Solving Maxwell's Equations Using Polarimetry Alone

TL;DR

This paper demonstrates that Maxwell's equations can be solved using only Stokes parameters, extending their fundamental role in electromagnetic scattering theory, especially relevant for nanophotonics applications.

Contribution

It introduces a novel method to solve Maxwell's equations solely with Stokes parameters, which are traditionally limited to the far-field zone.

Findings

Maxwell's equations can be solved using Stokes parameters alone.

The method applies to objects in nanophotonics.

Stokes parameters are shown to have a fundamental role in scattering theory.

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. Our method for solving Maxwell's equations endows the Stokes parameters an even more fundamental role in the electromagnetic scattering theory.