Sub-diffraction Focussing using Quadratic Measure Eigenmodes

TL;DR

This paper introduces a quadratic measure eigenmode method that locally surpasses the diffraction limit in optical focusing, achieving a fourfold smaller focus size by exploiting the quadratic nature of light-matter interactions.

Contribution

It presents a novel quadratic measure eigenmode approach enabling sub-diffraction focusing using a dynamic diffractive optical element.

Findings

Achieved 4x smaller focus than the diffraction limit.

Demonstrated the method's applicability to various quadratic electromagnetic properties.

Showed local beating of the diffraction limit in optical focusing.

Abstract

For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available. Here, we show that it is possible to locally beat the diffraction limit at the expense of efficiency. The method is based on the linearity of Maxwell's equations and that the interaction between light and its surroundings may be considered quadratic in nature with respect to the electromagnetic fields. We represent the intensity and spot size as a quadratic measure with associated eigenmodes. Using a dynamic diffractive optical element, we demonstrate optical focussing to an area 4 times smaller than the diffraction limit. The generic method may be applied to numerous physical phenomena relating to linear and measurable properties of the electromagnetic field that can be expressed in a quadratic form.