Transverse electric (TE) and transverse magnetic (TM) X-ray guided modes in a two-layer crystalline heterostructure: A comparison

Intensive X-ray standing-wave-like fields localized near a surface of a crystalline superlattice

“…2(b)]. Note that in this study rigorous X-ray dynamical diffraction theory based on the Darwin (1914) recursion equations is employed for numerical simulations (Durbin & Follis, 1995;Takahashi & Nakatani, 1995;Prudnikov, 2012).…”

“…By using the Darwin (1914) approach to X-ray dynamical diffraction, one can obtain the following rigorous expressions for the z-dependent transmitted [E 0 ðzÞ] and diffracted [E g ðzÞ] electric wavefields at the boundary z ¼ l 1 between the film and the SL [see Fig. 1(a); see also the work of Prudnikov (2012) and references therein for details]:…”

“…1a), and 0 are the linear absorption coefficient in the above layer and the real part of an appropriate Fourier coefficient of its polarizability, respectively, P is a standard polarization factor for and polarizations. Equation (2) results from a straightforward generalization of a relevant formula that was obtained in the case of a thin crystalline film sandwiched in between two crystalline cladding slabs (Prudnikov, 2012). A resonant character of the amplitude of the confined standing wave and the distance between its two adjacent nodes, 2=ð2q z Þ, are confirmed by (2).…”

“…It should be remarked that the results of Figs. 2 and 3 were obtained, without loss in generality, with the following structural model: (i) sharp transitions at all the interfaces/boundaries in the multilayer structure and no misfit dislocations; (ii) the unstrained GaAs layers of the SL, including the substrate and a uniform perpendicular strain caused by tetragonal distortion within both the AlAs layers and Al x Ga 1Àx As film [for details see, e.g., Prudnikov (2012) and references therein]. In addition, in Appendix A we briefly discuss the case in which the structure is illuminated by an X-ray beam rather than a plane (monochromatic) wave.…”