Helicity maximization below the diffraction limit

Abstract

Optimally-chiral electromagnetic fields with maximized helicity density, recently introduced in [1], enable chirality characterization of optically small nanoparticles. Here, we demonstrate a technique to obtain optimally-chiral nearfields that leads to the maximization of helicity density, under the constraint of constant energy density, beyond the diffraction limit. We show how optimally-chiral illumination induces balanced electric and magnetic dipole moments in an achiral dielectric nanoantenna which leads to generating optimally-chiral scattered and total nearfield. In particular, we explore helicity and energy densities in nearfield of a spherical dielectric nanoantenna illuminated by an optimally-chiral combination of azimuthally and radially polarized beams that generates parallel induced electric and magnetic dipole moments that in turn also generate optimally-chiral scattered field with the same handedness of the incident field. The application of helicity maximization to nearfields results in helicity enhancement at nanoscale which is of great advantage in the detection of nanoscale chiral samples, microscopy, and optical manipulation of chiral nanoparticles.

Helicity maximization in a planar array of achiral high-density dielectric nanoparticles

“…Another remarkable example of optimally chiral fields, highly related to this paper, is the nearfield of a high-density dielectric (e.g. of Si or TiO2) spherical particle with appropriate size and under suitable illuminations such as a Gaussian beam with circular polarization 8,36 , and as an azimuthally-radially polarized beam 36,55 used, respectively, which provides also helicity nearfield enhancement with respect to that of an illuminating plane wave.…”

“…Here and in the following a hat tags unit vectors. It has been shown that helicity density h of the total field around a NA is the sum of the helicity density of the incident field ℎ inc , the helicity density of the scattered field ℎ sca , and an interference helicity density ℎ int 36,55 , i.e.,…”

“…(2). Scattering helicity density ℎ sca at location 𝐫 = 𝑟 𝐫 ̂, generated by a NA in its surrounding, when the NA's scattering is represented by only dipole moments p and m is approximated by the expression 36,55 ℎ sca ≈ 𝜂 0…”

“…In Ref. 36,55 it is proved that balanced polarizabilities (when 𝛼 ee /𝜖 0 = 𝛼 mm ) are required to generate optimally chiral field around a NA, when it is illuminated by an optimally chiral incident field satisfying condition (3) such as a plane wave with circular polarization. This means that the maximum of helicity density does not corresponds to the "optimal chiral condition".…”

Force Detection of Electromagnetic Beam Chirality at the Nanoscale

“…The chiral state of circularly polarized light is well understood, which facilitates the analysis of such measurements. However, performing similar measurements at the nanoscale can be challenging [11][12][13], because the chiral state of light in the near zone, close to a nano-object, is generally unknown and cannot be directly assessed experimentally. Without experimental tools for extracting information about the chirality of the electromagnetic field, optical examination of chirality at the nanoscale is severely complicated.…”