Analytical Continuation of the Electromagnetic Field

The problem of analytical continuation lies in extending the electromagnetic field beyond the domain or surface of its initial determination. The general principles underlying analytical continuation of functions of a complex variable are outlined in Chap. 4, while those for an analytical vector field are treated in Sect. 7.1. We will apply these principles to the electromagnetic field. For the sake of simplicity, we will confine ourselves to a monochromatic field, although the results presented below also hold generally good for transient fields.