Sturm-Liouville Equation: The Bridge between Eigenvalue and Green's Function Problems

Guided wave problems can be grouped into two: eigenvalue (EV) problems (i.e., the effects of the environment on to the propagating waves) and the Green's function (GF) problem (the effects of the excitation in the environment). This chapter reviews guided wave theory (GWT) in one dimension (1D) which is represented by the Sturm-Liouville (SL) equation. In GWT, SL equation establishes a bridge between source-free (homogeneous) and source-driven (nonhomogeneous) wave equations. The GF problem in the physical domain differs from the EV problem due to the presence of the delta function (i.e., source terms) on the right-hand side.