Nonsquare transfer-matrix technique applied to the simulation of electronic diffraction by a three-dimensional...

The transfer-matrix methodology is frequently used to deal with elastic scattering problems that require a solution of the Schrodinger or homogeneous Maxwell equations in the continuous part of their spectra. Until now, this technique was limited to representations associated with square transfer matrices. This paper extends the transfer-matrix methodology to enable consideration of general representations associated with nonsquare matrices. The theory is illustrated by the diffraction of a field-emitted electronic beam by a three-dimensional circular aperture. The application focuses on the dependence of the long-range angular spread on the aperture radius, by highlighting the effects of the field-emission tip shape and dimensions.