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 "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes" [J. Chem. Phys. 120, 10871 (2004)]

In this Comment I discuss two incorrect statements which were made in the paper "Silver nanoparticle array structures that produce remarkably narrow plasmon line shapes" [J. Chem. Phys.120, 10871 (2004)] by Zou, Janel, and Schatz (ZJS). The first statement is about the use of quasistatic approximation in my earlier work on the similar subject, and the second statement concerns the possibility of exact cancellation of radiative relaxation in periodical chains of nanoparticles. The relationship between the quasistatic approximation, the dipole approximation, and the approximation due to Doyle [Phys. Rev. B39, 9852 (1989)] which was used by ZJS is clarified. It is shown that the exact cancellation of radiative relaxation cannot take place in the particular geometry considered by ZJS.Comment: 3 pages, no figure

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

Experimental demonstration of an analytic method for image reconstruction in optical tomography with large data sets

We report the first experimental test of an analytic image reconstruction algorithm for optical tomography with large data sets. Using a continuous-wave optical tomography system with 10^8 source-detector pairs, we demonstrate the reconstruction of an absorption image of a phantom consisting of a highly-scattering medium with absorbing inhomogeneities.Comment: 3 pages, 3 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

Can photonic crystals be homogenized in higher bands?

We consider conditions under which photonic crystals (PCs) can be homogenized in the higher photonic bands and, in particular, near the $\Gamma$-point. By homogenization we mean introducing some effective local parameters $\epsilon_{\rm eff}$ and $\mu_{\rm eff}$ that describe reflection, refraction and propagation of electromagnetic waves in the PC adequately. The parameters $\epsilon_{\rm eff}$ and $\mu_{\rm eff}$ can be associated with a hypothetical homogeneous effective medium. In particular, if the PC is homogenizable, the dispersion relations and isofrequency lines in the effective medium and in the PC should coincide to some level of approximation. We can view this requirement as a necessary condition of homogenizability. In the vicinity of a $\Gamma$-point, real isofrequency lines of two-dimensional PCs can be close to mathematical circles, just like in the case of isotropic homogeneous materials. Thus, one may be tempted to conclude that introduction of an effective medium is possible and, at least, the necessary condition of homogenizability holds in this case. We, however, show that this conclusion is incorrect: complex dispersion points must be included into consideration even in the case of strictly non-absorbing materials. By analyzing the complex dispersion relations and the corresponding isofrequency lines, we have found that two-dimensional PCs with $C_4$ and $C_6$ symmetries are not homogenizable in the higher photonic bands. We also draw a distinction between spurious $\Gamma$-point frequencies that are due to Brillouin-zone folding of Bloch bands and "true" $\Gamma$-point frequencies that are due to multiple scattering. Understanding of the physically different phenomena that lead to the appearance of spurious and "true" $\Gamma$-point frequencies is important for the theory of homogenization.Comment: Accepted in this form to Phys. Rev. B. Small addition in Sec.V (Discussion) relative to previous version. The title to appear in PRB has been changed to "Applicability of effective medium description to photonic crystals in higher bands: Theory and numerical analysis" per the journal policy not to print titles in the form of question