Operator theory for solving the eigenvalue problem of electromagnetic field

The boundary value problems of electromagnetic fields have been studied intensively but cannot be considered completely solved. In this paper, we explore the solution to the eigenvalue problem of electromagnetic field based on the vector partial differential operator theory. By means of this method, the problem can be separated into two eigenvalue problems of scalar field, which are the projection on the vector wave space. So an exact and accurate analytical or numerical solution to such problems is developed. This method can also be applied for other boundary value problems of electromagnetic fields