Chirality-selective optical transport of nanoparticles in the evanescent field of a nanofibre

Abstract

Selective optical manipulation of nanoparticles according to their chirality is a challenge due to the relatively small size of the chirality-dependent optical force. Here, we introduce the evanescent field of optical nanofibres as a promising tool for such manipulation. Using circularly polarised fibre modes, we demonstrate strongly chirality-selective optical transport of a chiral nanoparticle. Our experiments, backed by simulations, show that right- and left-handed circularly polarised modes produce clearly distinct velocities of optically trapped chiral nanoparticles along the nanofibre. Furthermore, using a counterpropagating mode configuration, the non-chiral component of the optical force can be cancelled, yielding selective forward and backward transport. The chiral optical force was found to be significant even for particle ensembles with natural variations in size and form, implementing optical separation of chiral enantiomers at the scale of 100 nm. Further development towards waveguide-assisted enantioselective manipulation approaching the molecular scale can be envisaged.

The authors demonstrate a method for the manipulation of the motion of chiral nanoparticles, which involves utilising circularly polarised light in an ultrathin optical fibre. The evanescent field of this fibre can both trap and propel particles near the fibre surface, with the direction of the particle motion depending on the circular polarisation state of the light.

Introduction

In the macroscopic world, chirality (for example, the handedness of a screw) can easily be exploited to control the translational degree of freedom of an object (the travel direction of the rotating screw, in this example). At the microscale, where manipulation is typically contactless, directional translation of objects determined by their chirality is much more challenging. One promising solution is the use of chiral light^1,2. For instance, microspheres of cholesteric liquid crystals exhibit chirality-selective propulsion^3,4, trapping⁵, and rotation^6,7 under circularly polarised (CP) illumination. Chiral optical manipulation has also been demonstrated with micrometre-long carbon nanotubes^8–10 - objects that are chiral at the nanoscale. Recently, CP-dependent optical gradient forces have been demonstrated with chiral nanoparticles (CNP), namely chemically synthesised gold cubes with twisted faces¹¹. While randomly moving in a water dispersion, D-forms (L-forms) of these nanocubes tend to be more strongly (weakly) localised in the focal spot of a left-handed circularly polarised (LCP) laser beam, and the picture reverses for the right-handed circular polarisation (RCP).

The trend of downsizing the manipulated objects in studies of chiral optomechanics is not arbitrary—it pursues the goal of molecular-scale enantioseparation, that is, sorting or selective manipulation of molecular enantiomers differing from each other only by their handedness. This is crucial for chemical processes such as drug synthesis, and thus optical enantioseparation has attracted considerable attention in recent years, yielding multiple theoretical proposals^12–22 (of which two propose sorting along the axis of a nanowaveguide^20,22) and, to the best of our knowledge, only one experimental demonstration of chiral optomechanical response¹¹ for nano objects.

Indeed, a convincing practical realisation of optical enantioseparation at the nanoscale still remains elusive, because downsizing of the particle also reduces its scattering and absorption cross-sections, thus weakening optical manipulation, which is eventually overwhelmed by thermal noise. Therefore, to keep chirality-selective manipulation efficient for nanoscale objects, it is necessary to use light with tighter spatial confinement. This calls for the employment of plasmonic fields, which are strongly localised at the surface of a metal¹⁸ or evanescent fields found near the surface of a waveguide^19,20.

In this study, we report on chirality-selective optical manipulation of metallic CNPs using the radiation pressure force induced by the evanescent field of an optical nanofibre (ONF). The effective one-dimensionality of the ONF-guided modes and strong gradient force in the evanescent field have yielded a number of recent advances in particle manipulation experiments^23–27. In contrast to a free-space light beam, an evanescent field near an ONF allows one to directly observe the chiral component of the radiation pressure by measuring the speed at which CNPs are transported along the fibre axis. Furthermore, by adding a counterpropagating mode in the fibre, it is possible to control the direction of chirality-selective transport by merely switching the mode polarisation. These findings advance the effective use of chiral optical forces, particularly for nanoscale optical enantioseparation.

Results

Chiral optomechanical effect

In our study, a single-mode ONF is submerged in an aqueous solution containing colloidal chiral nanocubes²⁸, as illustrated in Fig. 1, where k is the wave vector of the input laser beam coupled to the ONF. Note that we will use Cartesian coordinates throughout rather than cylindrical coordinates. This is due to the more straightforward geometrical definition of the CNP afforded by this choice, along with the fact that the use of a linearly polarised beam in our counter-propagating mode experiments breaks the cylindrical symmetry. We assume that the particle is in the position shown in Fig. 1, i.e. coordinates (x, y, z) with the z-axis parallel to the fibre axis and the centre of the particle located at x = 0. Once in the evanescent field, such a CNP is subject to an optical force, which has three independent and potentially chiral components, F_x, F_y, and F_z. The conservative component is the gradient force F_y, which traps the particles at the fibre surface. While its magnitude depends on the mode polarisation, its sign is constant (see simulation results below), and so particles are trapped for both RCP and LCP. We note that the gradient force on such CNPs has recently been investigated in a free-space beam setting¹¹.

Fig. 1. Experimental concept.

A chiral gold nanoparticle is depicted at the surface of an ONF and subject to axial optical forces F_z, L and F_z, R due to the evanescent field of a left- or right-handed circularly polarised fibre mode, respectively. Note that the whole experiment takes place in pure water.

