Solving Maxwell's Equations Using Polarimetry Alone

Abstract

Maxwell's equations are solved when the amplitude and phase of the electromagnetic field are determined at all points in space. Generally, the Stokes parameters can only capture the amplitude and polarization state of the electromagnetic field in the radiation (far) zone. Therefore, the measurement of the Stokes parameters is, in general, insufficient to solve Maxwell's equations. In this Letter, we solve Maxwell's equations for a set of objects widely used in Nanophotonics using the Stokes parameters alone. These objects are lossless, axially symmetric, and well described by a single multipolar order. Our method for solving Maxwell's equations endows the Stokes parameters an even more fundamental role in the electromagnetic scattering theory.

Keywords: Electromagnetism; Nanophotonics; Polarization of Light; Scattering Theory.

Figure 1

Real and imaginary parts of the dipolar electric and magnetic Mie coefficients obtained from both a Stokes measurement at θ = 90° (see a–d) and using exact Mie theory (see e–h). The excitation wavefield is a circularly polarized plane wave in both cases. The real and imaginary parts of the Mie coefficients are depicted vs the refractive index contrast m and the optical size x = ka = (2πa)/λ, λ and a being the radiation wavelength and the radius of the spherical nanoparticle. The intense red colors indicate the Mie resonances. The percentage relative error (i–l) calculated from using Mie theory and the Stokes measurement at θ = 90° is also shown to gain further insights.

Figure 2

Real and imaginary parts of the scattering (see a–d) and internal (see e–h) Mie coefficients of a GaP spherical object with radii a = 75 nm obtained from both a Stokes measurement at θ = 90° (dashed) and θ = 60° (dotted). The excitation wavefield is a circularly polarized plane wave in all cases. The scattering and internal Mie coefficients are depicted vs the incident wavelength λ.