Boundary conditions: An effect of average of microscopic Maxwell' s equations

摘要

It is well known that the macroscopic Maxwell' s equations can be obtained from the corresponding microscopic or atomic equations by a proper averaging process. The purpose of this paper is to present the macroscopic Maxwell' s equations which are valid in all regions of space, including an interface between two different media; and the boundary conditions can naturally emerge from the macroscopic equations as an effect of average of the microscopic Maxwell' s equations. In addition, the application of the unit step functions and the Di-rac delta function to our discussion not only permits great mathematical simplicity but also gives rise to convenient physical concepts for the description and representation of the actual fields in the vicinity of the interface.