Figure 73: a) electron in ionic crystal (KCL). Forces are symbolized by arrows. b) Electron in a
kind of equilibrium. The ions change there position so the effective mass of the electron
increases
11.3.2 Polaritons
A polariton is a combined wave between light and sound. In fig. 74(a) the photon dispersion is drawn
into a plot of the phonon dispersion. As you can see, the photon dispersion crosses the optical phonon
branch close tok= 0. At this point photons and phonons have the same wavelength and frequency
and thus the same energy. At this point, the optical phonons will couple to the photons and this
coupling is described by a polariton. Polaritons can only occur in materials where there more than
two atoms per unit cell, otherwise there would not be any optical phonons!
We will start the calculation to couple light and sound with Maxwell’s equation for light propagating
in a medium:
∇^2 E=μ 0
δ^2 D
δt^2, (125)
assuming a plane wave we get
k^2 E=μ 0 ω^2 (ε 0 E+P). (126)