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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