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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