An orthogonal Relation for Electromagnetic Fields in Two-Dimensional Multilayered Dispersive Dielectric Medium Including Evanescent Fields

A new method is developed to derive an orthogonal relation for electromagnetic fields in two-dimensional multilayered dispersive dielectric media. The orthogonal relation holds between the fields with two different wave vectors, where evanescent fields appear when the total reflection condition is satisfied at the boundary between different media. By means of the derived orthogonal relations, we show that the mode expansion of the total field energy, including evanescent waves, reduces to the sum of the energies of independent harmonic oscillators.