Divergence of Dipole Sums and the Nature of Non-Lorentzian Exponentially Narrow Resonances in One-Dimensional Periodic Arrays of Nanospheres

Origin and properties of non-Lorentzian spectral lines in linear chains of nanospheres are discussed. The lines are shown to be super-exponentially narrow with the characteristic width proportional to exp[-C(h/a)^3] where C is a numerical constant, h the spacing between the nanospheres in the chain and a the sphere radius. The fine structure of these spectral lines is also investigated.Comment: 9 pages, 4 figure

Anderson Localization of Polar Eigenmodes in Random Planar Composites

Anderson localization of classical waves in disordered media is a fundamental physical phenomenon that has attracted attention in the past three decades. More recently, localization of polar excitations in nanostructured metal-dielectric films (also known as random planar composite) has been subject of intense studies. Potential applications of planar composites include local near-field microscopy and spectroscopy. A number of previous studies have relied on the quasistatic approximation and a direct analogy with localization of electrons in disordered solids. Here I consider the localization problem without the quasistatic approximation. I show that localization of polar excitations is characterized by algebraic rather than by exponential spatial confinement. This result is also valid in two and three dimensions. I also show that the previously used localization criterion based on the gyration radius of eigenmodes is inconsistent with both exponential and algebraic localization. An alternative criterion based on the dipole participation number is proposed. Numerical demonstration of a localization-delocalization transition is given. Finally, it is shown that, contrary to the previous belief, localized modes can be effectively coupled to running waves.Comment: 22 pages, 7 figures. Paper was revised and a more precise definition of the participation number given, data for figures recalculated accordingly. Accepted to J. Phys.: Cond. Mat

Comment on "Optical Response of Strongly Coupled Nanopraticles in Dimer Arrays" (Phys. Rev. B 71(4), 045404, 2005)

I have re-calculated the extinction spectra of aggregates of two silver nanospheres shown in Figs.~2 and 3 of Ref.~8. I have used the approximate method of images according to Ref.~8 and an exact numerical technique. I have found that the three sets of data (those I have obtained by the method of images, the numerical results, and the results published in Ref.~8) do not coincide. In this Comment, I discuss the reasons for these discrepancies and the general applicability of the method of images to the quasi-static electromagnetic problem of two interacting nanospheres.Comment: 4 pages, 4 figures, submitted to Phys. Rev.

Multiple Projection Optical Diffusion Tomography with Plane Wave Illumination

We describe a new data collection scheme for optical diffusion tomography in which plane wave illumination is combined with multiple projections in the slab imaging geometry. Multiple projection measurements are performed by rotating the slab around the sample. The advantage of the proposed method is that the measured data can be much more easily fitted into the dynamic range of most commonly used detectors. At the same time, multiple projections improve image quality by mutually interchanging the depth and transverse directions, and the scanned (detection) and integrated (illumination) surfaces. Inversion methods are derived for image reconstructions with extremely large data sets. Numerical simulations are performed for fixed and rotated slabs

Bound whispering gallery modes in circular arrays of dielectric spherical particles

Low-dimensional ordered arrays of optical elements can possess bound modes having an extremely high quality factor. Typically, these arrays consist of metal elements which have significantly high light absorption thus restricting performance. In this paper we address the following question: can bound modes be formed in dielectric systems where the absorption of light is negligible? Our investigation of circular arrays of spherical particles shows that (1) high quality modes in an array of 10 or more particles can be attained at least for a refractive index $n_{r}>2$, so optical materials like TiO$_{2}$ or GaAs can be used; (2) the most bound modes have nearly transverse polarization perpendicular to the circular plane; (3) in a particularly interesting case of TiO$_{2}$ particles (rutile phase, $n_{r}=2.7$), the quality factor of the most bound mode increases almost by an order of magnitude with the addition of 10 extra particles, while for particles made of GaAs the quality factor increases by almost two orders of magnitude with the addition of ten extra particles. We hope that this preliminary study will stimulate experimental investigations of bound modes in low-dimensional arrays of dielectric particles.Comment: Submitted to Physical Review

