Circular Dichroism without absorption in isolated chiral dielectric Mie particles

TL;DR

This work shows that a circular dichroism–like response can arise in lossless, isotropic chiral Mie spheres when forward-scattered light is collected with a high numerical aperture, producing nonzero Stokes parameter $S_3$ across visible frequencies. The authors develop a rigorous theoretical model based on plane-wave expansion and Debye multipoles, with scattering coefficients $A_j^{\sigma}$ and $B_j^{\sigma}$ governed by the Pasteur chirality parameter $\kappa$, and analyze the forward-detected polarization via the Weyl integral. Key findings include large, nonresonant $S_3$ in the Mie regime ($a\sim\lambda$), sign changes in $S_3$ with wavelength, and regimes where $|S_3|$ surpasses $|S_2|$, all under high-NA detection and coherent superposition of nonparaxial components. The results offer a pathway to enantioselective manipulation and single-particle chiral characterization using all-dielectric platforms, bridging chiral photonics with Mie-tronics and enabling potential applications in enantioselection and single-particle chirality sensing.

Abstract

We demonstrate that an effect phenomenologically analogous to circular dichroism can arise even for dielectric and isotropic chiral spherical particles. By analyzing the polarimetry of light scattered from a chiral, lossless microsphere illuminated with linearly polarized light, we show that the scattered light becomes nearly circularly polarized, exhibiting large, nonresonant values of the Stokes parameter $S_3$ for a broad range of visible frequencies. This phenomenon occurs only in the Mie regime, with the microsphere radius comparable to the wavelength, and provided that the scattered light is collected by a high-NA objective lens, including non-paraxial Fourier components. Altogether, our findings offer a theoretical framework and motivation for an experimental demonstration of a novel chiroptical effect with isolated dielectric particles, with potential applications in enantioselection and characterization of single microparticles, each and every one with its own chiral response.

Figures (5)

• Figure 1: (a) Imaging configuration in an optical microscope with the collection of forward-scattered illumination. The incident illumination, described by a plane wave, is scattered by the microsphere, with radius $a$ and chirality parameter $\kappa$. Then, the illumination is collected by the objective lens OL and finally focused by the tube lens TL with respective focal lengths $f$ and $f'$. (b) Stokes parameters $S_1$ (black solid line), $S_2$ (red dashed line), and $S_3$ (blue dotted line), normalized by the Stokes parameter $S_0$, as functions of the numerical aperture (NA) of the objective lens, for a chirality parameter set to $\kappa=-0.02$ and a wavelength $\lambda=0.464\,\mu{\rm m}.$
• Figure 2: Color maps of the Stokes parameter $S_3$, normalized by the parameter $S_0$, as a function of the illumination wavelength $\lambda$ and the chirality parameter $\kappa$, for different values of microsphere radius (a) $a=0.5 \,\mu{\rm m}$, (b) $a=1.0\,\mu{\rm m}$, (c) $a=1.5\,\mu{\rm m}$ and (d) $a=2.0\,\mu{\rm m}$. The value of the numerical aperture is NA $=1.3$.
• Figure 3: Differential Stokes parameter $\frac{dS_3}{d\Omega}$ (normalized by $S_0$), associated with the field of an individual conical shell of scattered plane waves superimposed to the illumination field, as a function of the scattering angle $\theta$ for different wavelengths: (a) $\lambda=0.5\,\mu{\rm m}$, (b) $\lambda=0.7\,\mu{\rm m}$ and (c) $\lambda=0.9\, \mu {\rm m}$. We consider a microsphere of radius $a=1.5\, \mu{\rm m}$ and chirality parameter $\kappa=-0.02$.
• Figure 4: (a) Stokes parameters $S_1$ (black solid line), $S_2$ (red dashed line), and $S_3$ (blue dotted line), normalized by the Stokes parameter $S_0$, as functions of the microsphere chiral parameter $\kappa$ for the wavelength $\lambda=0.464\,\mu{\rm m}.$ (b) Slope $\delta S_3/ \delta \kappa$ near $\kappa=0$ as a function of $\lambda.$ The microsphere radius is $1.5\,\mu{\rm m}$ and the numerical aperture is NA$~=1.3$ for both panels.
• Figure 5: Color maps of $|S_3/S_2|$ (log scale) as function of the chirality parameter $\kappa$ and of (a) wavelength $\lambda$ or (b) numerical aperture NA. We take NA$~=1.3$ for the former and $\lambda=0.464\,\mu{\rm m}$ for the latter. The microsphere radius is $1.5\,\mu{\rm m}$ and the regions where $|S_3/S_2|<1$ are white.