The dissipative force has two components: (i) F_x which produces a torque on the particle about the fibre axis, and (ii) the radiation pressure force F_z which propels particles along the fibre axis. In the present study, the azimuthal component (i) was found to be unobservable experimentally, in line with the theoretical predictions that state ∣F_x∣ ≪ ∣F_z∣ (see simulation results below). Hence, in this study, we focus on the radiation pressure force, which can be expressed as F_z = F_nc + F_c, where F_nc is the non-chiral part (independent of either particle or field chirality), and F_c is the chiral one. While F_nc has been well researched for metal particles (including in the setting of ONFs), studies of F_c in the nanoscale regime are still few in number. As shown in ref. ¹³, the chiral component of the dissipative optical force exerted on a chiral dipole is related to the chirality flow $\mathrm{\Phi }=\left({ϵ}_0\mathcal{E}\times \stackrel{°}{\mathcal{E}}+{\mu }_0\mathcal{H}\times \stackrel{°}{\mathcal{H}}\right)/2$ of the field by the equation

$$F_{\mathrm{c}}^{\prime }=2\mathrm{Im}\left[\chi \right]\mathrm{\Phi },$$ 1

where ϵ₀ and μ₀ are the vacuum permittivity and permeability, $\mathcal{E}$ and $\mathcal{H}$ are the real parts of the electric and magnetic fields, and χ is the chiral polarisability in units of m²s following refs. ^11,13. Note that in the general (non-isotropic) case χ is a tensor. The sign of $F^{\prime }$ is controlled by flipping either the handedness of the circular polarisation—positive (negative) for LCP (RCP), or the sign of Im[χ]—negative (positive) for left- (right-) handed dipoles. Since the chirality of both the light and the particle determines the direction of the chiral force, either of these two parameters can be used to achieve a proof-of-concept demonstration of chiral optical manipulation, assuming $F_{\mathrm{c}}\propto F_{\mathrm{c}}^{\prime }$. Evidently, polarisation of light is much easier to control compared with the geometry of synthesised CNPs. Therefore, in order to achieve the cleanest possible experimental demonstration, here we used L-form chiral particles in our initial experiments, and switched between LCP and RCP states of the nanofibre-guided light. Results for both L-form and D-form particles are shown at the end of the Results Section.

Following Yamanishi et al.¹¹ where the chiral optomechanical effect was characterized by the dissymmetry of the position dispersion of CNPs in a chiral light beam, we define a dissymmetry factor for the chiral transport along the fibre axis, defined as the difference between the magnitudes of the radiation pressure optical forces for LCP and RCP divided by their mean value, that is

$$g_z=2\frac{\mid F_{z,\mathrm{L}}\mid -\mid F_{z,\mathrm{R}}\mid }{\mid F_{z,\mathrm{L}}\mid +\mid F_{z,\mathrm{R}}\mid }.$$ 2

Under the dipole approximation, the chiral components have equal magnitudes and opposite signs, $F_{\mathrm{c},\mathrm{R}}^{\prime }=-F_{\mathrm{c},\mathrm{L}}^{\prime }$, and hence the force dissymmetry can be expressed as $g_z^{\prime }=2F_{\mathrm{c},\mathrm{L}}^{\prime }/F_{\mathrm{nc}}^{\prime }$, where the sign of $g^{\prime }$ is equal to the sign of $\mathrm{Im}\left[\chi \right]$ which is negative for left-handed dipoles. Although our CNPs are not strictly small enough for the chiral dipole approximation to hold, it was shown in ref. ²⁹ that for the particles we use, the electric and magnetic dipole moments (which contribute to the chiral dipole moment) dominate over the next highest order moment (quadrupole moment) near the chiral resonance. Thus, we expect $g_z\propto g_{\mathrm{z}}^{\prime }<0$ for our L-form CNPs in the spectral region near their strongest chiral response.

Particle analysis and modelling

The CNPs used in our experiment are shown in a scanning electron microscope (SEM) image in Fig. 2A. The particles shown had L-form chirality (i.e. anti-clockwise twisting from the centre). To reduce incidents of adhesion to the ONF, the particles were silica-coated (coating thickness about 5 nm), see Fig. 2B. As an ensemble, the particles all tend to exhibit chirality, but also show a range of minor structural differences, particularly after coating.

Fig. 2. CNP.

Same scale SEM images of pristine (A) and silica-coated (B) L-form CNPs. C, D Geometric model of a chiral cube, without and with rounding, respectively. Refer to Supplementary Note 2, for the definition of vertices a₁–a₆. E Measured circular dichroism and extinction spectra of coated CNPs.

In order to numerically simulate the optical force on these particles, we used a parametrised particle model based on a modified version of the model of ref. ²⁸, as shown in Fig. 2C and detailed in Supplementary Note 1. To form the model, tilted cuts were made on all twelve edges of a cube with the following variable parameters: ℓ—side length, w—cut width, d—cut depth, and t—the tilt angle of the cut as measured from the normal to the edge. The sign of the chirality depends on the tilt, that is, L-form corresponds to (0 < t < 90°) and D-form to (−90° < t < 0). As shown in Fig. 2D, we also rounded all edges and corners of the cut cube with a radius r = 10 nm to mimic the shape of real particles. These geometric parameters were evaluated from SEM images of numerous coated and uncoated particles, see the summary in Table 1, along with details of the analysis in Supplementary Note 2.

