  In this paper, the scattering/transmission inside a step-modulated
subwavelength metal slit is investigated in detail. We firstly investigate the
scattering in a junction structure by two types of structural changes. The
variation of transmission and reflection coefficients depending on structural
parameters are analyzed. Then a multi-mode multi-reflection model based on ray
theory is proposed to illustrate the transmission in the step-modulated slit
explicitly. The key parts of this model are the multi-mode excitation and the
superposition procedure of the scatterings from all possible modes, which
represent the interference and energy transfer happened at interfaces. The
method we use is an improved modal expansion method (MEM), which is a more
practical and efficient version compared with the previous one [Opt. Express
19, 10073 (2011)]. In addition, some commonly used methods, FDTD, scattering
matrix method, and improved characteristic impedance method, are compared with
MEM to highlight the preciseness of these methods.
