ABSTRACT
Light is an electromagnetic wave, and its propagation can be derived from the well-known Maxwell equations, which in their differential form read as:
(5.1)
(5.2)
(5.3)
(5.4)
Here is the current density, and
ρ
is the free charge density. The electric displacement and electric field are connected through the
dielectric tensor as:
(5.5)
The magnetic induction and magnetic field are related through the magnetic permeability tensor as:
(5.6)
Here
µ
=
π
×
N/A
is the permeability of the vacuum. First we assume that there are no free charges (
ρ
=
0), and the material is insulating (DC conductivity
σ
=
0). Assuming also that the material is nonmagnetic (
µ
= 1
), and taking the time derivative of (5.1) and using the relation (5.3), we get:
(5.7)
∇ × − ∂∂ =H D t
j
∇ × + ∂∂ =E B t
∇ ⋅ =D ρ
∇ ⋅ =B 0
j E= σˆ
D E
D Eo= ε εˆ
B
H
B Ho= µ µˆ
∇ × ∂∂ =
∂ ∂
H t
E t
oε εˆ 2
Applying the
curl
operation on Eq.(5.2) and using Eq. (5.6), we arrive at:
(5.8)
This is the basic wave equation. Note that has a dimension of
s
m
,
i.e., the inverse of square of speed. It is customary, therefore, to replace it
with 1/
c
,
where is the velocity of light in vacuum.