Table 1.

Summary of SEM analysis of particle parameters

Particle type	Count	ℓ (nm)	d (nm)	w (nm)	t (degrees)
Uncoated	42	180 ± 10	65 ± 5	35 ± 5	30 ± 5
Silica coated	24	190 ± 10	70 ± 5	35 ± 5	30 ± 15

Mean values and standard deviations are given, rounded to the nearest 5 nm.

The particle chirality is experimentally ascertained by measuring the circular dichroism (CD) of particles in solution, see Fig. 2E. The CD is seen to exhibit an inverted peak with a minimum around 645 nm. Optical manipulation at wavelengths near to this value is expected to produce the most vivid demonstration of chiral aspects of the optical force on the CNPs.

Simulations of the CD and g_z were first performed for a particle model using the mean parameter values. We also performed simulations where each parameter in turn was set to its mean value ±1σ, where σ is the measured standard deviation of the parameter in question. This allowed us to determine the expected range of experimental measurements, see Supplementary Note 3.

Because of the relatively large size of the particles considered here, treatments of the chiral force developed in the dipole approximation^20,30–34 are not strictly applicable, and in general, we compare our experimental results with numerically calculated force dissymmetry. To this end, we simulated the optical force on the CNPs using the finite difference time domain (FDTD) method of electromagnetic field propagation. The force itself was calculated using the Maxwell stress tensor applied to the calculated fields, see Methods for more details.

In the experiments, we assume that the CNPs are in the maximally stable configuration where one face of the cube touches the ONF surface, that is, ϕ_x = ϕ_z = 0, see Fig. 2D. Any deviation from this configuration should be corrected by the gradient force, F_y. However, we have no knowledge about the rotation of the cubes about the y-axis through the cube centre. We therefore simulated the optical force over the whole range −45° ≤ ϕ_y ≤ 45° to investigate the behaviour as a function of rotation.

Figure 3A–C show the simulated x, y, and z components, respectively, of the optical force for both LCP (squares) and RCP (circles) states of the fibre mode. The curves in each of these panels are sinusoidal fits to the data and serve as a guide for the eye. As expected, all the force components for LCP and RCP are clearly different in both mean value and their dependence on ϕ_y. The most striking feature of the results is that the peak absolute value of the z-directed force is about five times larger than that for the y-directed gradient force, and up to two orders of magnitude larger than that of the x component. This fact justifies our approach here of focusing on the F_z force directed along the fibre axis and ignoring the transverse components for the present experiment. We also note that the variation of F_z with ϕ_y is of order 10%, with its average found at ϕ_y = 0 for both LCP and RCP. This allows us to restrict the subsequent simulations to ϕ_y = 0, being confident that the results for this value reflect the average behaviour.

Fig. 3. Simulated optical forces on an uncoated CNP near the surface of a 500 nm diameter ONF guiding a CP mode.

A–C Show the azimuthal (x-directed), radial (y-directed) and axial (z-directed) optical force, respectively, for RCP (circles) and LCP (squares), vs the orientation angle ϕ_y of the CNP. Solid and dashed curves are the best sinusoidal fits to the simulation data for RCP and LCP, respectively. The sketches below indicate the CNP orientations at the corresponding ϕ_y values. The wavelength of the mode was 640 nm in each case, corresponding to maximal dissymmetry in F_z. D Axial force dissymmetry, g_z (Eq. 2), calculated for the zero rotation (ϕ_y = 0, solid curve) and for the two orientations with the extrema of F_z; ϕ_y = +22.5° (dashed curve) and ϕ_y = −22.5° (dotted curve).

We note in passing that among all the force components, the behaviour of F_x (Fig. 3A) shows the largest variation as a function of ϕ_y, with a change in sign predicted in the case of RCP. This is due to the interplay of the torque produced by the CP mode on the particle (which doesn’t depend on the particle chirality, but does depend on ϕ_y) and the truly chiral component of F_x, which produces a torque dependent on the particle chirality. Although these numerical predictions are intriguing, the small magnitude of the force in this case means they could not be confidently detected in our experiments.

In Fig. 3D, one can see that the force dissymmetry has the same qualitative behaviour for all values of ϕ_y and that the case of ϕ_y = 0 corresponds to the average result, as expected. It is also worth noting the qualitative agreement between the simulated and analytically predicted results for the force dissymmetry near the resonance, that is, g_z < 0 in the resonant dip centred around the wavelength of 640 nm.

Demonstration of chirality-selective transport

The numerically predicted maximum force dissymmetry of g_z ≈ −0.5 corresponds to 40% difference between the optical forces (as normalised by the larger force) and the corresponding velocities for right- and left-handed CP modes. From previous experiments²⁶ on optical transport of gold nanoparticles along single-mode ONFs, we expect velocities of order 200 μm s⁻¹ for the typical mode power of 10 mW in the visible range. The corresponding expected velocity difference of about 80 μm s⁻¹ can be easily detected under an optical microscope via imaging the laser light scattered by the transported particle. We designed an experiment to make such measurements as depicted in Fig. 4A and described in detail in the Methods Section.

Fig. 4. Experimental details.

