The lack of mirror symmetry, chirality, plays a fundamental role in physics, chemistry and life sciences. The passive separation of entities that only differ by their handedness without need of a chiral material environment remains a challenging task with attractive scientific and industrial benefits. To date, only a few experimental attempts have been reported and remained limited down to the micron scale, most of them relying on hydrodynamical forces associated with the chiral shape of the micro-objects to be sorted. Here we experimentally demonstrate that material chirality can be passively sorted in a fluidic environment by chiral light owing to spin-dependent optical forces without chiral morphology prerequisite. This brings a new twist to the state-of-the-art optofluidic toolbox and the development of a novel kind of passive integrated optofluidic sorters able to deal with molecular scale entities is envisioned.
Harnessing material handedness is a topical challenge for many industries as it is a basic requirement towards the synthesis of drugs, additives or pesticides, to name a few. This implies the development of chiral sorting strategies that correspond to the ability to separate two entities that only differ by their handedness. Established chiral separation techniques at molecular scale are mostly based on the recognition of material chirality by another material that is designed to distinguish between the left- and right-handed versions of the entity to be sorted1,2. Instead, passive approaches free from such chiral recognition may also be considered, for instance by relying on transport phenomena, as discussed in the early 70s3. More recently, several options based on the coupling between translational and rotational mechanical degrees of freedom in fluid flows have been proposed4,5,6,7,8,9,10 and realized down to the micron scale by using various kinds of chiral-shaped microparticles made of non-chiral media11,12,13. In addition, hydrodynamic propeller effects driven by rotating electric fields have also been considered theoretically14,15. This principle has been demonstrated only recently by using screw-shaped micrometre-sized particles made of non-chiral medium subjected to the action of a rotating magnetic field16. Merging microfluidic and field-induced options into an optofluidic chiral sorting scheme may offer new possibilities for a technology that arouses interest regarding present achievements and promising developments (see ref. 17 and corresponding Focus Issue). Despite a few theoretical proposals to achieve photoinduced chiral separation18,19,20,21,22,23, the realization of an optical chiral sorter is, however, missing so far.
In this work, we experimentally demonstrate the passive optical separation, in a fluidic environment, of mirror-imaged chiral microparticles that differ only by opposite handedness by using chiral light fields. Importantly, the proposed optofluidic strategy does not require chiral-shaped microparticles and actually relies on the chirality of the medium, in contrast to previous experimental demonstrations of chiral sorting based on hydrodynamical effects11,12,13,16. Indeed, our method enables to sort material chirality by exploiting a universal feature of the light–matter interaction, namely the dependence of optical forces on the intrinsic handedness of matter and light.
To demonstrate our concept of chiral sorting by chiral light, we propose to use an optical field that consists of two counterpropagating circularly polarized collimated beams with opposite handedness Λ=±1 (so called helicity, namely the projection of the spin of a photon along its propagation direction) but equal power and waist. Then, let us consider a microsphere with spherically symmetric bulk material properties and assume that it passes perpendicularly through the latter two-beam configuration at constant velocity V0, say along the x axis. For a non-chiral material, the net optical force component exerted on the object along the propagation direction of the beams, say the z axis, is zero by virtue of cancelation of the two individual beam contributions. In the absence of additional external forces exerted on the particle, its trajectory is thus straight. In contrast, if the material is chiral, the force balance does not hold anymore and a non-zero net force, which originates either from circular birefringence or circular dichroism, is now exerted on the particle. This consequently leads to a curved trajectory in the (x, z) plane. Noteworthy the sign of the particle trajectory’s curvature is expected to be reversed by the change Λ→−Λ or χ →−χ, where χ=±1 refers to the material handedness, non-chiral media being associated with χ=0.
In practice, we used spherical liquid crystal microscopic droplets immersed in the bulk of an isodense and isotropic host fluid (≈25 wt% aqueous glycerol solution, refractive index next=1.36, dynamic viscosity η=2 mPa s) in a glass capillary. The driving optical field is provided by two continuous-wave Gaussian laser beams with vacuum wavelength λ0=532 nm and waist w0~50 μm. The experimental setup is sketched in Fig. 1. Trajectories and velocities of individual droplets are experimentally retrieved by direct optical video imaging using a microscope objective (magnification × 20, numerical aperture NA=0.35). Choosing a droplet lying in the (x, z) plane and displacing the capillary at a constant velocity V0 along the x axis, the chiral separation scenario described above can be verified.
