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

The transfer-matrix methodology is frequently used to deal with elastic sca ttering 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 ma trices. This paper extends the transfer-matrix methodology to enable consid eration 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 d ependence of the long-range angular spread on the aperture radius, by highl ighting the effects of the field-emission tip shape and dimensions.