Temporal Coupled-Mode Theory for Light Scattering and Absorption by Nanostructures

Abstract

Nanostructures enrich optical resonances in wavelength and even subwavelength region and consequently influence scattering and absorption properties profoundly. Temporal coupled-mode theory was initially developed and applied to analyzing waveguide-resonator interactions in integrated optics. In this chapter, we develop the temporal coupled-mode theory formalism to describe the coupling process and the interference effect involved with optical scattering and absorption in nanostructures. We first discuss the temporal coupled-mode theory based on the consideration of energy conservation and time-reversal symmetry and validate the theory with numerical simulations. Based on the theory, we then elucidate that both the Fano interference and electromagnetic induced transparency (EIT)-like effect can be unified in a temporal coupled-mode equation, but with different background phase shifts. Such a model provides a general line shape formula of scattering and absorption cross sections for both cases. At last we discuss the super-scattering effect of a single subwavelength particle, where an arbitrarily large total scattering cross section can be achieved provided that one maximizes the contributions from a sufficiently large number of resonances.