A Schematic diagram of the optical setup (not to scale). PBS polarising beam splitter, HWP half-wave plate, VR variable retarder, MPC motorised polarisation controller, WL white light source in Köhler configuration, MO microscope objective, TL tube lens, P linear polariser, LP linear polarisation, CP circular polarisation, g gravitational acceleration. B Camera image of the ONF waist region in transmission under WL illumination. C Image of the laser light (wavelength 637 nm) scattered from the same part of the ONF placed slightly out of focus (closer to the MO). Σ₁ and Σ₂ are the brightness sums in the top and bottom halves of the image. D Typical map of the total brightness of the imaged ONF-scattered laser light vs the orientation angles of the MPC paddles. The red circle indicates the position of maximum brightness sum.

Of principal importance is our ability to accurately control the polarisation of light in the fibre. In particular, for directional transport experiments, a single CP mode was injected in the +z direction, while for oscillating transport experiments, an additional linearly polarised (LP) mode was injected in the −z direction. In order to ensure accurate control of the mode polarisation in the ONF waist region (shown by the transmission white-light image and the scattered laser-light (wavelength 637 nm) image in Fig. 4B, C), we applied the two-step compensation method^35,36 where the first step (mapping of the horizontal polarisation) in this setup is realised by employing motorised polarisation controllers (MPC). We provide a sample of the measured scattered light intensity (in this case, the scattered laser-light intensity shown corresponding to Fig. 4C) as a function of the polarisation controller paddle angles in Fig. 4D for reference. (See Methods along with Supplementary Note 4 for more details.)

As demonstrated in Fig. 5, when the polarisation of the CP mode is switched between RCP and LCP states (by means of the variable retarder, VR1, shown in Fig. 4A), the transport velocity of a single CNP is visibly modulated. Indeed, the slope of the track, which indicates the particle position vs time, decreases from 471 μm s⁻¹ for the RCP state down to 297 μm s⁻¹ for LCP, and then rebounds to 609 μm s⁻¹ once the polarisation is switched back to RCP, see Fig. 5B and Supplementary Movie 1. These values were extracted by performing linear fits to the data (dashed lines in Fig. 5C). Note that we limited this analysis to the waist region where the ONF diameter was nearly constant. For the fibres used here, the taper design gives a nominal 1-mm-long region of diameter ~500 nm with about 10% variation between samples, as verified by SEM analysis of freshly prepared ONFs. Outside this region, the fibre diameter increases exponentially, leading to a fall off in the evanescent field and thus a reduction of the optical force leading to slowing of the particle, as seen near the start and finish of the track in Fig. 5B, C.

Fig. 5. Polarisation-dependent dynamics of a CNP.

A–C Transport by a single CP input mode, switching between right- and left-handed polarisation states. A First frame of the video recording where the bright spot indicated by the dashed arrow represents the transported CNP. The dotted arrow below indicates a fixed, smaller scatterer. B Sequential compilation of lines extracted from the video frames at x = 0 (ONF axis). Here, R indicates RCP and L indicates LCP. C Measured CNP position vs time. The dashed lines are the best linear fits to the data in the corresponding uniform pieces of the track. D–F Chirality-selective directional transport of a CNP by two counterpropagating modes, one of which is fixed at LP, while the other alternates between RCP and LCP states. In both one-mode and two-mode configurations, the CP mode wavelength is 660 nm, and the transmitted power is fixed at 6 mW. The LP mode has a 637 nm wavelength and approximately the same constant power, fine-tuned to achieve near-balanced particle dynamics prior to measurement. The numbers next to the lines in C, F indicate the fitted speed in the units of μm s⁻¹.

The measured steady state velocities v of the transported particles allowed us to characterise the chiral optical forces. Indeed, in the present case, the Reynolds number is low; thus, the flow around the particle is laminar, and the force is proportional to ηv, where η is the dynamic viscosity of water. Assuming that η is independent of the polarisation state (that is, temperature difference between the states is negligible), we express the force dissymmetry (Eq. 2) as

$$g_z=2\frac{v_L-v_R}{v_L+v_R},$$ 3

where v_L and v_R are respectively the LCP and RCP steady state velocities determined from the best linear fit to the particle track, and the modulus operators are omitted because velocities (and the forces, as follows from F_z simulations) have the same sign. Taking the average of the velocities in the two RCP regions in Fig. 5B, C as v_R, we find g_z = −0.58 for this track. Notably, this value is close to the numerically predicted one, see Fig. 3D.

The above demonstration proves that it is possible to manipulate the transport of CNPs contingent on their chiral property. However, the change in velocity measured due to the chiral optical force was still small compared to the overall transport velocity.

In order to perform more useful manipulation, it is desirable to isolate the chiral optical force by cancelling the non-chiral component. This can be done by introducing a constant counterpropagating mode (here, with x-oriented linear polarisation) into the ONF, as depicted in Fig. 5D. Note that the wavelength of the two modes is chosen to be different for experimental convenience, as it allows the modes to be separated at the fibre ends by filtering. By varying the power in this counterpropagating mode, the transport velocity for RCP and LCP may be adjusted, and for the appropriate power setting, the non-chiral part of the force, F_nc, can be completely cancelled. In this regime, the direction of transport is different for each polarisation handedness. It is therefore possible to keep the particle position at the ONF waist oscillating by altering the polarisation periodically. We show a realisation of this effect in Fig. 5E, F and Supplementary Movie 2 where the CNP position is seen to oscillate within approximately 0.25 mm. This is effectively a proof-of-concept demonstration of chiral optical sorting of nanoparticles along a nanofibre waveguide. A more detailed analysis of these results may be found in Supplementary Note 5.

