Slot antenna on a photonic crystal substrate Green's functions study

A magnetic field Green's function expressed as an eigenmodes expansion and based on the plane wave method (PWM) is formulated first for an infinite magnetic current line embedded in an unbounded two-dimensional (2D) photonic crystal (PC) and then for a magnetic dipole embedded in a 2D PC truncated by two metallic plates. The underlying idea of analyzing a slot antenna printed on a 2D PC with a standard method of moment (MoM) through the principle of equivalence is shown to motivate the present investigation. A complete solution for the line problem is derived, whereas the inadequacy of the method in its present form for the dipole problem is demonstrated rigorously. Numerical results of the Green's function for the first problem are shown for different positions of the source, and a discussion about radiation patterns, asymptotic behaviors and convergence problems of the Green's function is proposed.