Modeling of the electrostatic (plasmon) resonances in metallic and semiconductor nanoparticles

It is known that small dielectric objects can exhibit resonant behavior at certain frequencies for which the object permittivity is negative and the free-space wavelength is large in comparison with object dimensions (Fredkin and Mayergoyz, (2003). Currently these resonances in nanoparticles are found experimentally (or numerically) by probing dielectric objects of complex shapes with radiation of various frequencies, i.e. by using a "trial-and-error" method. There has not existed any technique for direct calculation of the negative values of dielectric permittivities, and the corresponding frequencies of electromagnetic radiation at which these resonances occur. In the paper, we present a new technique for direct calculation of resonance frequencies and to study unique physical features of these resonances for 3D nanoparticles. It is demonstrated that the resonance values of permittivity, and hence the resonance frequencies, can be directly (i.e. without laborious probing) found by computing the eigenvalues of a specific boundary integral equation. Once the resonance permittivity is known, the resonance frequency can be obtained by invoking appropriate dispersion relations. This approach also reveals the unique physical property of plasmon resonances: resonance frequencies depend on dielectric object shapes, but they are scale invariant with respect to object dimensions, provided that they remain appreciably smaller than the free-space wavelength.