This tutorial is devoted to the Maxwell Garnett approximation and related theories. Topics covered in this first, introductory part of the tutorial include the Lorentz local field correction, the Clausius-Mossotti relation and its role in the modern numerical technique known as the discrete dipole approximation, the Maxwell Garnett mixing formula for isotropic and anisotropic media, multicomponent mixtures and the Bruggeman equation, the concept of smooth field, and Wiener and Bergman-Milton bounds.

Local spectra of self-affine clusters of silver colloid particles recorded with subwavelength resolution by near-field spectroscopy are reported. Spectra were also simulated computationally. The observed and calculated near-field spectra consist of several resonances with highly location-dependent frequencies. The most highly resolved of these resonances correspond to individual surface plasmon ͑SP͒ normal modes. All of these features are only observable in the near field. Both theory and experiment also show that when excited by light in the SP region of the spectrum, the field-intensity distribution in the near field is very heterogeneous with most of the excitation concentrated in ''hot spots'' on the cluster surface that are strongly excitationwavelength dependent. This field-intensity localization provides a rationale for recently reported surfaceenhanced Raman enhancements in excess of

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.

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Abstract. 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 ∝ 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. One-dimensional periodic chains (ODPC) of metallic nanospheres have attracted significant recent attention due to their unusual optical properties. Although the general theoretical framework for analyzing electromagnetic interactions in ODPC has been built a decade ago [1], the recent dramatic advances in nanofabrication have reinvigorated the interest in ODPC, which, in turn, has led to several new results of high experimental relevancy. In particular, radiatively non-decaying surface plasmons (SPs) in ODPC with possible applications to building novel lasers were discussed in Ref.[2]; unusual shifts of plasmon resonance frequencies were found in Ref.[3] and a dramatic narrowing of SP spectral lines was found in Ref. [4,5] in finite chains of moderate length. In this letter I show that two of these phenomena (unusual shifts and narrowing of SP spectral lines) are directly related to a logarithmic divergence of dipole sums (electromagnetic eigenvalues) -a theoretical interpretation that has not been given so far. The SPs that can be excited as a result of this divergence posses highly unusual properties. In particular, the resonance line-shapes are essentially non-Lorentzian and are characterized by a vanishing integral weight. This is in a sharp contrast to spectral line broadening or narrowing due §

Absorption and extinction spectra of fractal and nonfractal small-particle composites are studied. General solutions of the coupled-dipole equations with the exact operator for the dipole interaction ͑including the near-, intermediate-, and far-zone terms͒ are found and compared with those in the quasistatic approximation. Broadscale numerical simulations of optical spectra for clusters containing a large number of particles ͑up to 10 000͒ are performed. A significant fraction of dipolar eigenmodes in fractal aggregates is shown to be strongly localized. The eigenmodes cover a wide spectral region providing resonant enhancement in the visible and infrared parts of the spectrum. In contrast to previous predictions, the absorption spectrum is shown to be significantly different from the spectral distribution of the density of dipole eigenmodes. It clearly indicates the importance of symmetry properties of the modes and corresponding selection rules for the absorption by different modes in random fractal composites. Our experimental data obtained for extinction spectra of silver colloid fractal aggregates are in good agreement with the results of numerical simulations.

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We consider the image reconstruction problem for optical tomography with diffuse light. The associated inverse scattering problem is analyzed by making use of particular symmetries of the scattering data. The effects of sampling and limited data are analyzed for several different experimental modalities, and computationally efficient reconstruction algorithms are obtained. These algorithms are suitable for the reconstruction of images from very large data sets. We consider the image recostruction problem for optical tomography with diffuse light. The associated inverse scattering problem is analyzed by making use of particular symmetries of the scattering data. The effects of sampling and limited data are analyzed for several different experimental modalities, and computationally efficient reconstruction algorithms are obtained. These algorithms are suitable for the reconstruction of images from very large data sets.