In present work, we used chiral (cholesteric) or non-chiral (nematic) liquid crystal spherical droplets having an overall radial structure of the director field n, which is a unit vector directed along the average local orientation of the liquid crystal molecules, as illustrated in Fig. 2a,b (see Methods for details regarding the nature and preparation of the droplets). The nematic droplets have a radial ordering of the director, whereas the cholesteric droplets are characterized by a helical order with pitch p (that is, the distance over which n rotates by 2π) and have a radial distribution of the helical axes. This radial symmetry formally saves us from the alignment of the droplet with respect to the beam axis. In practice, such symmetry is confirmed by a fourfold intensity pattern when imaging the droplets between crossed linear polarizers as shown in Fig. 2c,f.
Sensitivity of the chiral droplets to the helicity of the driving light field is illustrated in Fig. 2d,e that show distinct images for the same droplet observed under left- and right-handed circularly polarized illumination at wavelength λ0, whereas the non-chiral droplets exhibit identical images as shown in Fig. 2g,h. More precisely, the black circular area of radius RB for the chiral droplet shown in Fig. 2e corresponds to the circular Bragg reflection phenomenon, which is a generic optical property of cholesteric liquid crystals24. It refers to the fact that the propagation of light in one of the two circular polarization states along the cholesteric helical axis is forbidden over a well-defined wavelength range Δλ=p(n∥−n⊥) centred on the Bragg wavelength λB=np where n=(n∥−n⊥)/2 is the average refractive index of the cholesteric with n∥,⊥ the refractive indices parallel and perpendicular to n. By deliberately choosing Bragg cholesteric droplets, enhanced optomechanical separation of droplets having opposite chirality is achieved at relatively low optical power due to helicity-dependent optical radiation pressure exerted on the droplets25.
The experimental demonstration of optical chiral sorting is illustrated in Fig. 3, where panels 2a–c depict the light–matter interaction geometry, whereas panels 2d-f compile snapshots of the droplet dynamics for Λχ=−1, χ=0 and Λχ=+1, respectively, where χ=0 refers to the control experiment with a non-chiral radially ordered droplet. Due to the bounded nature of the light beams, a chiral droplet experiences a finite displacement along z, namely Δz=z+∞−z−∞, as depicted in Fig. 3d,f. Here z±∞ refers to the z coordinate of the droplet centre of mass at time t=t±∞, with t=0 when the droplet crosses the beam axis at x=0. In contrast, a non-chiral radial nematic droplet is not deviated while passing across the beams, as shown in Fig. 3e. Clearly, the fact that Δz is proportional to Λχ demonstrates the possibility to sort objects with different chirality by chiral light.
Importantly, optofluidic chiral sorting is not restricted to resonant chiral interaction as is the case for Bragg chiral droplets. Indeed it works for non-Bragg radial cholesteric droplets as well. This is demonstrated in Fig. 4 that presents the case of left- and right-handed radial cholesteric droplets with p≈2 μm (see Methods for details). Such droplets indeed do not exhibit circular Bragg reflection phenomenon as demonstrated by comparing the images of the droplet under LHCP and RHCP illumination, see Fig. 4a–d, where the material chirality reveals itself as spiralling texture in the images. Even if the optomechanical effect is visible (Fig. 4e,f), the light-induced deviation is typically 20 times smaller than the one obtained in the Bragg case when considering identical optical power, flow velocity and droplet radius. This basically results from the fact that the helicity-dependent scattering of light by non-chiral microparticles is not a resonant process, in contrast to circular Bragg reflection. In this regard, we note a recent theoretical study on optical forces exerted on isotropic chiral spherical scatterers26.
Put together, all these observations unambiguously demonstrate that a reliable optical sorting of material chirality can be achieved. Indeed, as shown in Fig. 1, one easily gets Δz≫R within a few seconds and with 100% efficiency. Typically we thus have Δz≈R in one second using P=10 mW and V0=10 μm s−1. Moreover, the obtained dependencies of Δz on (i) optical chirality at fixed material chirality (Fig. 3) and (ii) material chirality at fixed optical chirality (Fig. 4) fully demonstrate an optofluidic chiral sorting that is basically associated with light-induced separation scaling as Δz∝Λχ.
