Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

Libang
Mao‡
,
Peiyuan
Cheng
,
Kuan
Liu
,
Meng
Lian
and
Tun
Cao‡
*

School of Optoelectronic Engineering and Instrumentation Science, Dalian University of Technology, Dalian 116024, China. E-mail: caotun1806@dlut.edu.cn

Received
22nd October 2021
, Accepted 7th February 2022

First published on 8th February 2022

Enantioseparation of chiral molecules is an important aspect of life sciences, chemical syntheses, and physics. Yet, the prevailing chemical techniques are not effective. Recently, a few types of plasmonic apertures have been theoretically proposed to distinguish between chiral molecules that vary based on their handedness under circularly polarized illumination. Both analytic calculations and numerical simulation demonstrated that enantioselective optical sieving could be obtained at the nanoscale using a large chiral optical force based on plasmonic resonance enhanced near-field chiral gradients in the aperture. Nevertheless, scaling this scheme to chiral entities of a few nanometer size (i.e., proteins and DNA) faces formidable challenges owing to the fabrication limit of a deeply sub-nanometer aperture and the intense power levels needed for nanoscale trapping. In contrast, by extending the Friedrich–Wintgen theory of the bound states in the continuum (BIC) to photonics, one may explore another mechanism to obtain enantioselective separation of chiral nanoparticles using all-dielectric nanostructures. Here, we present a metasurface composed of an array of silicon (Si) nanodisks embedded with off-set holes, which supports a sharp high-quality (Q) magnetic dipolar (MD) resonance originating from a distortion of symmetry-protected BIC, so called quasi-BIC. We, for the very first time, show that such a quasi-BIC MD resonance can markedly improve the chiral lateral force on the paired enantiomers with linearly polarized illumination. This quasi-BIC MD resonance can enhance the chirality density gradient with alternating sign at each octant around the Si nanodisk, while exhibiting a small gradient for the electromagnetic (EM) density. This offers a chiral lateral force that is 1 order larger in magnitude compared to the non-chiral lateral forces on sub-2 nm chiral objects with a chirality parameter of ±0.01. Moreover, the quasi-BIC MD resonance can excite four pairs of diverse optical potential wells (−13k_{B}T) that are distributed uniformly along the outer edge of the resonator, enabling a simultaneous separation of four paired enantiomers. Our proposed dielectric metasurface may move forward the techniques of enantioseparation and enantiopurification, taking a novel perspective to advanced all-optical enantiopure synthesis.

Although an optical manipulation of sub-100 nm entities has been obtained using plasmonic tweezers,^{22–25} these traps do not discriminate the chirality of objects. Recently, a few theoretical attempts to achieve the enantioselectivity of chiral nanoparticles have been demonstrated,^{14,26,27} where the chiral gradient force on the paired enantiomers with different handedness is reversed in direction. Yet, the nanometer (nm)-sized molecules possess a minute amount of chiral polarizability, making its chiral gradient force concealed by the nonchiral gradient force. This causes the resulting lateral force to be undiscriminating to the handedness of the chiral entity. Hence, in practice, the enantioselective separation is only possible when the magnitude of the chiral gradient force is much larger compared to the non-chiral gradient force. To strengthen the enantioselective optical forces, plasmonic nanoapertures have recently been used to improve the interference between the chiral molecules and the helicity of light, which is based on enhanced near-field chirality gradients. This leads to the selective trapping of nm-sized enantiomers with a handedness that matches the incident beam around the nanoaperture.^{28} Nevertheless, the plasmonic resonance enhanced electric (E−) field improves not only the chirality density, but also the light energy density gradients, decreasing the essential variation between the chiral and non-chiral gradient forces. Therefore, although the resultant lateral force can capture the enantiomer when its handedness matches the incident CPL, it cannot repulse the enantiomer with the opposite handedness. Distinct, discriminatory resultant lateral forces remain necessary in order to divide the enantiomers with opposite handedness. Very recently, it was demonstrated theoretically that the plasmonic nanoapertures with a broken symmetry can further increase the chirality density in a local region,^{29–31} allowing them to provide a distinct enantioselective resultant lateral force on chiral nanoparticles under the CPL. Nevertheless, scaling this scheme to chiral biomolecules in a few nanometer size (i.e., proteins, bacteria, and DNA) still represents a formidable challenge due to the tricky fabrication of a deeply sub-nanometer aperture, the intense power levels needed for nanoscale trapping, and the very limited region in the nanoaperture simultaneously possessing both high chiral density gradients and low light energy density gradients.

