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

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

On the Convergence of the Born Series in Optical Tomography with Diffuse Light

We provide a simple sufficient condition for convergence of Born series in the forward problem of optical diffusion tomography. The condition does not depend on the shape or spatial extent of the inhomogeneity but only on its amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem

Coherently tunable third-order nonlinearity in a nanojunction

A possibility of tuning the phase of the third-order Kerr-type nonlinear susceptibility in a system consisting of two interacting metal nanospheres and a nonlinearly polarizable molecule is investigated theoretically and numerically. It is shown that by varying the relative inter-sphere separation, it is possible to tune the phase of the effective nonlinear susceptibility \chi^{(3)}(\omega;\omega,\omega,-\omega)$in the whole range from 0 to$2\pi$.Comment: 10 pages 5 figure

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

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

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.

Spectroscopic studies of fractal aggregates of silver nanospheres undergoing local restructuring

We present an experimental spectroscopic study of large random colloidal aggregates of silver nanoparticles undergoing local restructuring. We argue that such well-known phenomena as strong fluctuation of local electromagnetic fields, appearance of "hot spots" and enhancement of nonlinear optical responses depend on the local structure on the scales of several nanosphere diameters, rather that the large-scale fractal geometry of the sample.Comment: 3.5 pages, submitted to J. Chem. Phy

Propagation of Surface Plasmons in Ordered and Disordered Chains of Metal Nanospheres

We report a numerical investigation of surface plasmon (SP) propagation in ordered and disordered linear chains of metal nanospheres. In our simulations, SPs are excited at one end of a chain by a near-field tip. We then find numerically the SP amplitude as a function of propagation distance. Two types of SPs are discovered. The first SP, which we call the ordinary or quasistatic, is mediated by short-range, near-field electromagnetic interaction in the chain. This excitation is strongly affected by Ohmic losses in the metal and by disorder in the chain. These two effects result in spatial decay of the quasistatic SP by means of absorptive and radiative losses, respectively. The second SP is mediated by longer range, far-field interaction of nanospheres. We refer to this SP as the extraordinary or non-quasistatic. The non-quasistatic SP can not be effectively excited by a near-field probe due to the small integral weight of the associated spectral line. Because of that, at small propagation distances, this SP is dominated by the quasistatic SP. However, the non-quasistatic SP is affected by Ohmic and radiative losses to a much smaller extent than the quasistatic one. Because of that, the non-quasistatic SP becomes dominant sufficiently far from the exciting tip and can propagate with little further losses of energy to remarkable distances. The unique physical properties of the non-quasistatic SP can be utilized in all-optical integrated photonic systems

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