TABLE OF CONTENTS The undulatory nature of light is expressed in terms of an electromagnetic field whose electrical E(r, t) and magnetic H(r, t) components, which depend on time t and space r coordinates, are given by Maxwell equations. The latter can be reduced to the so called master equation, as expressed below (in the case of an isotropic and non-absorbing medium):
where ? is the pulsation, ?(r) the dielectric function of the medium and c the light velocity in vacuum. This is typically an eigenvalue/eigenvector problem.
Optical modes are the eigensolutions of Maxwell equations which correspond to a spatial distribution of the electromagnetic field which is stationary in the time scale.
These are given by the equations which relate the pulsation (eigenvalue) of optical modes to their propagation constants (eigenvector).
This is the simplest case, where the dielectric constant is invariant with space coordinates: the eigensolutions or eigenmodes of Maxwell equations are plane waves, with a continuous transitional symmetry.
The magnetic field (as well as the electric field) can be expressed as follows:
where k is the wave-vector or the propagation constant, with 
, n is the optical index of the medium, and ? is the wavelength. The dispersion characteristics can be simply written as below:
c/n is the phase velocity of the optical mode; in the...
