Applied Digital Optics: From Micro-optics to Nanophotonics

Appendix A

Rigorous Theory of Diffraction

A.1 Maxwell's Equations

Light is identified as an electric field and a magnetic field , linked by Maxwell's equations [1]:

where ε is the permittivity tensor and μ is the permeability tensor related to the medium property in which the wave propagates.

If we restrict our analysis to a linear, isotropic but nonhomogeneous media, ε = ε(x, y, z) and μ = μ(x, y, z) are scalar functions depending on position only (time dependence is not considered here). It is then possible to derive equations in which either the or fields appear separately:

A.2 Wave Propagation and the Wave Equation

If we further restrict our analysis to linear, isotropic and homogeneous media, permittivity and permeability are then scalar constants and all gradient functions are null functions. The previous equations then become the vector wave equation:

where v is defined ...