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 | JOURNAL OF SYNCHROTRON RADIATION |
X-ray third-order nonlinear plane-wave Bragg-case effects in a perfect crystal. Erratum
aFaculty of Physics, Department of Solid State Physics, Yerevan State University, Alex Manoogian 1, Yerevan 0025, Armenia
*Correspondence e-mail: mbalyan@ysu.am
Formulae in the paper by Balyan (2015) [J. Synchrotron Rad. 22, 1410–1418] are corrected.
Keywords: nonlinear diffraction; Bragg case; reflection region; third-order nonlinearity; two-wave diffraction.
The formulae (2) and (4) in the paper Balyan (2015![[Balyan, M. K. (2015). J. Synchrotron Rad. 22, 1410-1418.]](../../../../../../logos/arrows/s_arr.gif "Balyan, M. K. (2015). J. Synchrotron Rad. 22, 1410-1418.")
) have the same essential typographical error. The correct forms of these equations are
![[{\rm{rot\,rot\,}}\,{\tilde{\tilde{\bf{E}}}} + {1\over{{c^2}}} {{ {\partial^2}{\tilde{\tilde{\bf{E}}}}}\over{{\partial{t^2}}}} = -{1\over{{{{\varepsilon}}_0}{c^2}}} {{{\partial^2}{\tilde{\tilde{\bf{P}}}}} \over {\partial{t^2}}} \eqno(2)]](teximages/mo5143fd1.gif)
and
![[{\rm{rot\,rot\,}}\,{\tilde{\bf{E}}}({\bf{r}},{\omega_q})- {{\omega_q^2}\over{{c^2}}} \left[1 + {\chi ^{(1)}}({\bf{r}},{\omega _q})\right]{\tilde{\bf{E}}}({\bf{r}},{\omega _q}) = {{\omega _q^2} \over {{{\rm{\varepsilon }}_0}{c^2}}}{\tilde{\bf{P}}}_{}^{\rm NL}({\bf{r}},{\omega _q}). &\quad(4)}]](teximages/mo5143fd2.gif)
In the same paper, the formulae (17) and (19) are also incorrect. The correct forms of these equations are
![[{E^{\,(i)}}(x,0) = E_0^{\,(i)}\exp (ik\cos {{\rm{\theta }}^{\,(i)}}x) \eqno(17)]](teximages/mo5143fd3.gif)
and
![[\eqalign{ {E_0}(x,0) & = E_0^{\,(i)}\exp (-ik\sin {\rm{\theta }}\,\Delta {\rm{\theta }}x), \cr {E_h}(x,T)& = 0.}\eqno(19)]](teximages/mo5143fd4.gif)
These equations are used for derivation of the third-order nonlinear Takagi's equations.
References
Balyan, M. K. (2015). J. Synchrotron Rad. 22, 1410–1418. Google Scholar
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