300
9 Optical Properties
0
5 0
25
GaAs
75
Fig. 9.51 Far-infrared absorption (linear scale) of GaAs. In the region around 35 meV is the reststrahlenbande with high
absorption due to optical phonons. The sharp little peak at 45 meV is a LVM, probably from Al Ga . Adapted from [935]
the reflectance (9.17) will be close to 1. This energy range is the so-called reststrahlenbande. This
term stems from multiple reflections in this wavelength regime that suppresses neighboring spectral
regions and thus achieves a certain monochromatization in the far-infrared spectral region. Within the
semiconductor the absorption is large in the reststrahlenbande (Fig. 9.51).
9.10.3 Polaritons
The coupled propagation of phonons and electromagnetic radiation is (without phonon damping)
related to the dielectric function given in (9.27),
=
ω
2
LO − ω
2
ω
2
TO − ω 2
=
c
2 k
2
ω 2 .
(9.87)
There are two branches of propagating waves (real k):
ω
2
=
1
2
ω
2
LO +
c
2 k
2
(∞)
±
1
4
ω
2
LO +
c 2 k 2
(∞)
2
−
c 2 k 2 ω
2
TO
(∞)
2
.
(9.88)
For k = 0 we find the solutions ω = ω LO and ω = k c/
√ (0). For large k we find ω = ω TO
and ω = k c/
√ (∞). These solutions are shown in Fig. 9.52. Both branches have a phonon- and a
photon-like part. The coupled state between the phonon and the photon field is called the (phonon-)
polariton.
In the interval [ω TO , ω LO ] the wavevector is purely imaginary, i.e. k = i ˜
k with real ˜
k. For this case
there is only one solution that is also depicted in Fig. 9.52,
ω
2
=
1
2
ω
2
LO +
c
2 ˜
k
2
+
1
4
ω
2
LO +
c 2 ˜
k 2
(∞)
2
+
c 2 ˜
k 2 ω
2
TO
(∞)
2
.
(9.89)
9.10.4 Phonon–Plasmon Coupling
The coupling of phonons and plasmons in the spectral region of the reststrahlenbande leads to the
development of two new branches, the longitudinal phonon plasmon modes (LPP+ and LPP−), in the
9 Optical Properties
0
5 0
25
GaAs
75
Fig. 9.51 Far-infrared absorption (linear scale) of GaAs. In the region around 35 meV is the reststrahlenbande with high
absorption due to optical phonons. The sharp little peak at 45 meV is a LVM, probably from Al Ga . Adapted from [935]
the reflectance (9.17) will be close to 1. This energy range is the so-called reststrahlenbande. This
term stems from multiple reflections in this wavelength regime that suppresses neighboring spectral
regions and thus achieves a certain monochromatization in the far-infrared spectral region. Within the
semiconductor the absorption is large in the reststrahlenbande (Fig. 9.51).
9.10.3 Polaritons
The coupled propagation of phonons and electromagnetic radiation is (without phonon damping)
related to the dielectric function given in (9.27),
=
ω
2
LO − ω
2
ω
2
TO − ω 2
=
c
2 k
2
ω 2 .
(9.87)
There are two branches of propagating waves (real k):
ω
2
=
1
2
ω
2
LO +
c
2 k
2
(∞)
±
1
4
ω
2
LO +
c 2 k 2
(∞)
2
−
c 2 k 2 ω
2
TO
(∞)
2
.
(9.88)
For k = 0 we find the solutions ω = ω LO and ω = k c/
√ (0). For large k we find ω = ω TO
and ω = k c/
√ (∞). These solutions are shown in Fig. 9.52. Both branches have a phonon- and a
photon-like part. The coupled state between the phonon and the photon field is called the (phonon-)
polariton.
In the interval [ω TO , ω LO ] the wavevector is purely imaginary, i.e. k = i ˜
k with real ˜
k. For this case
there is only one solution that is also depicted in Fig. 9.52,
ω
2
=
1
2
ω
2
LO +
c
2 ˜
k
2
+
1
4
ω
2
LO +
c 2 ˜
k 2
(∞)
2
+
c 2 ˜
k 2 ω
2
TO
(∞)
2
.
(9.89)
9.10.4 Phonon–Plasmon Coupling
The coupling of phonons and plasmons in the spectral region of the reststrahlenbande leads to the
development of two new branches, the longitudinal phonon plasmon modes (LPP+ and LPP−), in the