Electromagnetic Wave Source Conditions

This chapter discusses the relationships between current sources and the resulting electromagnetic waves in FDTD simulations. First, the "total-field/scattered-field" approach to creating incident plane waves is reviewed and seen to be a special case of the well-known principle of equivalence in electromagnetism: this can be used to construct "equivalent" current sources for any desired incident field, including waveguide modes. The effects of dispersion and discretization are discussed, and a simple technique to separate incident and scattered fields is described in order to compensate for imperfect equivalent currents. The important concept of the local density of states (LDOS) is reviewed, which elucidates the relationship between current sources and the resulting fields, including enhancement of the LDOS via mode cutoffs (Van Hove singularities) and resonant cavities (Purcell enhancement). We also address various other source techniques such as covering a wide range of frequencies and incident angles in a small number of simulations for waves incident on a periodic surface, sources to excite eigenmodes in rectangular supercells of periodic systems, moving sources, and thermal sources via a Monte Carlo/Langevin approach.