Variation of experimental parameters

The results of the previous Section provide a striking demonstration of the chiral optical force in real time. However, to quantitatively estimate g_z, it is necessary to make measurements for many particles. For the chiral optical force to be useful in controlling optical transport in realistic situations, F_c should dominate over fluctuations in F_z due to other experimental factors. Principally among these are the inhomogeneity of particle size and form. The effect of small structural deviations between individual CNPs on the chiro-optical responses has been discussed previously^37,38. These factors lead to differences in both F_nc and F_c from particle to particle.

To assess the relative size of such effects compared to the chiral force effect, we performed measurements of particle velocity for at least 10 individual nanoparticles for both LCP and RCP modes (in the one-mode regime). Note that in these experiments, particles were tracked over the same portion of the ONF (close to the centre of the waist) at a fixed polarisation. We also checked the effect of wavelength and performed control measurements using non-chiral nanoparticles (NCNPs)—gold nanospheres of 150 nm diameter—at 637 nm, which gives the largest chiral response for our CNPs. The results for these control measurements are shown in the left-most panel of Fig. 6A. Although a wide spread was seen for the measured velocities in the case of both LCP and RCP, no significant difference was found in the mean velocities for the two polarisations, as may be seen by the almost total overlap of the error bars. This null experiment with NCNPs was essential as it verified the validity of F_nc, L = F_nc, R assumption in our setup. Note that we also provide data from experiments with non-chiral nanocubes in Supplementary Note 9, where we also give reasons why the spherical NCNPs used here arguably function as a better control.

Fig. 6. Experimental results for multiple chiral and nonchiral nanoparticles transported by a single CP mode.

A Leftmost panel, measured transport velocities for NCNPs (gold nanospheres) are shown for RCP (blue circles, label R) and LCP (orange circles, label L) states. The subsequent panels from left to right show the results for CNPs at mode wavelengths of 637 nm, 660 nm, and 785 nm, respectively. In each panel, blue (orange) squares show results for RCP (LCP), and black squares with error bars show the mean and ±1σ of the data sets, respectively. B Axial force dissymmetry for each data set, with the white circle showing the result for NCNPs, and the red squares those for CNPs. The overlaid dashed curve shows the simulation result for the geometric parameters' values listed in Table 1.

Conversely, in the results for CNPs at both 637 nm and 660 nm, the distributions of v_L and v_R do not overlap within one standard deviation, i.e., they are statistically significantly different at the 2σ level. Specifically, the RCP mode on average produces larger velocities than LCP for both wavelengths. Furthermore, in agreement with the numerical simulations, when the mode wavelength was set to 785 nm, the difference became insignificant.

The results for 637 nm and 660 nm show that even in the presence of particle geometry variation, which affects the optical force, the chiral force still dominates. To confirm this, we also calculated the force dissymmetry from the above data, see Fig. 6B. As expected, the dissymmetry in the case of NCNPs is zero within the error of the measurement. Simulation results for the mean geometric parameters listed in Table 1 are overlaid as a red dashed line. Although the experimentally measured dissymmetries have a large variance, the mean g_z values are seen to be close to their numerically predicted ones. We also note that the wavelength dependence of the force dissymmetry broadly follows the dependence shown by the CD in Fig. 2E, which finding suggests that the key physical mechanism behind the force dissymmetry is the chirality-selective absorption of light by CNPs.

Experiments with enantiomers

Finally, we offer a comparison between transport of D and L-form particles in a counter-propagating configuration similar to that used in Fig. 5D–F, but with the LP mode wavelength set to 785 nm, so that the evanescent field penetration is sufficient even in thicker parts of the fibre. The CP mode had a wavelength of 660 nm as before. In a tapered portion of the fibre (diameter 500 nm–700 nm) near the waist, it is possible to bring particles to a stop by balancing the forces due to the counterpropagating modes^25,26,39 (details of the taper profile are given in Supplementary Note 6). For chiral particles, the diameter of the taper at which this force balance is achieved depends on the polarisation state of the CP mode. Initially, we bring particles to a stop using the LCP state of the 660 nm mode, and then switch the polarisation to RCP. As seen earlier in Figs. 5D–F, for L-form particles, RCP produces a stronger axial force. In the current experiment, this leads to the particle being pushed by the CP mode to a thicker position on the fibre. On the other hand, for D-form particles, RCP produces a weaker force in the direction of the CP mode propagation, and the particle thus moves in the opposite direction to L-form particles, i.e. to a thinner portion of the taper.

We performed this experiment for three L-form and three D-form CNPs, and also for non-chiral gold nanospheres. Typical mode powers were 4.0 mW in the 660 nm mode and 3.5 mW in the 785 nm mode. The polarisation was changed at time t = 0 s. The results are shown in Fig. 7. Note that the position attained by the particles under LCP was adjusted to zero for each data set to allow comparison of behaviour after the switch to RCP. We note that after the polarisation is changed from LCP to RCP, the CNPs are seen to move as expected, with enantiomers moving in opposite directions. On the other hand, the gold nanospheres do not show any systematic deviation in their position. Note that for the sake of experimental purity, the particles were tracked one by one, using a homochiral solution for each particle type.

Fig. 7. Directional transport of CNP enantiomers.

