Letter Cite This: ACS Photonics XXXX, XXX, XXX−XXX
pubs.acs.org/journal/apchd5
Enantiospecific Optical Enhancement of Chiral Sensing and Separation with Dielectric Metasurfaces Michelle L. Solomon,*,† Jack Hu,† Mark Lawrence,† Aitzol García-Etxarri,‡,§ and Jennifer A. Dionne*,† †
Materials Science and Engineering, Stanford University, 496 Lomita Mall, Stanford, California 94305, United States Donostia International Physics Center and Centro de Fsica de Materiales CSIC-UPV/EHU, Paseo Manuel de Lardizabal 4, Donostia-San Sebastian 20018, Spain § IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain ‡
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S Supporting Information *
ABSTRACT: Circularly polarized light (CPL) exhibits an enantioselective interaction with chiral molecules, providing a pathway toward all-optical chiral resolution. High index dielectric nanoparticles have been shown to enhance this relationship, but with a spatially varying sign (or enantiospecificity) that yields a near zero spatially averaged enhancement. Using full field electromagnetic simulations, we design metasurfaces consisting of high index dielectric disks that provide large-volume, uniform-sign enhancements in both the optical density of chirality, C (the figure of merit for sensing and spectroscopy), and Kuhn’s dissymmetry factor, g (the figure of merit for separation). By varying disk radius, we achieve local enhancements in C and g up to 138-fold and 15-fold, respectively, as well as volumetric enhancements of 30-fold and 4.2fold. The uniform-sign enhancements in C occur near the first Kerker condition, where overlapping electric and magnetic modes maximize field strength and preserve the π/2 phase lag between the electric and magnetic fields of CPL; in contrast, uniformsign enhancements in g occur with spectrally separated modes, where fields and phase remain optimal without reduced molecular absorption. Using first-order kinetics of the molecule thiocamphor, we show how this optically enantiopure metasurface could enable 20% enantiomeric excesses with a >2000-fold increase in yield for a photoionization reaction compared to CPL alone. KEYWORDS: dielectric nanoparticles, chirality, enantiomer separation, Mie resonances, Kerker conditions
C
photoionize one of the enantiomers in a racemic solution, producing an excess of the opposite enantiomer. The efficiency of this separation is determined by Kuhn’s dissymmetry factor, g:
hirality, a geometric property in which an object is nonsuperimposable with its mirror image, is centrally important to biochemistry, where structure strongly dictates function.1−3 In the pharmaceutical industry, chiral specificity is critical because opposite enantiomers of a molecule can have beneficial or harmful biological effects.4,5 However, chemical syntheses often produce racemic mixtures with equal concentrations of both enantiomers. Since the enantiomers share the same scalar physical properties, conventional chemical separation techniques, such as chiral chromatography, are expensive and specific to molecular families. Illumination with chiral light is a potentially efficient and versatile method to both sense and identify chiral molecules and produce enantiopure solutions.6 Opposite enantiomers exhibit preferential absorption of left/right circularly polarized light (L-/R-CPL), a phenomenon known as circular dichroism (CD): CD ∝ A+ − A− +
g=
2(A+ − A−) A+ + A−
(2)
Asymmetric photoseparation with UV-CPL has been experimentally demonstrated, but is only able to achieve enantiomeric excesses of 2% while maintaining yields of 40% or higher.2,7 This low excess is because the preferential absorption of either R-CPL or L-CPL of most chiral biomolecules is relatively small. Significantly higher excesses could be produced in systems with a larger Kuhn’s dissymmetry factor.8 Recent studies have explored various photonic and plasmonic approaches to locally enhance chiral fields compared with CPL. For example, thin metallic mirrors, plasmonic
(1)
−
where A and A are a molecule’s rate of absorption of R-CPL and L-CPL, respectively. This differential absorption allows for chiral sensing and spectroscopy. It can also selectively © XXXX American Chemical Society
Received: September 29, 2018
A
DOI: 10.1021/acsphotonics.8b01365 ACS Photonics XXXX, XXX, XXX−XXX
ACS Photonics
Letter
Subsequently, the enantioselectivity of the system can be described by Kuhn’s dissymmetry factor, combining eq 2 with eq 4 and assuming that μ02χ″|H|2 is negligible (a valid assumption for most small molecules):
spheres, rods, and chiral helixes and high-index dielectric nanoparticles have been shown to enhance locally C up to 150fold.9−24 Many of these structures have also augmented g, up to 7-fold.12,24 However, the enhancements are generally only over very localized spatial regions, with both positive and negative enhancements around the structure. For practical chiral sensing, spectroscopy, and separation applications, large area, uniform-sign enhancements in C and g in tractable experimental geometries are crucial. Here, we show how large-area, enantiopure enhancements in the local density of optical chirality and Kuhn’s dissymmetry factor can be achieved. We consider metasurfaces consisting of high-index dielectric disks, tuning their aspect ratio to independently tune their electric and magnetic modes.25−31 These modes allow us to identify conditions that maximize local electromagnetic near-field intensities and maintain the perfectly circular π/2 phase lag of the incident light, leading to increased absorption of either right- or left-CPL, but not both. We find that an optimized metasurface can support enhancements in C and g that locally are as high as 138- and 15-fold, respectively. Due to the uniform sign, when averaged over large regions of the metasurface, these enhancements are as high as 30-fold (C) and 4.2-fold (g). Because we rely on the lowest order electric and magnetic modes, we achieve these large, enantiopure enhancements across visible and near-infrared frequencies, where many chiral molecules exhibit CD and VCD peaks. As a proof-of-concept, we project all-optical yields and enantiomeric excesses for the molecule thiocamphor via a photoionization reaction at a wavelength of 520 nm. In order to determine the chiral properties of an electromagnetic field, we first calculate the electromagnetic density of chirality, C, which is defined as21,32,33 C=−
