Chiral Optical Stern-Gerlach Newtonian Experiment

We report on a chiral optical Stern-Gerlach experiment where chiral liquid crystal microspheres are selectively displaced by means of optical forces arising from optical helicity gradients. The present Newtonian experimental demonstration of an effect predicted at molecular scale [New J. Phys. 16, 013020 (2014)] is a first instrumental step in an area restricted so far to theoretical discussions. Extending the Stern-Gerlach experiment legacy to chiral light-matter interactions should foster further studies, for instance towards the elaboration of chirality-enabled quantum technologies or spin-based optoelectronics.

Figure 1

(a) Sketch of the setup. $Q$ and $S$, respectively, refer to cemented quartz crystal (double arrow shows the optical axis orientation) and silica wedges. The incident laser beam is linearly polarized at 45° from the $x$ axis. (b) Optical intensity distribution in the plane of the sample having an elliptical Gaussian shape associated with waists radii at $\exp (-2)$ of the maximal intensity $w_x=700\mu \mathrm{m}$ and $w_y=20\mu \mathrm{m}$ along the $x$ and $y$ axes. (c) 1D reduced harmonic optical helicity $\tilde{h}(x,0)/I(x,0)$ in the plane of the sample, with spatial period $\mathrm{\Lambda }\simeq 200\mu \mathrm{m}$. Thick red curve: Experimental data obtained by spatial averaging along the $y$ axis in the range $-w_y/2<y<w_y/2$. Thin dark curve: Expected sinusoidal behavior.

Figure 2

(a) Onionlike chiral liquid crystal droplet where the layered structure refers to the periodic modulation of the dielectric permittivity tensor of the liquid crystal with the period being half the helical pitch $p$ of the supramolecular helix organization, see Ref. [31] for a detailed structural description. (b) Sketch of the spectroscopic setup. BS: beam splitter; P: linear polarizer; AQWP: achromatic quarter-wave plate. FS: fiber spectrometer. (c) For each of the four combinations $(\chi ,h)=(\pm 1,\pm 1)$, the reflection spectrum for a $8\mu \mathrm{m}$-thick film of the liquid crystal mixture with uniform alignment of helical axis along the normal to the film is shown (left panel) as well as the polarized reflection image, at 532 nm, of a droplet with radius $R\simeq 30\mu \mathrm{m}$ (right panel, where the contour of the droplet appear as a white dashed circle). Every spectrum is the average of five independent measurements and is normalized by the spectrum obtained from the Fresnel reflection from a bare glass substrate, while ${\mathcal{R}}_{\max }$ refers to the maximal reflectance of the whole set of measured spectra.

Figure 3

Direct observation of chiral-selective displacement under an optical helicity gradient illustrated by snapshots of an irradiated droplet with radius $R\simeq 30\mu \mathrm{m}$ initially placed at $x=0$ at time $t=0$ and after 20 min illumination by the laser beam with space-varying helicity and total optical power $P=400\mathrm{mW}$, for $\chi =-1$ (a) and $\chi =+1$ (b). The dashed white circle refers to the contour of the droplet.

Figure 4

Quantitative analysis of chiral-selective displacement by discriminatory lateral optical forces illustrated by the displacement dynamics over 20 min duration illumination. (a) Discriminatory dynamics for the same conditions as in Fig. 3. Dashed curves refer to the average over $\sim 10$ independent measurements and colored bands refer to the corresponding standard deviation. Solid lines: Simulations according to the model discussed in the text. Blue color: $\chi =-1$; red color: $\chi =+1$. (b) Control experiment using a uniform linearly polarized with null helicity, all other parameters being the same as in panel (a).

Figure 5

Calculated maps of the $x$ and $y$ components of the optical force field exerted on the droplet, $F_x$ and $F_y$, in the plane $(x,y)$ for $\chi =\pm 1$, in the presence (a) and absence (b) of a helicity gradient using all experimental values for all the model parameters and ${\vartheta }_B\simeq 19°$ from the adjustment described in the text. Straight cross markers indicate the origin, where the droplet is placed at $t=0$. Oblique cross markers in panel (a) indicate the asymptotic position of the droplet after 20 min.