A dielectric material is characterized
by its refractive index n(n) = c0/c(n) where c(n) is the phase
velocity of the monochromatic light component of frequency n. The
propagation constant b(n) = n(n)×k is then frequency dependent and can be expressed as
|
(4-15) |
For a stationary light wave for which
the electrical field function E(t) is known at a position z = 0, the
same field at position z is given by
|
(4-16) |
where the phase term f(n) from equation
(4-6) has been omitted.
In most cases, the spectral width Dn is small
enough to allow a limited development at the first or at the second order of b around the central frequency n0
|
(4-17) |
The group velocity vg that
corresponds to the propagation velocity in a dielectric material of a light
pulse centered at a frequency n is defined as
|
(4-18) |
and the dispersion coefficient Dn
|
(4-19) |
The equation (4-17) can then be
written as
|
(4-20) |
where the group
velocity and dispersion coefficients are defined at n0. Since b(n0) = k(n0)×n(n0), the equation (4-20) can be
expressed as
|
(4-21a)
(4-21b) |
where k0 = k(n0) and ng is the group refractive index defined from the
group velocity as
|
(4-22) |
|
