Giant In-Particle Field Concentration and Fano Resonances at Light Scattering by High-Refractive Index Particles

A detailed analytical inspection of light scattering by a particle with high refractive index m+i\kappa and small dissipative constant \kappa is presented. We have shown that there is a dramatic difference in the behavior of the electromagnetic field within the particle (inner problem) and the scattered field outside it (outer problem). With an increase in m at fix values of the other parameters, the field within the particle asymptotically converges to a periodic function of m. The electric and magnetic type Mie resonances of different orders overlap substantially. It may lead to a giant concentration of the electromagnetic energy within the particle. At the same time, we demonstrate that identical transformations of the solution for the outer problem allow to present each partial scattered wave as a sum of two partitions. One of them corresponds to the m-independent wave, scattered by a perfectly reflecting particle and plays the role of a background, while the other is associated with the excitation of a sharply-m-dependent resonant Mie mode. The interference of the partitions brings about a typical asymmetric Fano profile. The explicit expressions for the parameters of the Fano profile have been obtained "from the first principles" without any additional assumptions and/or fitting. In contrast to the inner problem, at an increase in m the resonant modes of the outer problem die out, and the scattered field converges to the universal, m-independent profile of the perfectly reflecting sphere. Numerical estimates of the discussed effects for a gallium phosphide particle are presented.Comment: 18 pages, 10 figure

Hydrodynamic Waves in Regions with Smooth Loss of Convexity of Isentropes. General Phenomenological Theory

General phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of isentropes is developed based on the fact that for most media these regions in p-V plane are anomalously small. Accordingly the waves are usually weak and can be described in the manner analogous to that for weak shock waves of compression. The corresponding generalized Burgers equation is derived and analyzed. The exact solution of the equation for steady shock waves of rarefaction is obtained and discusses.Comment: RevTeX, 4 two-column pages, no figure

Extensive Chaos in the Nikolaevskii Model

We carry out a systematic study of a novel type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter $\epsilon$. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wavenumbers and small frequency.Comment: 4 pages (including 5 figures) LaTeX file. Submitted to Phys. Rev. Let

Bifurcation scenario to Nikolaevskii turbulence in small systems

We show that the chaos in Kuramoto-Sivashinsky equation occurs through period-doubling cascade (Feigenbaum scenario), in contrast, the chaos in Nikolaevskii equation occurs through torus-doubling bifurcation (Ruelle-Takens-Newhouse scenario).Comment: 8pages, 9figure

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, $\partial_t u= \partial_x^2 u + u - u|u|^2$, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it global} theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift-Hohenberg equation, of which the Ginzburg-Landau equation is the amplitude approximation. This sheds light on how one should deal with local and global aspects of phase slips for this and many other similar systems.Comment: 22 pages, Postscript, A

Tails of probability density for sums of random independent variables

The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are distributed according to the Gauss Law. In all other cases the tail for $p_{_N}(x)$ differs from the Gaussian. If the variances of random terms diverge the non-Gaussian tail is related to a Levy distribution for $p_{_N}(x)$. However, the tail is not Gaussian even if the variances are finite. In the latter case $p_{_N}(x)$ has two different asymptotics. At small and moderate values of $x$ the distribution is Gaussian. At large $x$ the non-Gaussian tail arises. The crossover between the two asymptotics occurs at $x$ proportional to $N$. For this reason the non-Gaussian tail exists at finite $N$ only. In the limit $N$ tends to infinity the origin of the tail is shifted to infinity, i. e., the tail vanishes. Depending on the particular type of the distribution of the random terms the non-Gaussian tail may decay either slower than the Gaussian, or faster than it. A number of particular examples is discussed in detail.Comment: 6 pages, 4 figure

Directional Fano resonances in light scattering by a high refractive index dielectric sphere

We report the experimental evidence of directional Fano resonances at the scattering of a linearly polarized electromagnetic plane wave by a homogeneous dielectric sphere with a high refractive index and low losses. We observe a typical asymmetric Fano profile for the intensity scattered in practically any given direction, while the overall extinction cross section remains Lorentzian. The phenomenon originates in the interference of the selectively excited electric dipolar and quadrupolar modes. The selectivity of the excitation is achieved by the proper choice of the frequency of the incident wave. Owing to the scaling invariance of the Maxwell equations, in these experiments we mimic the scattering of the visible and near IR radiation by a nanoparticle made of common semiconductor materials (Si, Ge, GaAs, GaP) by the equivalent scattering of a spherical particle of 18 mm in diameter in the microwave range. The theory developed to explain the experiments extends the conventional Fano approach to the case when both interfering partitions are resonant. A perfect agreement between the experiment and the theory is demonstrated. © 2016 American Physical Society.Acknowledgments. This research has been supported by MICINN (Spanish Ministry of Science and Innovation, Project No. FIS2013-45854-P). We also acknowledge the opportunity provided by the Centre Commun de Ressources en Microondeto use its fully equipped anechoic chamber

Pattern formation and localization in the forced-damped FPU lattice

We study spatial pattern formation and energy localization in the dynamics of an anharmonic chain with quadratic and quartic intersite potential subject to an optical, sinusoidally oscillating field and a weak damping. The zone-boundary mode is stable and locked to the driving field below a critical forcing that we determine analytically using an approximate model which describes mode interactions. Above such a forcing, a standing modulated wave forms for driving frequencies below the band-edge, while a ``multibreather'' state develops at higher frequencies. Of the former, we give an explicit approximate analytical expression which compares well with numerical data. At higher forcing space-time chaotic patterns are observed.Comment: submitted to Phys.Rev.

In situ size sorting in CVD synthesis of Si microspheres

[EN] Silicon microspheres produced in gas-phase by hot-wall CVD offer unique quality in terms of sphericity, surface smoothness, and size. However, the spheres produced are polydisperse in size, which typically range from 0.5 mu m to 5 mu m. In this work we show through experiments and calculations that thermophoretic forces arising from strong temperature gradients inside the reactor volume effectively sort the particles in size along the reactor. These temperature gradients are shown to be produced by a convective gas flow. The results prove that it is possible to select the particle size by collecting them in a particular reactor region, opening new possibilities towards the production by CVD of size-controlled high-quality silicon microspheres.The authors acknowledge financial support from the following projects: ENE2013-49984-EXP, MAT2012-35040, MAT2015-69669-P and ESP2014-54256-C4-2-R of the Spanish Ministry of Economy and Competitiveness (MINECO), and PROMETEOII/2014/026 of the Regional Valencian Government.Garín Escrivá, M.; Fenollosa Esteve, R.; Kowalski, L. (2016). In situ size sorting in CVD synthesis of Si microspheres. Scientific Reports. 6:1-10. https://doi.org/10.1038/srep38719S110

Theoretical Criteria for Scattering Dark States in Nanostructured Particles

Nanostructures with multiple resonances can exhibit a suppressed or even completely eliminated scattering of light, called a scattering dark state. We describe this phenomenon with a general treatment of light scattering from a multiresonant nanostructure that is spherical or nonspherical but subwavelength in size. With multiple resonances in the same channel (i.e., same angular momentum and polarization), coherent interference always leads to scattering dark states in the low-absorption limit, regardless of the system details. The coupling between resonances is inevitable and can be interpreted as arising from far-field or near-field. This is a realization of coupled-resonator-induced transparency in the context of light scattering, which is related to but different from Fano resonances. Explicit examples are given to illustrate these concepts.Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies (Contract W911NF-13-D-0001)National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Grant DMR-0819762