Light is a propagating
electromagnetic wave, i.e. a wave that is composed of two oscillating fields -
one of them is electric and the other magnetic.
For simplicity, here, we will consider only the electric field. For a light wave
propagating along the positive Cartesian z direction, its oscillation can then
be expressed by a cosine function:
(Eq.1.1)
where
A is the amplitude of the wave, z is the spatial coordinate, t
is time, k is the wave number and w
is the angular frequency. The wave number is defined as k = 2p
/ l and ensures that, at any fixed time, the spatial representation
of the wave will have a periodicity of l, that
is, the wavelength of light. The angular frequency
w=2p / T
ensures that at any given location, the number of radians of the wave per
unit time correspond to the light wave period(T). The ratio
l/T is the speed at which the shape of
the wave is moving, i.e., the speed at which any fixed phase of the cycle is
displaced. Hence it is called the phase velocity and is denoted by vP.
Consequently, vP = w / k. The
minus sign in Eq.1 means that if we hold t constant and increase z
we are moving towards the positive z direction along the cosine function,
whereas if we focus on a fixed spatial location and allow time to increase, we
are effectively moving towards the negative z direction along the
function (or rather, the function is moving towards the positive z and we are
stationary).
In figure 1 it is shown that linearly polarized light
(blue arrow) can be represented as a combination of left (s
-) and right (s +) circularly polarized light (black arrows). As you can see, the
latter have equal amplitudes and angular velocities.
Fig. 1 Linearly polarized light as a combination of left (s
-) and right (s +
) circularly polarized light.
When light encounters a
material medium, it interacts with the electric fields in the atoms and
molecules. As a result the electromagnetic wave is affected by a quantity known as the
complex
refractive index. This is a complex number defined by
where the real part is called the refractive index while the
imaginary part is the extinction coefficient. Physically,
k corresponds to a measure of how much
a substance scatters and absorbs electromagnetic radiation and affects A
in Eq.1.
As for n, it indicates the reduction of the speed of light in the
material.
Depending on the particular material, light can interact with either n, or
k , or both.
