Wave equation in dielectric media

Wave equation in dielectric media

A perfect dielectric medium is defined as a material in which the conductivity is σ = 0.
In this category fall most of the substrate materials used for integrated optical devices,
such as glasses, ferro-electric crystals or polymers, while metals do not belong to this
category because of their high conductivity. Then, for dielectric media (σ = 0) the
wave equations simplify on the forms:



where we have introduced the magnitude relative dielectric permittivity εr, also often
called dielectric constant, defined as the relation between the dielectric permittivity of
the material medium and that of the free space. Table 2.1 summarises the refractive
indices of the most relevant materials used in integrated photonic technology. Besides
the refractive index of 1 corresponding to propagation through the free space, as can
be seen in the Table 2.1 the refractive index ranges from values close to 1.5 for glasses
and some dielectric crystals to values close to 4 for semiconductor materials.



Glass (BK7) 1.51 633
Glass (ZBLAN) 1.50 633
Polymer (PMMA) 1.54 633
Silica (amorphous SiO2) 1.45 633
Quartz (SiO2) 1.55 633
Silicon nitride (Si3N4) 2.10 633
Calcium fluoride (CaF2) 1.43 633
Lithium niobate (LiNbO3) 2.28 (no) 633
2.20 (ne)
Silicon (Si) 3.75 1300
Gallium arsenide (GaAs) 3.4 1000
Indium phosphide (InP) 3.17 1510




The fact of using an averaged value instead of an instant value to define the intensity
of an EM wave is because, as we will see in the next section, the electric and magnetic
fields associated with the EM wave oscillate at very high frequency, and the apparatus
used to detect that intensity (light detectors) cannot follow the instant values of the
Poynting vector modulus.