The phase shift of light scattering at sub-wavelength dielectric structures

We present a new theoretical analysis for the light scattering at sub-wavelength dielectric structures. This analysis can provide new intuitive insights into the phase shift of the scattered light that cannot be obtained from the existing approaches. Unlike the traditional analytical (e.g. Mie formalism) and numerical (e.g. FDTD) approaches, which simulate light scattering by rigorously matching electromagnetic fields at boundaries, we consider sub-wavelength dielectric structures as leaky resonators and evaluate the light scattering as a coupling process between incident light and leaky modes of the structure. Our analysis indicates that the light scattering is fundamentally dictated by the eigenvalue of the leaky modes. It indicates that the upper limit for the scattering efficiency of a cylindrical cylinder in free space is 4n, where n is the refractive index. It also indicates that the phase shift of the forward scattered light at dielectric structures can only cover half of the phase space [0, 2π], but backward scattering can provide a full phase coverage.