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PublicationNonlinear Inverse Scattering and Three-Dimensional Near-Field Optical Imaging(2006-11-29) Panasyuk, George Y; Markel, Vadim A; Schotland, John C; Carney, P. ScottThe nonlinear inverse scattering problem for electromagnetic fields with evanescent components is considered. A solution to this problem is obtained in the form of a functional series expansion. The first term in the expansion corresponds to the pseudoinverse solution to the linearized inverse problem. The higher order terms represent nonlinear corrections to this result. Applications to the problem of three-dimensional optical imaging with subwavelength resolution are described and illustrated with numerical simulations. PublicationSingle-scattering optical tomography(2009-03-25) Florescu, Lucia; Schotland, John C; Markel, Vadim AWe consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean-free path is on the order of the system size. It is shown that a tomographic imaging technique can be devised which is based on the assumption of single scattering and utilizes a generalization of the Radon transform which we refer to as the broken-ray transform. The technique can be used to recover the extinction coefficient of an inhomogeneous medium from angularly resolved measurements and is illustrated with numerical simulations. The forward data for these simulations were obtained by numerically solving the radiative transport equation without any approximations. Tomographic imaging in slabs of different widths was considered and it was shown that the technique can tolerate a maximum width that corresponds to approximately six scattering events. It is also shown that the use of broken rays does not result in additional ill posedness of the inverse problem in comparison to the classical problem of inverting the Radon transform. Applications to biomedical imaging are described. PublicationSpectroscopic Studies of Fractal Aggregates of Silver Nanospheres Undergoing Local Restructuring(2006-09-18) Karpov, Sergei V.; Gerasimov, Valeriy S.; Isaev, Ivan L.; Markel, Vadim AWe 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 than the large-scale fractal geometry of the sample. PublicationClassical Theory of Optical Nonlinearity in Conducting Nanoparticles(2008-02-01) Panasyuk, George Y; Schotland, John C; Markel, Vadim A.We develop a classical theory of electron confinement in conducting nanoparticles. The theory is used to compute the nonlinear optical response of the nanoparticle to a harmonic external field. PublicationEffects of Size Polydispersity on the Extinction Spectra of Colloidal Nanoparticle Aggregates(2012-01-12) Ershov, Alexander E; Isaev, Ivan L; Semina, Polina N; Markel, Vadim A.; Karpov, Sergei VWe investigate the effect of particle polydispersity on the optical extinction spectra of colloidal aggregates of spherical metallic (silver) nanoparticles, taking into account the realistic interparticle gaps caused by layers of stabilizing polymer adsorbed on the metal surface (adlayers). The spectra of computer-generated aggregates are computed using two different methods. The coupled-multipole method is used in the quasistatic approximation and the coupled-dipole method beyond the quasistatics. The latter approach is applicable if the interparticle gaps are sufficiently wide relative to the particle radii. Simulations are performed for two different particle size distribution functions (bimodal and Gaussian), varying the number of particles per aggregate, and different distribution functions of the interparticle gap width. The strong influence of the latter factor on the spectra is demonstrated and investigated in detail. PublicationComment on “Green’s function theory for infinite and semi-infinite particle chains”(2012-07-11) Markel, Vadim A.; Sarychev, Andrey K.In this Comment, we argue that the criticism of our previous paper, which was recently articulated by Hadad and Steinberg, is unwarranted. PublicationSingle-scattering Optical Tomography: Simultaneous Reconstruction of Scattering and Absorption(2010-01-05) Markel, Vadim A; Florescu, Lucia; Schotland, John CWe report theory and numerical simulations that demonstrate the feasibility of simultaneous reconstruction of the three-dimensional scattering and absorption coefficients of a mesoscopic system using angularly resolved measurements of scattered light. Image reconstruction is based on the inversion of a generalized (broken ray) Radon transform relating the scattering and absorption coefficients of the medium to angularly resolved intensity measurements. Although the single-scattering approximation to the radiative transport equation (RTE) is used to devise the image reconstruction method, there is no assumption that only singly scattered light is measured. That is, no physical mechanism for separating single-scattered photons from the rest of the multiplyscattered light (e.g., time gating) is employed in the proposed experiments. Numerical examples of image reconstruction are obtained using samples of optical depth of up to 3.2. The forward data are obtained from numerical solution of the RTE, accounting for all orders of scattering. PublicationComment on "Optical Response of Strongly Coupled Metal Nanoparticles in Dimer Arrays"(2006-12-12) Markel, Vadim AI have recalculated the extinction spectra of aggregates of two silver nanospheres shown in Figs. 2 and 3 of the paper by J. J. Xiao, J. P. Huang, and K. W. Yu [Phys. Rev. B 71, 045404 (2005)]. I have used the approximate method of images according to the formulas published in that reference 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 the reference in question do not coincide. In this Comment, I discuss the reasons for these discrepancies and the general applicability of the method of images to the quasistatic electromagnetic problem of two interacting nanospheres. PublicationPropogation of Surface Plasmons in Ordered and Disordered Chains of Metal Nanospheres(2007-02-15) Markel, Vadim A; Sarychev, Andrey K.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 nonquasistatic. The nonquasistatic SP cannot 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 nonquasistatic SP is affected by Ohmic and radiative losses to a much smaller extent than the quasistatic one. Because of that, the nonquasistatic 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 nonquasistatic SP can be utilized in all-optical integrated photonic systems. PublicationCan the Imaginary Part of Permeability be Negative?(2008-08-18) Markel, Vadim A.When new composite optical materials are developed experimentally or studied in numerical simulations, it is essential to have a set of fundamental constraints that the optical constants of such materials must satisfy. In this paper I argue that positivity of the imaginary part of the magnetic permeability may not be one of such constraints, particularly in naturally occurring diamagnetics and in artificial materials that exhibit diamagnetic response to low-frequency or static magnetic fields.