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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: (380 62) 311 52 77, fax: (380 62) 342 90 18, E-mail : vladimir. firstname.lastname@example.org email@example.com@yandex.ru
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. Nature PHOTONICS PUBLISHED ONLINE: 27 FEBRUARY 2013 | DOI: 10.1038/NPHOTON.2013.29 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.
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) a)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) C x Eu y O z film
SEM-images of the CN x :Eu y O z films Quasi-striped structure 2014 Experimental part
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. 2. European project FP7-PEOPLE-2013-IRSES № 612600 "LIMACONA" (2013-2016): "Light-Matter Coupling in Composite Nano-Structures"
Theoretical part 1.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
Exciton-like electromagnetic excitation in a non-ideal lattice of coupled resonators Hamiltonian of a “ virtual ” system obtained after configurational averaging (using VCA) is : (1) 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 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.
(5) gives the dispersion law of electromagnetic excitations in the considered resonator lattice: Solvability condition of system (2) (4) (3) are eigenfunctions of the matrix whose elements are expressed through the corresponding characteristics of (2) 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 For a two-sublattice ( ) system of cavities a second-order determinant (4) gives the following dispersion law :
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
Fig. 3 Cavity concentration dependence of the photonic gap width in the studied microcavity system
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 10 15 Hz. Black diamonds indicate saddle points, which yield singularities in the corresponding densities of states (see Fig. 5).
Fig. 5. Densities of states for the upper (a) and lower in the range of concentrations where (see Fig. 3). Solid lines correspond to Fig. 2a. Curves a) are valid for any value of in the range (0…1). Curves d) are valid for any value ofin the range (0…0.8). 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. (d) dispersion surfaces
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)
Fig. 6. Dispersion of electromagnetic excitations in the non-ideal one-dimensional two-sublattice system of microcavities for b)b) а) b)b) is equal 0.1 and 0.9 for 1 and 2 correspondently
а) b)b) Fig. 7. The density of states of exciton-like electromagnetic excitations b)b) а) is equal 0.1 and 0.9 for 1 and 2 correspondently is equal for 1, for 2 and for 3 correspondently
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: (10) (8) (12) (13) (14) Fig. 8 (9) (11)
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.