Optical and dielectric properties of partially resonant composites.

We analyze the two-dimensional potential around a coated cylinder placed in a nonuniform field. In two special cases the system behaves as if the core of the cylinder were enlarged and the shell absent. These are when the shell dielectric constant is the negative of either the core dielectric constant or the matrix dielectric constant. When the shell dielectric constant has a small imaginary part, the field can exhibit large fluctuations which remain localized near the surface of the coated cylinder. Under certain circumstances the dielectric response of a three-phase composite structured as a square array of coated cylinders embedded in a matrix of dielectric con stant Cm can be exactly the same as the response of a square array of solid cylinders embedded in the same matrix material.' This occurs when the core dielectric constant (e,) and the shell dielectric constant (e 9) sat isfy some special relations. Two of these circumstances are genuinely surprising: c,-I-e, = 0, when the core properties are extended up to the outer boundary of the shell, and e + Em = 0, the properties of the core being extended beyond the shell into the matrix. Both of these are what we call a partially-resonant system. More generally, we take partially-resonant to mean a compound system, containing a component with a given volume fraction (f), whose properties are equivalent to those of a system with that component having a larger volume fraction. In particular, it may be possible for a partially-resonant system with a van.ishingly small concentration to exhibit properties like those of a concentrated system. In the cases studied here, the " magnified " component is the core, and this behavior is due to some new sort of res ace, what we might call partial resonance since the system has a finite, rather than an infinite, response to the applied field. Here we will show that the notion of partial resonance extends to bodies containing any number of coated-cylinder inclusions, each aligned parallel to the z axis, and is not just particular to regular arrays. Also we will show the equivalence extends to coated inclusions with noncircular boundaries. Naturally, for either e + c, = 0 or e 1 + Em = 0 to be satisfied, at least one dielectric constant must be the negative of another dielectric con stant. Although seemingly unphysical, this condition comes close to being satisfied for various pairs …