We have also studied the optical sorting process versus the driving velocity V0 and the beam power P in the Bragg case. We found that larger the P is at fixed V0, the larger is Δz, whereas larger the V0 is at fixed P, the smaller is Δz. Quantitatively, one obtains Δz=a(P/V0), a being a constant, as demonstrated in Fig. 5a that gathers the results of 48 independent realizations for a radial cholesteric droplet with radius R=15 μm and where the solid line refers to the best linear fit. More quantitatively, the best fit slope value a=31.8 nm N−1 can be compared with the predictions for the net optical force exerted on the droplet based on a ray-optics model (see Supplementary Figure 1 for illustration), by calculating the net change of linear momentum of the light field as it interacts with the droplet, which is done by attributing the Minkowski linear momentum ℏk (ℏ is the reduced Planck constant, k the wavevector magnitude) per photon pointing along each geometrical ray.
Although we refer to Supplementary Note 1 for details regarding the derivation of the model, the main result is worth to be mentioned. Namely, assuming that the beam propagating towards z>0 is associated with Λχ=−1, the z component of the net optical force exerted on the droplet can be approximated by
where the x coordinate is the distance from the droplet centre of mass to the propagation axis of the two beams, c is the speed of light in vacuum and θB,ext=arcsin(RB/R) is the half-apex angle of the cone that defines the circular cross-section of radius RB for which the droplet is assumed to behave as a perfect curved mirror (see Supplementary Figure 2). We notice that such an angle is related to the angle θB=arcsin[(next/n)sinθB,ext], which is an intrinsic characteristic of the cholesteric medium that depend neither on the droplet radius nor on the refractive index of the host fluid. In the limit of small Reynolds number, as is the case in our experiments, the expression for the light-induced droplet velocity is then obtained from the balance between the viscous force exerted by the surrounding fluid on the moving droplet and the driving optical force. The z component of the droplet velocity thus expresses as
There is also a non-zero component of the optical force along the x axis, Fx(x), whose cumbersome expression can be found in Supplementary Information. The ensuing light-induced x component for the droplet velocity is written vx(x)=Fx(x)/(6πηR). The total droplet velocity along x therefore expresses as Vx(x)=V0+vx(x). Once the expression of the force exerted on the droplet is determined, the droplet trajectory can be retrieved, which is the key feature of the optical sorting. This is done by noting that Vx(x)=dx/dt and vz(x)=dz/dt, from which one gets dz=vz(x)/(vx(x)+V0)dx. Integration of dz along the x axis thus gives access to the droplet trajectory z(x) and total deviation Δz. In particular, under the approximation vx<<V0 one gets
where we recognize the factor introduced above as the slope of the linear fit shown in Fig. 5a. Taking θB,ext as the only adjustable parameter, we obtain θB,ext=25.1±1.1°, hence θB=21.3±0.9° (next=1.36 and n=1.60), which fairly agrees with a previous measurement25.
Remarkably, when Equation (1) is valid and under the approximation vx≪V0, the expression of the droplet trajectory simplifies to
where Φ is the normal cumulative distribution function,
By introducing the reduced coordinates and , the droplet trajectory adopts the universal expression . This is demonstrated in Fig. 5 where the universal trajectory is displayed as a dashed line. In this figure, the experimental reduced trajectories as a function of P at fixed V0 are shown in Fig. 5b, whereas those as a function of V0 at fixed P are shown on Fig. 5c.
Still, slight deviations from the universal behaviour, with a clear trend, are identified within the presented range of parameters for V0 and P. This is qualitatively illustrated by the insets of Fig. 5b,c. Namely, the larger is the parameter ρ=P/V0, the larger is the deviation from the universal behaviour. A more quantitative assessment of it is presented in Fig. 6a that displays the reduced distance from the beam axis at versus the reduced parameter ξ=ρ/ρc. Here ρc is the critical value of ρ above which a droplet is eventually trapped by light and consequently guided along the z axis towards the ±z direction depending on the sign of Λχ, whereas the transverse location of the droplet centre is constant. Using actual experimental parameters and R=15 μm, we numerically find ρc=9.66 kN, which typically corresponds to P=100 mW and V0=10 μm s−1. In fact, these predictions regarding the trapping regime fit well our observations as the experimental data presented in Fig. 5a indeed fall in the range 0.1<ξ<0.6, hence dealing with the chiral sorting regime without trapping. The quantitative agreement with the model (accounting for both Fx and Fz) is emphasized by the solid curve in Fig. 6a. Moreover, for the sake of a thorough presentation of the two regimes, a few simulated trajectories for various values of the reduced parameter ξ=ρ/ρc are shown in Fig. 5b both in the sorting (ξ<1) and trapping (ξ>1) cases.