A First frame of the video recording where the bright spot shows the transported nanoparticle. Arrows above and below the frame indicate propagation directions of the CP and LP modes, respectively. B Squares show extracted CNP positions, with red, yellow, and purple (green, blue, and cyan) points corresponding to separate L-form (D-form) CNPs. Positions for NCNP data are shown as grey circles for comparison.

Discussion

The results presented above show that it is possible to transport a particle according to its chiral property using the evanescent portion of chiral light guided by a nanofibre. The effective one-dimensional nature of the system reduces the degrees of freedom of particle movement so that motion along the fibre axis can be easily measured. Indeed, this method offers sufficient sensitivity that the difference in chiral optical force between LCPs and RCPs can be distinguished in the one-mode particle transport observations alone. Measurements of the effect at different wavelengths agreed quantitatively with simulation results, and the same experiment run using non-chiral particles produced no force dissymmetry, as expected.

Moreover, a counterpropagating mode configuration enabled isolation of the chiral optical force, allowing us to tie the direction of chiral nanoparticle transport to the handedness of the chiral light in the nanofibre. This method holds promise for more sophisticated manipulation, e.g. chirality-selective nanoparticle trapping and sorting, which we aim to explore in the future.

Another important prospect is to further reduce the size of the nanoparticles, which can be manipulated by these techniques, with the ultimate goal being the selective optical manipulation of chiral molecules. Given the current signal-to-noise ratio, it should be possible to measure velocities down to 10 μm s⁻¹ before the thermal noise swamps the velocity signal. This corresponds to forces of ~15 fN and to a reduction in particle volume by  ~ 10 times. The corresponding ~2-fold downsizing of the particle brings us to the sub-100-nm size regime. Further downscaling requires more optical power (see Supplementary Note 8), which can become problematic when using metallic nanoparticles near the plasmonic resonance, but should not be an issue for dielectric enantiomers such as drug molecules. Importantly, the relatively simple method and the robust nature of our experimental findings suggest that the nanofibre platform is ripe for further applications to chirality-selective optical manipulation.

Methods

Simulations

Numerical simulations were performed using a commercial implementation of the finite-difference time-domain method (Lumerical FDTD), with force calculations made from numerical evaluation and integration of the Maxwell stress tensor

$$T_{ij}=\frac{1}{4\pi }\left(E_i{E}_j+H_i{H}_j-\frac{1}{2}\left({∣\mathbf{E}∣}^2+{∣\mathbf{H}∣}^2\right){\delta }_{ij}\right),$$ 4

where E and H are amplitudes of the electric and magnetic fields E and H, respectively, and the indices i and j range over the {x, y, z} components.

We simulated the chiral cube nanoparticle using a parametric model in OpenSCAD software, following the same approach as in previous studies of such CNPs^11,28,37. More details of this model, along with the parameter selection, can be found in Supplementary Notes 1 and 2. The refractive index of CNP was set using a textbook model for gold⁴⁰.

The nanofibre was modelled as a constant diameter silica cylinder centred at (x = 0, y = 0) and parallel to the z-axis. The simulation included a 10 μm length of the fibre extending through the perfectly matched layer simulation boundaries. Field evaluations for the calculation of the stress tensor take place at the faces of a box which surrounds the CNP, but does not intersect with the nanofibre. The simulation meshing was non-uniform with a minimum grid size of 5 nm inside the CNP. In addition, we applied the conformal mesh refinement method⁴¹.

The particle was considered to be placed between 0 and 20 nm above the fibre surface. Although the exact distance does affect the absolute value of the force, our numerical tests showed that the value of the force dissymmetry g_z was not significantly affected by this placement, due to the chirality of the evanescent field being essentially independent of position. Note that the entire simulation used room temperature water as a background material, in correspondence to the experimental situation where colloidal particles are used.

LCP and RCP fibre modes were created by overlapping x- and y-polarised fundamental modes of the fibre with a phase difference of π/2 or −π/2, respectively. The modes propagated in the +z direction.

Scattering and absorption cross-sections of the CNPs were calculated using the supplied and purpose-made total-field scattered-field (TFSF) source in the commercial software. Scattered field intensities in the region around the CNP may be found in Supplementary Note 7.

Nanoparticle fabrication

The CNPs used in this study were prepared by a peptide-directed synthesis method²⁸. Pre-synthesised octahedral seeds were dispersed in an aqueous solution of hexadecyltrimethylammonium bromide (CTAB, 1 mM) before use. The growth solution was prepared by adding CTAB solution (0.8 mL, 100 mM) and aqueous gold chloride trihydrate solution (0.1 mL, 10 mM) to deionised water (3.95 mL). Aqueous ascorbic acid solution (0.475 mL, 100 mM) was then added to reduce Au³⁺ to Au⁺. The growth of CNP was initiated by adding aqueous L-glutathione solution (0.005 mL, 5 mM), followed by the addition of octahedral seed solution (0.05 mL). After stirring for 60 s, the growth solution was kept undisturbed at 30 °C for 2 h. The solution was centrifuged twice and redispersed in CTAB solution (1 mM).

