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Рис. 2. Diagrammatic view of
polariton curves in lattice and
exiton spectrum ranges
non-symmetrical crystals may provide
conversion of photons into transverse and
longitudinal lattice excitations of material
media. In the case of spontaneous Raman
scattering, a transformation coefficient at
such a conversion is very low and
constitutes approximately
10
−
6
.
In exciton spectrum band in dielectric
and semiconductor crystals so called
exciton polaritons or transverse and
longitudinal exciton polaritons (TE, LE)
are formed. When both lattice and exciton
polaritons are taken into consideration in
the simplest model, we arrive to the
dispersion law for the transverse waves in
the following form:
ω
2
=
c
2
0
k
2
ε
(
ω
)
=
c
2
0
k
2
(
ω
2
01
−
ω
2
)(
ω
2
02
−
ω
2
)
(
ω
2
l
1
−
ω
2
)(
ω
2
l
2
−
ω
2
)
.
Diagrammatic representation of the dispersion law for lattice and
exciton polaritons is given in Fig. 2. When spatial dispersion is taken into
account, parameters of (2) depend on a wave vector, i.e. can be expressed
as the following functions:
ω
01
=
ω
01
(
k
);
ω
02
=
ω
02
(
k
);
ω
l
1
=
ω
l
1
(
k
);
ω
l
2
=
ω
l
2
(
k
)
.
Let us note that polariton curves (see Fig. 2) have irregularities
corresponding to the so-called unitary polaritons for which
ω
=
с
0
k
,
i.e. the respective index of refraction
n
= 1
.
In material media along with polar (vector) bosons, there are scalar
bosons corresponding to the totally symmetrical (“respiratory”) modes.
According to the selection rules, Raman scattering for scalar bosons is
allowed for many molecular structures both in non-centrosymmetrical
and in centrosymmetrical media. Scalar bosons correspond to the totally
symmetrical oscillations of atoms (ions) in molecules and crystals, as well
as to the shape oscillations of macroparticles, which constitute the material
media. These modes are detected in spectra of the inelastic scattering
of light in the form of additional sattelites defined by the “particular”,
especially, globular light scattering.
At present, photon crystals are of particular interest for the research
[7, 8], these crystals feature a superstructure with a period congruent to
the visible spectrum electromagnetic wave length. In particular, globular
ISSN 1812-3368. Herald of the BMSTU. Series “Natural Sciences”. 2015. No. 1
39