Unscrambling Structured Chirality with Structured Light at the Nanoscale Using Photoinduced Force

Abstract

We introduce a microscopy technique that facilitates the prediction of spatial features of chirality of nanoscale samples by exploiting the photo-induced optical force exerted on an achiral tip in the vicinity of the test specimen. The tip-sample interactive system is illuminated by structured light to probe both the transverse and longitudinal (with respect to the beam propagation direction) components of the sample's magnetoelectric polarizability as the manifestation of its sense of handedness, i.e., chirality. We specifically prove that although circularly polarized waves are adequate to detect the transverse polarizability components of the sample, they are unable to probe the longitudinal component. To overcome this inadequacy and probe the longitudinal chirality, we propose a judiciously engineered combination of radially and azimuthally polarized beams, as optical vortices possessing pure longitudinal electric and magnetic field components along their vortex axis, respectively. The proposed technique may benefit branches of science like stereochemistry, biomedicine, physical and material science, and pharmaceutics. 1) LOCAL FIELDS AT THE TIP-APEX AND SAMPLE LOCATION, EXCITED BY AN ARPBWe prove that under ARPB excitation (a superposition of two coaxial beams: an APB and an RPB with proper phase shift  ) the local fields at the tip-apex and sample locations (both on the ARPB axis, see Fig. 1 of the paper) lack transverse components and we determine the longitudinal field components that include the near-field interaction. We consider the schematic of the problem in Fig. 1 of the manuscript and assume that the tip-apex and chiral sample are located at t z and s z , respectively, at a distance d from each other.

Force Detection of Electromagnetic Beam Chirality at the Nanoscale

“…Conversely, a chiral tip having solely transverse chirality with α em,xx = α em,yy = α em and α em,zz = 0 produces a map that reports on the central transverse helicity density, as shown in 4(f). In the supporting information, we also present the helicity density maps determined with the differential force of a focused azimuthally radially polarized beam (ARPB) [17,31,47].…”

Helicity maximization below the diffraction limit

“…The APB and RPB are obtained by superposing Laguerre Gaussian beams with opposite angular momenta [29], [31], [32], [37], [68]. The electric field vector in an APB propagating along the +z-direction (optical axis of the beam) is polarized along the azimuthal direction  in the transverse plane that, after suppressing the time dependence exp( ) , where 0 w and  are, respectively, the beam parameter and the excitation wavelength.…”

“…Note, an RPB has a nonzero longitudinal electric field component along its axis (for the longitudinal field expressions see Refs. [29], [38], [69]). ARPB is the superposition of these two vortex beams, i.e.,…”

“…A practical example of an optimally-chiral field is the superposition of an azimuthally polarized beam (APB) [29]- [34] and a radially polarized beam (RPB) [34]- [36], called an ARPB, with appropriate relative amplitudes and phase difference [26], [37], [38]. In optimally-chiral ARPB, reducing the beam waist results in simultaneous enhancement in energy and helicity densities [26].…”

Optical force microscopy: combining light with atomic force microscopy for nanomaterial identification

“…In addition, the field is assumed to be monochromatic, where B = c/iω∇ × E. To involve more generalized particles, Refs. [33][34][35][36][37][38][39][40][41][42][43][44][45][46]…”