For the preparation of silica-coated nanoparticles, an aqueous solution of methoxy polyethene glycol thiol (mPEG-SH, 5 kDa, 0.03 mL, 0.25 mM) was added to the as-synthesised chiral nanoparticle solution (1 mL) and stirred continuously for 30 min. The mPEG-modified nanoparticle solution was centrifuged three times and redispersed in ethanol (0.58 mL). Deionised water (0.167 mL) and an ethanol solution of ammonia (0.07 mL, 2 M) were added while stirring continuously. The reaction was started by adding an isopropanol solution of tetraethyl orthosilicate (0.014 mL, 10 vol%), and the solution was stirred continuously for 2 h. The silica-coated nanoparticle solution was centrifuged three times with ethanol. For the transport experiment and further characterisation, the nanoparticles were redispersed with deionised water. The circular dichroism spectrum of the silica-coated nanoparticle solution was measured using a commercial spectrophotometer (J-1500, JASCO Corp.) with a 1 mm path length quartz cell.

Non-chiral particles were gold nanospheres with a nominal diameter of 150 nm, obtained commercially from Nanopartz (A11-150-BARE-DIH).

Nanofibre fabrication and mounting

ONFs were manufactured in-house by tapering a commercial optical fibre (780HP by Thorlabs, Inc.) using a standard heat-and-pull technique^42,43 with hydrogen flame brushing. The waist region of the ONF had a typical diameter of 400 nm with a variation of about 10% between pulls. The adiabaticity of the pulling process was verified by measuring the transmission of the coupled laser light at 780 nm wavelength. A typical fibre taper profile may be found in Supplementary Note 6.

Once fabricated, the fibre was immersed in a drop (around 0.1 mL) of Milli-Q water and fixed to a microscope glass slide using an ultraviolet light-cured adhesive. In order to improve bright-field imaging of the fibre and to eliminate the adverse effects of the liquid evaporation, the immersed part of the fibre was covered with a second glass slide (150 μm-thick cover slip), in contact with water and supported at the corners by plastic patches around 1.5 mm thick. The meniscus of the air-water interface confined the liquid on the sides, so it acquired a cylindrical volume of radius ~10 mm. After being thus prepared, the sample was mounted on the 3D micrometric stage of the optical setup and connected to the fibre cables by fusion splicing. We performed bright-field transmission imaging of the ONF in order to locate its waist region and realised the polarisation compensation protocol for both forward (+z) and backward (−z) directions of propagation. Once these preparatory steps were done, we carefully lifted the cover slide and deposited a small drop (around 10 μL) of the aqueous solution with CNPs (or NCNPs) on top of the ONF, and repositioned the slide in order to stop diffusive flows and to protect the sample from dust. Because particles enter the volume around the fibre where the evanescent field is non-negligible only by chance, the particle solution must have a high enough concentration so that single particle events happen with sufficient frequency. For clear observations of individual optical transport events, we selected an appropriate concentration of the particles in a water solution by trial and error.

Optical setup

The experimental setup is sketched in Fig. 4A. As the laser sources, we used fibre-coupled laser diodes LP637-SF60 (P ≤ 70 mW, wavelength 637 nm), LP600-SF60 (≤60 mW, 660 nm), and LP785-SF100 (≤100 mW, 785 nm), all from Thorlabs, Inc. For better mechanical stability and a smaller footprint, the laser-linked parts of the setup were designed to be all-fibre, except the short free-space segment in the fibre bench (FB-76 with PAF2-2B fibre ports by Thorlabs, Inc.) containing pin-mounted optical elements for the polarisation control at the CP-mode side. The fibre-coupled diode Laser 1 of the chosen wavelength was connected directly to the fibre bench, whose output port was connected to a single-mode patch cable (P1-630Y-FC-1 by Thorlabs, Inc.) fixed on the paddles of MPC1. The cleaved end of this patch cable was fusion-spliced to one of the fibre pigtails of the ONF sample, and all loose fibres were taped to the optical table to ensure the stability of polarisation and power of the fibre modes. In the two-mode scheme (Fig. 3D), the second fibre pigtail of the sample was spliced to the patch cable running through MPC2 and connected (through the second fibre bench, not shown) to the fibre-coupled output of Laser 2, the source of the counterpropagating LP mode. The mode power was measured in transmission through the ONF (S130C photodiode sensor with the fibre bench mount FBSM, by Thorlabs, Inc.), while no particles were transported.

In order to locate the waist region, the water-immersed ONF sample was imaged in transmission using a microscope objective lens (Nikon Plan Fluor 40 × /0.60) under condensed illumination from a light-emitting diode. Light collected by the objective lens was focused by a plano-convex tube lens (focal length 150 mm) and imaged by a CMOS camera (Zelux CS165CU by Thorlabs, Inc.) fixed on a rotating mount, which was adjusted in order to have the fibre parallel to the horizontal sides of the image.

Polarisation control

Two MPCs, MPC1 and MPC2, and a liquid crystal variable retarder, VR2 (LCC1513-B by Thorlabs, Inc., on a custom 3D-printed pin-mount), were the only adjustable elements in the polarisation compensation stage of the experiment. The key to this procedure was imaging of the laser light scattered by natural imperfections of the ONF waist in pure water.

