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We calculate the optical second harmonic ͑SH͒ radiation generated by small spheres made up of a homogeneous centrosymmetric material illuminated by inhomogeneous transverse and/or longitudinal electromagnetic fields. We obtain expressions for the hyperpolarizabilities of the particles in terms of the multipolar bulk susceptibilities and dipolar surface susceptibilities of their constitutive material. We employ the resulting response functions to obtain the nonlinear susceptibilities of a composite medium made up of an array of such particles and to calculate the radiation patterns and the efficiency of SH generation from the bulk and the edge of thin composite films illuminated by finite beams. Each sphere has comparable dipolar and quadrupolar contributions to the nonlinear radiation, and the composite has comparable bulk and edge contributions which interfere among themselves yielding nontrivial radiation and polarization patterns. We present numerical results for Si spheres and we compare our results with recent experiments.

A new model for the characterization of porous materials using quartz crystal impedance analysis is proposed. The model describes the equivalent electrical and/or mechanical impedance of the quartz crystal in contact with a finite layer of a rigid porous material which is immersed in a semi-infinite liquid. The characteristic porosity length (ξ), layer thickness (d), liquid density (F), and viscosity (η) are taken into account. For films thick compared with the characteristic porosity length (d . ξ), the model predicts a net increase of the area which is translated into a linear relationship between the quartz equivalent impedance Z ) R + XL (XL ) iωL, ω ) 2πf, f being the oscillation frequency of the quartz resonator) and the ratio d/ξ. For low-viscosity Newtonian liquids, for which the velocity decay length δ ) (2ωη/F) 1/2 is much smaller than ξ, Z corresponds to the impedance of a semi-infinite liquid in contact with an increased effective quartz area which scales with the ratio d/ξ. In this case, R ) XL in agreement with Kanazawa equation. For liquids of higher viscosity, the effect of the fluid trapped by the porous matrix is apparent and is reflected in the impedance, which has an imaginary part (XL) higher than its real part (R). In the limit of a very viscous liquid, the movement of the porous film is completely transferred to the liquid and all the mass moves in-phase with the quartz crystal electrode. In this limiting case the model predicts a purely inductive impedance, which corresponds to a resonant frequency in agreement with the Sauerbrey equation. The model allows us, for the first time, to explain the almost linear behavior of R vs XL along the growth process of conducting polymers, which present a well-known open fibrous structure. Films of polyanilinepolystyrenesulfonate were deposited on the quartz crystal under several conditions to test the model, and a very good agreement was found.

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