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2nd International Conference and Exhibition on
Lasers, Optics Photonics (September 08-10, 2014
, Philadelphia, USA)Light-matter coupling in
Imperfect Lattice of Coupled Microresonators

• Vladimir Rumyantsev
• A.A.Galkin Donetsk Institute for Physics
• and Engineering,
• NASU, Ukraine
• 83114 Donetsk, Ukraine
• Tel [phone], fax [phone],
  
• E-mail vladimir. rumyantsev2011_at_yandex.ru

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Nature PHOTONICS PUBLISHED ONLINE 27 FEBRUARY
2013 DOI 10.1038/NPHOTON.2013.29

• Disordered photonics
• Diederik S. Wiersma
• What do lotus flowers have in common with human
  bones, liquid crystals with colloidal
  suspensions, and white beetles with the beautiful
  stones of the Taj Mahal? The answer is they all
  feature disordered structures that strongly
  scatter light, in which light waves entering the
  material are scattered several times before
  exiting in random directions. These randomly
  distributed rays interfere with each other,
  leading to interesting, and sometimes unexpected,
  physical phenomena. This Review describes the
  physics behind the optical properties of
  disordered structures and how knowledge of
  multiple light scattering can be used to develop
  new applications. The field of disordered
  photonics has grown immensely over the past
  decade, ranging from investigations into
  fundamental topics such as Anderson localization
  and other transport phenomena, to applications in
  imaging, random lasing and solar energy.

a) b) c)
Samples that are used to study the multiple
scattering of light, microwaves and sound waves
a) Titanium dioxide particles, b) Porous gallium
phosphide etched in sulphuric acid, c)
Mono-dispersed spheres of a photonic glass.
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A.M.Prudnikov, A.I.Linnik, R.V.Shalaev,
V.V.Rumyantsev, A.O. Kucherik, A.P. Alodjants,
S.M. Arakelian "The features of formation and
modification of nanostructured films of carbon
nitride "Nanosystems physics, chemistry,
mathematics. 2012. - V.3, P. 134-145.

• a)
  b)
• SEM-images of the carbon nitride film surfaces at
  different magnification. Catalyst-free method of
  producing carbon columnar nanostructures by
  magnetron sputtering of graphite was developed in
  DonIPE. The method does not require the use of
  metal catalysts, special substrate preparation,
  and high substrate temperatures. Ordered
  nanostructures spontaneously grow perpendicular
  to the substrate
• b) CxEuyOz film

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2014 Experimental part
Quasi-striped structure
SEM-images of the CNxEuyOz films
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1. Theoretical and experimental studies of the
effects of disordering in quasi-two-dimensional
nanofilms and layered structures during the
propagation of electromagnetic radiation and
acoustic excitations

• The work is performed by groups of Vladimir State
  University and our Institute in the frame of the
  joint Ukrainian-Russian project ? 0112U004002 of
  the National Academy of Science of Ukraine and
  Russian Fundamental Research Fund (2012-2013)
• 2. European project FP7-PEOPLE-2013-IRSES ?
  612600 "LIMACONA" (2013-2016) "Light-Matter
  Coupling in Composite Nano-Structures"

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Theoretical part

• Peculiarities of band gap width dependence upon
  concentration of the
• admixtures randomly included in
• 1.1. layered crystalline system,
• 1.2. striped thin film,
• 2. Dependence of the specific angle of the light
  polarization plane rotation on
• concentration of an admixture in
  1D-superlattice
• 3. Polariton dispersion dependence on
  concentration of admixture in imperfect lattice
  of coupled microresonators

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Peculiarities of band gap width dependence upon
concentration of the
admixtures randomly included in
1.1. layered crystalline system- Rumyantsev
V.V. Interaction of the electromagnetic radiation
and light particles with imperfect crystalline
media. Donetsk Nord-Press, 2006. 347 p.ISBN
966-380-061-5.- Rumyantsev V.V., Fedorov S.A.
Propagation of Light in Layered Composites with
Variable Thickness of the Layers // Technical
Physics. - 2008. V.78, ? 6. - P. 54 58.-
Rumyantsev V.V. Peculiarities of propagation of
electromagnetic excitations through nonideal 1D
photonic crystal // J. of Electrical Electronic
Systems. 2013. V.1, N 1. - P. 109. 1.2.
striped thin film- Rumyantsev V.V., Fedorov
S.A., Shtaerman E.Ya. Light-matter coupling in
imperfect quasi-two-dimensional Si/SiO2 photonic
crystal // Superlattices and Microstructures.
2010. V. 47, N 1. P. 29-33. - Rumyantsev
V.V., Fedorov S.A. Effect of random variations
of both the composition and thickness on photonic
band gap of one-dimensional plasma photonic
crystal // Proceeding of PIERS 2012. The
Electromagnetic Academy, 2012. P. 1411-1414.
ISSN 1559-9450.
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• 2. Dependence of the specific angle of the light
  polarization plane rotation on concentration of
  an admixture in 1D-superlattice
• Rumyantsev V.V., Fedorov S.A., Gumennyk K.V.
  Theory of Optically Active Imperfect Composite
  Materials. Selected Topics. - Colne, Germany
  LAMBERT Academic Publishing, 2012 52?. ISBN
  978-3-659-31055-3
• Rumyantsev V.V., Fedorov S.A., Gumennyk K.V.
  Dependence of the specific angle of optical
  rotation on the admixture concentration in a
  1D-superlattice // Superlattices and
  Microstructures. - 2012. - V. 51, N1. - P. 86-91.
• Rumyantsev V.V., Fedorov S.A., Gumennyk K.V.,
  Proskurenko M.V. Peculiarities of Propagation
  of Electromagnetic Excitation through a Nonideal
  Gyrotropic Photonic Crystal // Physica B. 2014
  - V. 442?  P. 57-59.
• 3. Polariton dispersion dependence on
  concentration of admixture in imperfect lattice
  of coupled microresonators
• Alodjants A.P., Rumyantsev V.V., Fedorov S.A.,
  Proskurenko M.V. Polariton Dispersion Dependence
  on Concentration ofAdmixture in Imperfect
  Superlattice of Coupled Microresonators //
  Functional Materials. 2014. V.21, N2. P.
  211-216.

