[en] In this paper, using a quantum mechanical technique and introducing the so-called V representation (where the representation transformation is made by using the potential Hamiltonian V), we studied x-ray propagation in a linear plasma medium both analytically and numerically. A modified relation between the phase of the probe and the reference light and the electron density of the plasma is derived, in which the contribution of the gradient of the electron density has been taken into account. It is shown that this relation has the advantage in measurements of the electron density of a plasma using the x-ray interferometry technique of lessening the errors originating from the electron density gradient. The validity of x-ray interferometry is discussed in both mathematical and physical terms

[en] In this Letter a four-cornered two-waveguide-connected network (FCTWCN) is proposed to generate comb-like optical transmission spectrum, where nearest-neighbor nodes are connected by two segments of one-dimensional waveguides. We investigate the band structure and transmission spectrum of electromagnetic waves propagating through FCTWCNs and find that the transmission through a FCTWCN exhibits periodic comb-like characteristic and the range, number and width of continuous equidistant frequency bands can be controlled by adjusting the lengths of the two types of segments. The comb-like frequency bands may be useful for the designing of optical switches, optical narrowband filters, high capacity telecommunications, and multichannel filters, etc.