Following the two-step method³⁶, we first found and set the optimum angles α₁ and α₂ (marked by the red circle in Fig. 4D) for the MPC1 paddles, which were wrapped in three loops of the fibre patch cable (to ensure the complete coverage of the Poincaré sphere). At these angle values, the total polarisation transformation in the fibre was such that the horizontal state (provided by the polarisation beam splitter, FBT-PBS052, by Thorlabs, Inc.) was transferred from the fibre bench to the ONF waist unchanged. The horizontal (along the x-axis in the sample frame, see Fig. 4A–C) polarisation was verified by locating the maximum of the brightness sum of the laser-scattering image (Fig. 4C). In order to maximise the contrast of the brightness sum map, the longitudinal component of the light field was blocked by a linear polariser, P. We note that compared to the previously reported realisation of this first compensation step by random manual rotation of two quarter-wave plates^35,36, the automated approach realised here is quicker and much less sensitive to the operator’s errors, and therefore it is much more accurate.

For the second step of the compensation procedure, we inserted a half-wave plate, HWP, and the variable retarder, VR2. The HWP was pre-aligned using a free-space polarisation analyser (PAX1000VIS, by Thorlabs, Inc.) to produce the diagonal linear polarisation after the PBS. Then the retardance of VR2 was tuned such that the fibre mode at the ONF waist was also diagonally polarised (that is, having the electric field in the longitudinal plane tilted at +45° to the x-axis). This was checked by locating the absolute minimum of Δ = Σ₁ − Σ₂, where Σ₁ and Σ₂ are the brightness sums in the top (x > 0) and bottom (x < 0) parts of the scattering image (Fig. 4C), respectively. Once these two steps were done, any polarisation state—including CP states—was considered to be transferred from the fibre bench to the ONF waist unchanged³⁵. We then inserted (directly after the HWP) another full-wave variable retarder, VR1 (same as VR2), operated by a custom controller (square-wave generator based on OP07 operational amplifier, oscillation frequency 2 kHz) with two preset voltage values corresponding to RCP and LCP states (verified by PAX1000VIS in free space). During the experiments, the CP mode polarisation could be toggled between these two states.

For the two-mode scheme, only a fixed horizontal LP state was required. It was achieved by the partial compensation procedure, where we located and set the paddle angles of MPC2 corresponding to the maximum brightness sum of the scattering image, with only Laser 2 being coupled to the ONF. The MPCs were operated by a custom executable programme (developed in C# language for Windows OS, requires the Kinesis software package by Thorlabs, Inc.), which is available as Supplementary Code 1. The acquisition of the scattering image is realised by capturing the portion of the computer screen where the (appropriately adjusted) camera image is displayed, see also the user interface in Supplementary Note 4.

Measurement and analysis of particle transport

Scattered laser light from nanoparticles trapped and transported in the ONF evanescent field was recorded by the CMOS camera to movie files, which were the raw data from the experiment. In order to maximise the field of view and the frame rate, we used the lower-magnification objective lens (Olympus LU Plan Fluor 5 × /0.15) and cropped the image to fit the ONF and about ±50 μm in the x direction. The position of the particle along the fibre axis in each video frame was extracted from the raw data by a custom Python code. The best linear fit to these positions vs time, as shown in Fig. 5C, F, gave the transport velocity as the slope of the line.

We note that it was very occasionally necessary to exclude events from our analysis, principally due to particles and debris sticking to the fibre or very strong scattering, which we assumed to be due to particle clusters near the fibre. The majority of events showed scattered light of a similar intensity, indicating particles close to the standard geometry.

The ±1σ confidence ranges for v_L and v_R shown in Fig. 6A are respectively σ_L and σ_R, calculated as the standard deviations of the measured velocities from their mean values. The error bars for the force dissymmetry, g_z, in Fig. 6B were calculated using the error propagation for uncorrelated variables (since v_L and v_R were measured independently). Namely, the standard deviation for g_z was defined as

$${\sigma }_g=\sqrt{{\left(\frac{\partial g_z}{\partial v_L}{\sigma }_L\right)}^2+{\left(\frac{\partial g_z}{\partial v_R}{\sigma }_R\right)}^2}=\frac{4}{{\left(v_L+v_R\right)}^2}\sqrt{{\left(v_R{\sigma }_L\right)}^2+{\left(v_L{\sigma }_R\right)}^2}.$$ 5

Author contributions

G.T., H.O., and M.S. developed the original concept. G.T. developed the apparatus, performed the experiment, and analysed the data. A.S. took part in the data, contributed to the data analysis, and developed the original simulations. Y.I., I.K., and K.S. took part in the data collection and contributed to the data analysis. H.-Y.A., I.H.H. and K.T.N. synthesised and provided the nanoparticles, and contributed to the interpretation of the results. Y.X. contributed to the numerical simulations, and measured the fibre profile. G.T., A.S, H.-Y.A. and M.S. contributed to the particle model, and electromagnetic simulations. G.T. and M.S. wrote the paper. H.O. and M.S. co-supervised the project. All authors discussed the results, commented on the manuscript, and contributed to revisions.

Peer review

Peer review information

Nature Communications thanks Francisco Rodríguez-Fortuño and the other anonymous reviewer for their contribution to the peer review of this work [A peer review file is available].

Data availability

The data generated in this study have been deposited in the Figshare database under accession code https://figshare.com/s/de256b32dcce7b26e3d4. The raw data for the main findings of the paper, shown in Figs. 5b, e, are included (with annotations) are provided in the Supplementary Information as Supplementary Movies 1 and 2.

Code availability

Code to produce our 3D particle model used in simulations and to control the polarisation state in our experiments is given in the Supplementary Information. Python code for creating each figure is available at the following link: https://figshare.com/s/de256b32dcce7b26e3d4.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-71585-8.