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Рис. 3. Globular photonic crystals

formed on the base of artificial opals (

a

)

and a photografic image of surface (111)

of a globular photonic crystal, obtained

by the electron microscope (

b

)

photon crystals can be formed with

dense packing of the dielectric balls

(globules) having the same size

which lies within the range of 200. . .

. . . 800 nm (Fig. 3). In the spectrum

of the photon crystal elementary

excitations, additional frequencies

corresponding to “respiratory”

oscillations of the globules making

up the crystal. In the Raman

scattering spectrum such oscillations

give rise to the so-called boson

peak. The analysis of the Raman

scattering spectra determined by the

“respiratory” modes of the globules

(spectra of the “particular” light

scattering) provides calculation of

the frequencies for these oscillations,

their damping, and distribution of the

globules according to their sizes.

Dispersion curves of the

electromagnetic waves derived for

the globular photon crystal, having a

globular size of 250 nm are presented

in Fig. 4. According to the figure, the dispersion law of the electromagnetic

waves in the photon crystal differs substantially from that in the vacuum

one.

Dispersion curves correspond to photon-like bosons. At the same time,

in the range of the small-wave vectors near the Brillouin zone boundary,

the dispersion law for such bosons for the third and second dispersion

branches can be approximated by the quasi-relativistic equations:

ω

2

3

=

ω

2

0

+

S

2

k

2

;

ω

2

2

=

ω

2

0

S

2

k

2

;

ω

2

2

=

ω

2

2

b

+

c

2

χ

2

;

χ

=

π

a

k.

At the same time, curve

2

(see Fig. 4) features a negative index of refraction,

since in this case, group and phase velocities have opposite directions.

Photons in photon crystals have non-zero effective rest mass, either positive

or negative. Unitary photons corresponding to the second dispersion curve

(see Fig. 4) have a negative index of refraction:

n

=

1

.

Papers [9–11] showed that in case of photon-photon non-harmonical

oscillations which take place in non-linear optical media coupled pairs

of photons — paraphotons of the material medium may be formed. After

40

ISSN 1812-3368. Herald of the BMSTU. Series “Natural Sciences”. 2015. No. 1