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In surface-enhanced Raman scattering experiments that use plasmonic nanostructures as substrates, the scattering spectrum contains a broad background usually associated with photoluminescence. This background exists above and below the frequency of the incident wave. The low-frequency part of this background is similar to the scattering spectrum of a plasmon nanoparticle, while the high-frequency part follows the Gibbs distribution. We develop a theory that explains experimentally observed features in both the high- and low-frequency parts of the photoluminescence spectrum from a unified point of view. We show that photoluminescence is attributed to the cascade Brillouin scattering of the incident wave by metal phonons under the plasmon resonance conditions. The theory is in good agreement with our measurements over the entire frequency range of the background.

We present a new approach for search of coexisting classes of localised modes admitted by the repulsive (defocusing) scalar or vector nonlinear Schr\"odinger-type equations. The approach is based on the observation that generic solutions of the corresponding stationary system have singularities at finite points on the real axis. We start with establishing conditions on the initial data of the associated Cauchy problem that guarantee the formation of a singularity. Making use of these sufficient conditions, we identify the bounded, nonsingular, solutions --- and then classify them according to their asymptotic behaviour. To determine the bounded solutions, a properly chosen space of initial data is scanned numerically. Due to asymptotic or symmetry considerations, we can limit ourselves to a one- or two-dimensional space. For each set of initial conditions we compute the distances $X^{\pm}$ to the nearest forward and backward singularities; large $X^+$ or $X^-$ indicate the proximity to a bounded solution. We illustrate our method with the Gross-Pitaevskii equation with a $\PT$-symmetric complex potential, a system of coupled Gross-Pitaevskii equations with real potentials, and the Lugiato-Lefever equation with normal dispersion., Comment: 28 pages, 14 figures; accepted for Physica D

The optical properties of inhomogeneous cerium dioxide (CeO2) films on aluminum (Al) sublayer are investigated. The dependencies of the reflection, scattering, and absorption of coherent electromagnetic radiation as functions of the incidence angle and polarization are studied. The experimental and numerical studies show the existence of an incidence angle at which the scattering and absorption of coherent radiation with s-polarization increase simultaneously and the specular reflection becomes just about a few percents. The angle corresponds to an excitation of Fabry-Perot resonator modes. This effect opens up great prospects for manipulation (tuning) of the reflection from the inhomogeneous films., Comment: 9 pages, 11 figures

We demonstrate the application of the efficient semi-inverse asymptotic method to resonant interaction of the nonlinear normal modes belonging to different branches of the CNT vibration spectrum. Under condition of the 1:1 resonance of the beam and circumferential flexure modes we obtain the dynamical equations, the solutions of which describe the coupled stationary states. The latter are characterized by the non-uniform distribution of the energy along the circumferential coordinate. The non-stationary solutions for obtained equations correspond to the slow change of the energy distribution. It is shown that adequate description of considered resonance processes can be achieved in the domain variables. They are the linear combinations of the shell- and beam-type normal modes. Using such variables we have analyzed not only nonlinear normal modes but also the limiting phase trajectories describing the strongly non-stationary dynamics. The evolution of the considered resonance processes with the oscillation amplitude growth is analyzed by the phase portrait method and verified by the numerical integration of the respective dynamical equations., Comment: 20 pages; 9 figures

We demonstrate the new specific phenomenon of the long-time resonant energy exchange in the carbon nanotubes (CNTs) with the radial breathing mode as a carrier. This process turns out to be stable in the wide range of the excitation energy. It is shown that the modified nonlinear Schr\"odinger equation, obtained in the framework of nonlinear elastic thin shell theory, describes the CNT nonlinear dynamics in the considered frequency band. The numerical integration of the thin shell theory equations confirms the results of the analytical study., Comment: arXiv admin note: text overlap with arXiv:1412.7864

We consider a propagation of exotermic transition front in a discrete conservative oscillatory chain. Adequate description of such fronts is a key point in prediction of important transient phenomena, including phase transitions and topochemical reactions. Due to constant energy supply, the transition front can propagate with high velocities, precluding any continuum-based considerations. Stationary propagation of the front is accompanied by formation of a non-stationary oscillatory tail with complicated internal structure. We demonstrate that the structure of the oscillatory tail is related to a relationship between phase and group velocities of the oscillations. We suggest also an approximate analytic procedure, which allows one to determine all basic characteristics of the propagation process: velocity and width of the front, frequency and amplitude of the after-front oscillations, as well as the structure of the oscillatory tail. As an example, we consider a simple case of biharmonic double-well on-site potential. Numeric results nicely conform to the analytic predictions., Comment: 5 pages and 6 figures

A finite (periodic) FPU chain is chosen as a convenient point for investigating the energy exchange phenomenon in nonlinear oscillatory systems. As we have recently shown, this phenomenon may occur as a consequence of the resonant interaction between high-frequency nonlinear normal modes. This interaction determines both the complete energy exchange between different parts of the chain and the transition to energy localization in an excited group of particles. In the paper, we demonstrate that this mechanism can exist in realistic (asymmetric) models of atomic or molecular oscillatory chains. Also, we study the resonant interaction of conjugated nonlinear normal modes and prove a possibility of linearization of the equations of motion. The theoretical constructions developed in this paper are based on the concepts of "effective particles" and Limiting Phase Trajectories. In particular, an analytical description of energy exchange between the "effective particles" in the terms of non-smooth functions is presented. The analytical results are confirmed with numerical simulations., Comment: 15 pages, 8 figures

We demonstrate that the modulation instability of the zone boundary mode in a finite (periodic) Fermi-Pasta-Ulam chain is the necessary but not sufficient condition for the efficient energy transfer by localized excitations. This transfer results from the exclusion of complete energy exchange between spatially different parts of the chain, and the excitation level corresponding to that turns out to be twice more than threshold of zone boundary mode's instability. To obtain this result one needs in far going extension of the beating concept to a wide class of finite oscillatory chains. In turn, such an extension leads to description of energy exchange and transition to energy localization and transfer in terms of 'effective particles' and Limiting Phase Trajectories. The 'effective particles' appear naturally when the frequency spectrum crowding ensures the resonance interaction between zone boundary and two nearby nonlinear normal modes, but there are no additional resonances. We show that the Limiting Phase Trajectories corresponding to the most intensive energy exchange between 'effective particles' can be considered as an alternative to Nonlinear Normal Modes, which describe the stationary process.