X}$-ray Third-Order Nonlinear Plane-Wave Bragg-Case Dynamical Diffraction Effects in a Perfect Crystal”, J. Synchrotron Rad., 22 (2015), 1410–1418 | DOI

[4] M.K. Balyan, “Third-Order Nonlinear and Linear Time-Dependent Dynamical Diffraction of $\mathrm{X}$-rays in Crystals”, J. Synchrotron Rad., 23 (2016), 919–928

[5] M.K. Balyan, “Diffraction of $\mathrm{X}$-ray Spatially Inhomogeneous Beam in a Crystal with Cubic Nonlinearity”, Journal of Contemp. Phys. (Armenian Ac. Sci.), 51 (2016), 391–397 | DOI

[6] M.K. Balyan, “$\mathrm{X}$-ray Plane Wave Dynamical Diffraction Effects in a Crystal with Third-Order Nonlinearity”, Crystallography Reports, 61 (2016), 1039–1046 | DOI

[7] A. Nazarkin, S. Podorov, I. Uschmann, E. Forster, R. Sauerbrey, “Nonlinear Optics in the Angstrom Regime: Hard- $\mathrm{X}$-ray Frequency Doubling in Perfect Crystals”, Phys. Rev. A, 67 (2003), 041804 (R) | DOI

[8] K.Tamasaku, T. Ishikawa, “Idler Energy Dependence of Nonlinear Diffraction in $X\to X +EUV$ Parametric Down-Conversion”, Acta Cryst. A, 63 (2007), 437–438 | DOI

[9] K.Tamasaku, T. Ishikawa, “Interference Between Compton Scattering and $\mathrm{X}$-ray Parametric Down-Conversion”, Phys. Rev. Lett., 98 (2007), 244801 | DOI

[10] C. Conti, A. Fratalotcchi, G. Ruocco, F. Sette, “Nonlinear Optics in the $\mathrm{X}$-ray Regime: Nonlinear Waves and Self-Action Effects”, Optics Express, 16 (2008), 8324–8331 | DOI

[11] A. Authier, Dynamical Theory of $\mathrm{X}$-ray Diffraction, Oxford University Press, UK, 2001

[12] R.W. Boyd, Nonlinear Optics, Academic Press, NY, 2003 | MR