9.10 Lattice Absorption
301
Fig. 9.52 Dispersion of the polariton. The dotted line displays the dispersion for a purely imaginary wavevector with
the absolute value k
(a)
(b)
Fig. 9.53 a Frequency of the coupled longitudinal-phonon plasmon (LPP) modes (lower (upper) polariton branch in
blue (red)) as a function of the plasma frequency. Dashed line shows uncoupled plasmon frequency (ω = ω p ), grey area
indicates spectral region between TO and LO modes. b Experimental data on the polariton energies in n-type GaAs with
different carrier concentration ω p ∝
√
n m ∗ (9.77). Dashed (dash-dotted) line is plasmon frequency ω p without (with)
consideration of conduction band non-parabolicity (cf. Fig. 6.37b). Data from [918, 936]
common dispersion. The dielectric function is
=
1 +
ω
2
LO − ω
2
ω
2
TO − ω 2 −
ω
2
p
ω 2
.
(9.90)
For = 0 for k = 0 (coupling to photons) the two solutions ω LPP+ and ω LPP− do not cross as a
function of ω p (Fig. 9.53),
ω LPP± =
1
2
ω
2
LO + ω
2
p ±
(ω
2
LO + ω 2
p ) 2 − 4 ω
2
TO ω 2
p
.
(9.91)
For small plasma frequencies ω LPP+ = ω LO , i.e. the optical phonons couple to the electromagnetic
field without change. Also ω LPP− = ω p . For large carrier density, i.e. ω p ω LO , we find ω LPP− = ω TO
and ω LPP+ = ω p . Thus, the carriers have effectively screened the electric field of the phonon that had
led to the increase of the TO to the LO frequency.