Surface waves in three-dimensional electromagnetic composites and their effect on homogenization

Reflection and transmission of electromagnetic waves at the boundaries of periodic composites (electromagnetic/optical metamaterials) depends in general on both bulk and surface waves. We investigate the interplay of these two contributions using three-dimensional full-wave numerical simulations and a recently developed non-asymptotic homoge-nization theory. © 2013 Optical Society of America.postprin

Local anisotropy and giant enhancement of local electromagnetic fields in fractal aggregates of metal nanoparticles

We have shown within the quasistatic approximation that the giant fluctuations of local electromagnetic field in random fractal aggregates of silver nanospheres are strongly correlated with a local anisotropy factor S which is defined in this paper. The latter is a purely geometrical parameter which characterizes the deviation of local environment of a given nanosphere in an aggregate from spherical symmetry. Therefore, it is possible to predict the sites with anomalously large local fields in an aggregate without explicitly solving the electromagnetic problem. We have also demonstrated that the average (over nanospheres) value of S does not depend noticeably on the fractal dimension D, except when D approaches the trivial limit D=3. In this case, as one can expect, the average local environment becomes spherically symmetrical and S approaches zero. This corresponds to the well-known fact that in trivial aggregates fluctuations of local electromagnetic fields are much weaker than in fractal aggregates. Thus, we find that, within the quasistatics, the large-scale geometry does not have a significant impact on local electromagnetic responses in nanoaggregates in a wide range of fractal dimensions. However, this prediction is expected to be not correct in aggregates which are sufficiently large for the intermediate- and radiation-zone interaction of individual nanospheres to become important.Comment: 9 pages 9 figures. No revisions from previous version; only figure layout is change

Homogenization of Maxwell's equations in periodic composites

We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a computationally-efficient continued-fraction expansion for the effective permittivity. Our results are illustrated by numerical computations for the case of two-dimensional systems. The homogenization theory of this paper is designed to predict various physically-measurable quantities rather than to simply approximate certain coefficients in a PDE.Comment: Significantly expanded compared to v1. Accepted to Phys.Rev.E. Some color figures in this preprint may be easier to read because here we utilize solid color lines, which are indistinguishable in black-and-white printin

On the human nature (following in the steps of Belyaev)

This article was inspired by some works of Belyaev in which he discussed the biosocial human nature, and is dedicated to the 100 year anniversary of Belyaev’ birth. The main views and theories of the human nature and the main paths of genome and culture evolution during anthropogenesis are overviewed. The views of the leading past and present world-wide scientists on the basic principles of the genome-culture interactions are discussed. The seeming contradictions between “geneticists” and “sociologists” are resolved due to the development of the concept of co-evolution of the genome and culture. The evolution of genes and culture is a whole, but not separate processes. During their evolution, humans modify and reconstruct their sociocultural environment. The new environment creates new selection vectors and forms new ways and directions for genetic evolution. In response to the culture development, the genetic determination of human cognitive processes also changed. A good example of the co-evolution of culture and the genome is the development of human speech, the voice and mimic apparatus of communication. The vital importance of the new possibilities for social communication in human populations disposes to the fixation of genetic features that facilitate such communication. At the early stages of human evolution, the areas of the cerebral cortex that were responsible for the development of speech expanded and reorganized. The point of genome-culture co-evolution is well illustrated by niche construction theory. It is emphasized that the evolution of culture, which is widely regarded as a non-biological phenomenon, is quite similar in all its respects to the Darwinian process, as a result of which a sociocultural environment that is adaptive for a given community is formed through selection and transmission in a series of generations. In fact, we are talking about epigenetic inheritance in the evolution of culture and morality. The review details the views and theoretical concepts of geneticists, sociologists, social psychologists, anthropologists, behaviorists and ethologists in explaining the phenomenon of human evolution. Some contradictions caused by different rates of evolution of culture and genome are considered. In conclusion, it is shown that Belyaev’s interpretation of the biosocial nature of humans finds confirmation in modern studies by geneticists, sociologists and psychologists