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