Fn. Chukhovskii et E. Forster, TIME-DEPENDENT X-RAY BRAGG-DIFFRACTION, Acta crystallographica. Section A, Foundations of crystallography, 51, 1995, pp. 668-672
The theory of time-dependent X-ray Bragg diffraction by crystals is de
veloped on the basis of the Green-function (point-source) formalism. A
general case of incident radiation partially coherent in time and spa
ce is considered. The time-delay effect of the diffracted radiation is
described when the ultrashort time duration incident pulse strikes th
e crystal surface. The problem in question is closely connected with t
he effect of time delay in the resonance scattering of synchrotron rad
iation by nuclei in a crystal. It is found that, for the case where th
e incident wave is plane (or is an incoherent superposition of plane w
aves) and the time-dependent pulse is a pseudo delta function in time,
the instantaneous crystal reflectivity is a smooth temporal function
and tends to the value corresponding to the integrated reflectivity ca
lculated by means of the conventional dynamical-kinematical X-ray diff
raction theory. If the incident X-ray pulse profile is a pseudo delta
function in both time and space, the temporal crystal response has the
same functional dependence as the spatial distribution of the diffrac
ted intensity under the condition of conventional Bragg diffraction of
the X-ray beam with lateral width < t(o)c, where the time delay t(o)
is equal to Lambda/2 pi c and (mu(o)c)(-1) in the cases of dynamical a
nd kinematical X-ray scattering within a crystal respectively (Lambda
is the X-ray extinction length, mu(o), is the linear absorption coeffi
cient and c is the velocity of light in vacuum).