With the extension of the Friedrich–Wintgen theory of bound states in the continuum (BIC) to photonics,^{32} one may find another method to obtain distinct enantioselective separation of nanometer-sized objects using all-dielectric nanostructures. Bound states in the continuum (BIC) are a wave phenomenon observed generally in hydrodynamics, acoustics, and optics.^{33–35} Initially, the BIC existed in quantum mechanics.^{36} Later, it was interpreted based on destructive interaction when the coupling constant with radiating waves disappeared accidentally through a continuous modulation of parameters,^{37} a phenomenon referred to as the so-called Fridrich–Wintgen scenario. If the coupling constant disappears owing to symmetry, this BIC is symmetry protected.^{38} An ideal BIC possesses infinite quality (Q) factor and fading resonance width, which exists in ideal lossless infinite structures.^{32,39} Recently, BIC in photonic nanostructures^{38,40} has attracted intense attention in the fields of filtering, lasing, second-harmonic generation, and light shaping,^{41–49} where the bound states theoretically have infinite Q-factor. Nevertheless, practical techniques associated with the finite size of the device and structural imperfection lead to small coupling of BIC to the radiation continuum, providing leaky modes realized as quasi-BIC.^{50} These quasi-BICs can be treated as the supercavity mode when their Q-factor is finite.^{51} The BIC-induced mechanism of light localization enables the quasi-BICs to possess sharp Fano resonances (FRs) with extremely large Q-factors in coupled optical waveguides,^{52,53} subwavelength dielectric particles,^{54} photonic crystal slabs^{55,56} and optical cavities.^{57} In particular, the symmetry-protected BICs, where the radiative leakage is prohibited due to the incompatible symmetry between the external field and excited mode,^{58,59} can become radiative quasi-BICs by breaking the symmetry of the resonator or via off-normal incidence.^{60} It should be noted that, by coupling an optical mode of a large optical Q-factor to a mechanical mode of a large mechanical Q-factor, an intense optomechanical interference can be achieved.^{32} Thus, quasi-BICs may be promising for optomechanics.

Herein, we propose a dielectric metasurface made of an array of silicon (Si) nanodisks embedded with off-set holes to obtain enantioseparation of chiral nanoparticles. Such a design has recently been considered for exciting the quasi-BIC phenomenon.^{61} We systematically explored the optical force and potential endured by the paired enantiomers interfering with the near-field scattered by the meta-atom. Unlike many preceding plasmonic nanoapertures, our proposed dielectric structure can enantio-select and trap the entities at the outer edge of the resonator. As a consequence, it can be more straightforward to manipulate and process the trapped objects compared to the plasmonic nanoapertures. Moreover, this nanostructure is rather easy to fabricate and it needs neither nanometer-sized aperture nor free-standing substrates. Under linearly polarized illumination, a quasi-BIC induced FR can be observed in the metasurface by slightly shifting the circular hole away from the center of the Si nanodisk. This leads to a significant enhancement of the chirality density gradient with alternating sign at each octant around the resonator, while exhibiting a low gradient for electromagnetic (EM) density. This enables the chiral gradient force to be about one order bigger than the nonchiral gradient force. Hence, the proposed dielectric metasurface offers a distinct enantioselective resultant lateral force on 2 nm-radius chiral nanoparticles – a region that may allow optical enantioseparation and trapping of single proteins like enzymes. Meanwhile, we show that the quasi-BIC resonance can produce four pairs of diverse optical potential wells that are distributed uniformly along the outer edge of the meta-atom, which can concurrently separate four paired enantiomers. Our findings provide a fundamental design principle to make the future experimental study of the optical enantioseparation of chiral nano objects possible.

