Unconventional Fano resonances in light scattering by small particles

We introduce a new concept of Fano-like resonances for the extinction cross-section at light scattering by small (relative to the light wavelength) particles. The resonances occur beyond the applicability of the Rayleigh approximation, when the interference of different electromagnetic modes excited in the particle with the same multipole moment is crucial, while the partition of the incident wave bypassing the particle is unimportant. We present two examples of these fundamentally new Fano-like resonances: at the light scattering by a particle with large dielectric permittivity and by a particle with spatial dispersion. In both cases the extinction cross-section as a function of the incident light frequency exhibits a sequence of the Fano-like resonances, while each individual resonance is described by the conventional Fano profile. Copyright c © EPLA, 2012 Being originated in the pioneer paper by Fano [1], the Fano resonances have become one of the most appealing phenomena in the wave scattering. There exist many papers devoted to this topic (see, e.g., the recent review articles [2,3] and references therein). The study of the Fano resonances in light scattering by small particles is an important subfield of this general problem. However, many authors are focused on rather specific problems related to practical applications of the resonances [4,5]. Meanwhile, the original Fano theory deals with a scattering of a quantum particle by a potential with a quasi-discrete level [1], i.e., it is based upon the Schrödinger equation. Its application to the light scattering is not so straightforward, because though the Maxwell equations have a certain similarity with the Schrödinger equation, they are not identical at all. On the other hand, the general theory of the Fano resonances in optics does not exist yet. In this letter, we reveal the fundamental features of the Fano resonances for the extinction cross-section at light scattering by small (relative to the light wavelength) (a)E-mail: tribelsky at mirea.ru particles. Our analysis is based on the exact Mie solution of the Maxwell equations for a spherical spatially homogeneous nonmagnetic particle and on a generalization of this solution to the case of a particle with spatial dispersion of its dielectric permittivity. We demonstrate that the Fano resonances occur beyond the applicability of the Rayleigh approximation, and the fundamental role in the resonances is played by the interference of different electromagnetic modes with the same multipole moment l (see footnote ). We name those resonances unconventional Fano resonances. It is remarkable that, despite the drastic differences in the nature, the unconventional resonances exhibit in the leading approximation the conventional Fano profile [1]. 1The origin of a Fano profile in [1] is in interference of a background partition of a scattering wave, bypassing a scatterer, and a resonance partition, which first is trapped, exciting a quasi-discrete state, and then reemitted by the scatterer owing to finiteness of lifetime for the quasi-discrete state. In contrast, the discussed optical resonances would correspond to intereference of partitions reemitted from different quasi-discrete levels, while the partition bypassing the scatterer is unimportant.