The reliability of our experimental approach and its quantitative description are further emphasized by looking at the droplet dynamics in the sorting regime. Its statistical analysis is presented in Fig. 7a,b where the longitudinal and the transverse light-induced droplet velocity components vz and vx, divided by P for the sake of universalization, are presented for the data shown in Fig. 5a.
The obtained quantitative agreement between our observations and our model (which neglects absorption) without need for adjustable parameters eliminates the possibility that thermal effects are at the origin of the reported effects. Also, this demonstrates that the reported optical sorting scheme is immune to unavoidable (according to the hairy ball theorem) presence of a radial defect in radial cholesteric droplets27,28 that formally breaks the spherical symmetry of the radial cholesteric droplets, as shown in Fig. 2d for Bragg droplets and in Fig. 4a–d for non-Bragg ones. This emphasizes the generality of the reported results on optofluidic sorting of chiral microparticles by chiral light.
A natural extension of the present work would consist in the downsizing from the micron scale down to the molecular scale. Indeed, despite an obvious practical interest there are only a few theoretical works dealing with electromagnetic field-induced mechanical separation of nanometre-sized chiral entities14,15,18,19,20,21,22,23, whereas no experimental realization has been reported so far. However, straightforward downsizing of an approach based on the circular Bragg reflection phenomenon has obvious inherent limitations. Indeed the formation of Bragg droplets requires a droplet diameter sufficiently larger than the pitch, which scales as the wavelength and thus prevents from considering sub-micrometric droplets. Outside the resonance, optomechanical effects are less efficient, as experimentally shown here in Fig. 4, and are thus expected to be more sensitive to thermal noise. To overcome this limitation, one might consider an alternative strategy that combines robustness and efficiency of the optomechanically resonant Bragg approach with material chiral recognition applied in standard separation techniques, as sketched in Fig. 8. In that case, chiral microparticles act as ‘conveyers’ whose appropriate surface functionalization allows sorting chiral or non-chiral entities at molecular scale. Of course, solid Bragg chiral microparticles would be desirable for this purpose and protocols actually exist to fabricate them29. In addition, large-scale accurate fabrication of photopolymerized Bragg chiral conveyers can be considered exploiting microfluidic preparation protocols30.
To conclude, these results present the first experimental demonstration of passive optical sorting of material chirality. As chiral sorting strategies have a huge application potential, we anticipate that this study will promote further developments of the existing optofluidic toolbox31,32. It may also contribute to the emergence of other kinds of field-induced chiral sorting strategies more generally based on the use of angular momentum of light, be it of spin or orbital nature.
Preparation of liquid crystal droplets
Radial nematic droplets are obtained by dispersing the nematic E7 (from Merck) in water with a small fraction (0.2 g l−1) of surfactant CTAB (cetyltrimethylammonium bromide, from Sigma-Aldrich) that promotes a perpendicular alignment of n at the nematic/water interface. On the other hand, radial cholesteric droplets are obtained by dispersing the material in an aqueous glycerol solution that promotes a parallel alignment for the director at the cholesteric/fluid interface, hence a radial distribution of the cholesteric helix axes. The solution contains ≈25 wt% of glycerol in order to get an isodense emulsion. Different cholesteric mixtures have been used: (i) the nematic E7 doped with ≈5 wt% of either left-handed S811 or right-handed dopant R811 (both from Merck), which give p≈2 μm and (ii) the cholesteric mixture MDA-02-3211 (from Merck) with pitch p=347nm at room temperature.
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Tkachenko, G., Brasselet, E. Optofluidic sorting of material chirality by chiral light. Nat Commun 5, 3577 (2014). https://doi.org/10.1038/ncomms4577
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