(1) |

(2) |

In Fig. 1c, the C/C_{0} is calculated to evaluate the chirality enhancement through the quasi-BIC MD resonance. With increasing s from 0 to 40 nm, the C/C_{0} obtains the largest enhancement factor of 1.36 × 10^{6} at s = 1 nm. Therefore, in our simulation, the resonator is optimized at s = 1 nm. In Fig. 1d, we demonstrate the distributions of chirality density enhancement C/C_{0} in the resonator with the off-sets of s = 0, 1, 2, and 5 nm, together with the simulated transmittance spectra shown in ESI Fig. S2.† It is obvious that changing the s allows for direct control on the quality (Q) factor of the dip resonance in the transmittance spectrum, which can drastically engineer the intensity of the chirality of the system. As is seen, the largest enhanced chiral field can be obtained at s = 1 nm for λ = 6203 nm. These enhanced chiral fields are confined along the outer edge of the Si nanodisk where the largest cos(θ_{iE,H}) appears (see ESI Fig. S1d†).

By introducing an asymmetry to the system that supports a symmetry-protected BIC, a pure BIC can be transformed to a quasi-BIC. For instance, by introducing an off-centered hole in the Si nanodisk, it is possible to open a radiation channel of the BICs in our proposed metasurface and transform the BIC state into a quasi-BIC state. In Fig. 1e, we calculate the band structure of the transverse electric (TE) mode for the symmetric metasurface made of an array of the Si nanodisk penetrated by a centered hole. Initially, the BIC response is produced by the symmetric Si rings supporting the MD resonance at the Γ point of the first Brillouin zone. By embedding the off-centered hole into the Si nanodisk to break the symmetry of the structure, we can change the BIC MD state possessing an infinite Q-factor to the quasi-BIC MD state with a finite Q-factor. The EM-field distribution of the eigenmode, presented in the inset of Fig. 1f, explores the MD feature of the BIC state. Moreover, other than the traditional confined guided modes supported by the periodic structure that is under the light cone, the BIC-inspired method permits directly exciting the quasi-BIC MD modes by free transmitting plane waves, enabling it to be a much more flexible platform for nanophotonics applications. In the real experiment, the Q-factor is composed of the nonradiative part Q_{nr} and radiative part Q_{r}via 1/Q = 1/Q_{nr} + 1/Q_{r}. In particular, the Q_{nr} includes a disorder of the structure, roughness of surface, the variation of fabricated device from the design, among others. The Q-factors of most dielectric metasurfaces under normal excitation are as small as a few thousand caused by the small Q_{nr} in the optical region. It has hugely hampered the exploitation of novel physics under intensely enhanced light-matter interference and their applications for opto-mechanics. In order to excite a MD resonance with high-Q factor under a normal excitation, one needs to break the symmetry of the system to transit the resonant mode from the BICs to quasi-BICs. With a lower degree of asymmetry, a larger Q_{r} is obtained.^{38,69} Thus, the ultrasmall degree of asymmetry is important for realizing high-Q quasi-BICs. Herein, the evolution of the quasi-BIC Q_{r} on the asymmetry parameter (ρ = s/600 nm) of the resonator follows the clearly inverse quadratic law,^{38} as presented in Fig. 1f,

Q_{r} = Q_{0}ρ^{−2} | (3) |

F_{t} = F_{α,β} + F_{χ} | (4) |

(5) |

(6) |

Since our sorting strategy relied on the near-field effect, it was important to investigate U_{t} for enantiomers that were located at different distances above the metasurface. In Fig. 5, we have presented the U_{t} around the enantiomeric pair (r_{p} = 2 nm) with κ_{p} = +0.01 (left column) and κ_{p} = −0.01 (right column), respectively, positioned at different distances above the meta-atom under an illumination of linearly polarized light. The magnitude of U_{t} was reduced with increasing distance between the enantiomers and metasurface. The stable trapping can be achieved by placing the enantiomers within 30 nm above the metasurface, where the magnitude of U_{t} was larger than 10k_{B}T. Although U_{t} can obtain the maximum value just on the surface of the meta-atom, the particle-surface force interaction may induce a strong dispersion force that damages the optical sorting of the molecules.^{83} Therefore, we placed the particle 20 nm above the surface of metasurface.

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## Footnotes |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1na00764e |

‡ These authors contributed equally. |

This journal is © The Royal Society of Chemistry 2022 |