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Exciton-like electromagnetic excitation in a
non-ideal lattice of coupled resonators

Fig. 1
(the dispersion dependence of exciton-like
electromagnetic excitations in a non-ideal
two-dimensional lattice of coupled microcavities
on concentrations of point-like defects (the
defect is vacancy absence of cavity).
In general the lattice can have multiple
sublattices. Subscripts n and m are
two-dimensional integer lattice vectors, and
numerate sublattices, whose total number is
Hamiltonian of a virtual system
obtained after configurational averaging (using
VCA) is
(1)
is the frequency of photonic mode localized in
the -th site (cavity),
defines the overlap of optical fields of the
and m cavities and the transfer of
the corresponding excitation,
are Bose creation and annihilation operators of
the photonic mode.
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Eigenvalues of Hamiltonian (1) are determined via
its diagonalization by the Bogolyubov-Tyablikov
transformation, and are ultimately found from the
system of algebraic equations of order
(2)
are eigenfunctions of the matrix
whose elements are expressed through the
corresponding characteristics of
(3)
(4)
Solvability condition of system (2)
gives the dispersion law of electromagnetic
excitations in the considered resonator lattice
For a two-sublattice ( ) system of
cavities a second-order determinant (4) gives the
following dispersion law
(5)
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Fig. 2. Dispersion of
electromagnetic excitations in the non-ideal
two-dimensional two-sublattice system of
microcavities for
a)
b)
c)
We performed calculation for modeling frequencies
of resonance photonic modes in the cavities of
the first and second sublattices
,
respectively and for the overlap parameters of
resonator optical fields
The lattice period was set equal to
This situation is analogous to Davydov splitting
of excitons in molecular crystals with two
molecules in a cell
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• Fig. 3 Cavity concentration dependence of the
  photonic gap width in the studied
• microcavity system

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Fig. 4. Isofrequency lines for a), d) upper and
lower surfaces in Fig. 2a b), e) upper and lower
surfaces in Fig. 2b c), f) upper and lower
surfaces in Fig. 2c. Function (frequency) values
are given in the units of 1015Hz. Black diamonds
indicate saddle points, which yield singularities
in the corresponding densities of states (see
Fig. 5).
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Fig. 5. Densities of states
for the upper (a)
and lower
(d) dispersion surfaces
(see Fig. 3).
where
in the range of concentrations
in the range
Solid lines correspond to Fig. 2a. Curves a) are
valid for any value of
(01). Curves d) are valid for any value of
in the range (00.8). b) and e) depict
respectively the densities of states for the
upper and lower surfaces in Fig. 2b. c) and f)
depict the densities of states for surfaces in
Fig. 2c .
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Dispersion of exciton-like electromagnetic
excitation in a non-ideal chain of coupled
resonators
Hamiltonian of a virtual system
obtained after configurational averaging
contains
In this case, the configuration averaging is
performed as in composition (respectively use the
subscript " C "), and in the distance between two
resonators (using the subscript "T").
In the approximation of nearest neighbors the
dispersion law for the electromagnetic
excitations has the form (when
)
(6)
For non-ideal 1D system of microresonators
expression for the function
is
(7)
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?)
b)
Fig. 6. Dispersion of
electromagnetic excitations in the non-ideal
one-dimensional two-sublattice system of
microcavities for
?)
is equal 0.1 and 0.9 for 1 and 2
correspondently is equal 0.1 and 0.9 for 1 and
2 correspondently
b)
20
?)
b)
Fig. 7. The density of states of exciton-like
electromagnetic excitations
?)
is equal 0.1 and 0.9 for 1 and 2
correspondently is equal
for 1, for 2 and for 3
correspondently
b)
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Polariton Dispersion Dependence on Concentration
of Admixture in Imperfect Lattice of Coupled
Microresonators (the polaritonic crystal
with the atomic subsystem )
The hamiltonian of the system considered is
(8)
(9)
(10)
(11)
(12)
(13)
(14)
Fig. 8
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Conclusion

• Our results show that the optical characteristics
  of imperfect superlattice may be significantly
  altered owing to transformation of their
  polariton spectrum resulted a presence of
  admixture. The case of nonideal systems with a
  larger number of sublattices and components of
  defects supposes a wide variety of specific
  behaviors of the photonic gap width. This
  circumstance extends considerably the promises of
  modeling composite materials with predetermined
  properties.
• We study exciton-like electromagnetic excitations
  in a quasi-two-dimensional non-ideal binary
  micro-cavity lattice with the use of the virtual
  crystal approximation. The effect of point
  defects (vacancies) on the excitation spectrum is
  being numerically modeled. The adopted approach
  permits to obtain the dispersion law and the
  energy gap width of the considered quasiparticles
  and to analyze the dependence of their density of
  states on defect concentrations in a microcavity
  supercrystal.
• In the experimental part of the project we
  develop the new methods of laser micro - and
  nanostructuring of semiconductor film materials.
  With the help of the laser radiation with
  different duration and energy of the pulse, we
  offer to create ordered periodic micro - and/or
  nanostructure on the surface of a semiconductor
  film.

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• Thank you very much!

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