Generalized optical theorem for reflection, transmission, and extinction of power for scalar fields

We present a derivation of the optical theorem that makes it possible to obtain expressions for the extinguished power in a very general class of problems not previously treated. The results are applied to the analysis of the extinction of power by a scatterer in the presence of a lossless half space. Applications to microscopy and tomography are discussed

Clausius-Mossotti Relation Revisited: Media with Electric and Magnetic Response

A reexamination of the Clausius-Mossotti relation in which material with both electric and magnetic responses yields surprising results. Materials with indices near zero and with real parts less than zero, that is the real part of both the permeability and permittivity are negative, are found to emerge from the interaction of electric and magnetic responses in a self-consistent theory. The new results point the way to artificial and natural materials with exotic responses. A simulation with 10^10 particles shows good agreement with the analytical results

Near-Field Scanning Optical Tomography: A Nondestructive Method for Three-Dimensional Nanoscale Imaging

We present the theoretical foundation for near-field scanning optical tomography, a method for three-dimensional optical imaging with subwavelength resolution. An analysis of the forward problem for both scalar and vector optical fields is described. This is followed by the construction of the pseudoinverse solution to the linearized inverse scattering problem. The results are illustrated by numerical simulations

Strong Tip Effects in Near-field Scanning Optical Tomography

A model for the interaction of the scanning probe in near-field scanning optical microscopy is presented. Multiple scattering of the illuminating field with the probe is taken into account. The implications of this so-called strong tip model for the solution of the associated inverse scattering problem are studied through simulations

Diffraction tomography using power extinction measurements

We propose a new method for determining structures of semitransparent media from measurements of the extinguished power in scattering experiments. The method circumvents the problem of measuring the phase of the scattered field. We illustrate how this technique may be used to reconstruct both deterministic and random scatterers