ω ω Im(E*·H) = − 2 |E||H| cos(βiE, H) 2c 2 2c
i G″ yij 8C yzz z g = −jjj zzzjjj 2z k α″ {jk ωϵ0|E| z{
Noting that gCPL = −4G″/cα″ for the studied regime, we can express enhancements in Kuhn’s dissymmetry factor as g gCPL
ω 2 (α″|E|2 + μ02 χ ″|H|2 ) ∓ G″C ϵ0 2
(3)
(4)
where α″, χ″, and G″ are the imaginary components of the molecule’s electric polarizability, magnetic polarizability, and chiral polarizability. The difference in these absorption rates, described in eq 1, can be combined with eq 4 as CD ∝ −
4 G″ C ϵ0
=
2c C 1 |E||H|cos(βiE, H) =− 2 ωϵ0 |E| ωc |E|2
(7)
Many prior systems have relied on the reduction of the electric field intensity to increase the dissymmetry factor. However, such an approach limits overall molecular absorption, thereby limiting practical utility.9 Designing a system with enhanced local magnetic fields and a π/2 phase separation between E and H could allow for large g enhancements while maintaining incident field intensities. Accordingly, we only consider enhancements in g, where |E| ≥ |E0|, to explore the potential for efficient optical photoseparation. We use three-dimensional full-field finite difference time domain simulations to calculate the total fields from square arrays of dielectric disks with n = 3.5 (representative of silicon in the infrared) illuminated at normal incidence with CPL, as shown in the schematic in Figure 1a. Our metasurfaces consist of disks with height h = 200 nm, lattice constant a = 1000 nm, radii ranging from r = 150 to r = 350 nm, and a background index of n = 1. The transmission spectrum of the metasurface is shown in Figure 1b. For an array of disks with 280 nm radius, the lowest order mode occurs at λ = 1378 nm and the second-lowest order mode occurs at λ = 1262 nm, corresponding to an electric and magnetic mode, respectively. We confirm the dipolar nature of the two modes by plotting the magnitude and direction of the electric field, denoted by the colormaps and the arrows in Figure 1c, respectively. As we change the aspect ratio of the disks by decreasing the radius, the resonant frequencies shift. Figure 1d shows that while both resonances shift to shorter wavelengths, the electric dipolar mode is more sensitive than the magnetic dipolar mode, and the two begin to overlap. This result can be seen as the peak intensities of the electric and magnetic field, marked by dotted lines, decrease in spectral separation and finally overlap at a radius of 230 nm, corresponding to a radius to height aspect ratio of 1.15 to 1. At this aspect ratio, transmission through the array approaches 1; no light is scattered back to the source due to interference of the resonances, indicating a first Kerker-like condition in which the handedness of the incident light is conserved.34 As the radius is further decreased, the resonant frequencies shift apart again. To understand how enhancements in C and g external to the disks relate to these metasurface resonances, we study both spectral trends and spatial field distributions. Figure 2a plots the external maximum of C/CCPL at a single point as we vary the radius and incident wavelength. As in Figure 1d, the dotted lines mark the peak intensities of the electric and magnetic fields to visualize the resonant frequencies. As seen, the enhancements in C track the magnetic dipolar mode for radii smaller than 230 nm. At a radius of 230 nm, the electric and magnetic mode are simultaneously resonant at λ = 1219 nm;
Here E and H represent the complex electric and magnetic fields, and ω, ϵ0, and μ0 are the angular frequency of light, permittivity of free space, and permeability of free space, respectively. βiE,H describes the phase angle between E multiplied by the complex number i and H. From the above expression, it is clear that chiral fields must have parallel components of E and H that are phase shifted. For CPL, the parallel components of E and H have a π/2 phase difference, ϵω giving cos(βiE,H) = ±1; for CPL in a vacuum, CCPL = ± 20c E02 , where E0 is the magnitude of the incident electric field. Thus, C/CCPL will represent enhancements in the optical chirality due to the metasurface. The absorption of R-CPL (+) or L-CPL (−) by a chiral molecule is expressed as A± =
(6)
(5)
where enhancements in C will translate into enhancements of the CD signal. B
DOI: 10.1021/acsphotonics.8b01365 ACS Photonics XXXX, XXX, XXX−XXX
ACS Photonics
Letter
Figure 2. (a) Spatial maximum in C around the outside of a silicon metasurface with varying disk radii and incident wavelengths. Black dotted lines mark the spectral peaks of electric and magnetic fields for the two dipolar modes. (b) Normalized electric field amplitude, magnetic field amplitude, phase lag cos(βiE,H), and enhancement in local density of chirality, plotted for a disk with r = 230 nm and incident wavelength λ = 1219 nm. The white box indicates an interface between disk and air.
to track the electric dipolar mode. To elucidate these phenomena further, we turn to the field distributions at the ideal condition for enhancement in C: λ = 1219 nm and r = 230 nm. First, we see both high electric and magnetic field strength, as expected due to the concurrent resonances. Furthermore, cos(βiE,H), which is directly related to the phase difference between the electric and magnetic dipoles, is at its maximum in the entire region around the disk, indicating a phase lag of π/2. This consistent phase lag is due to the coincidence of resonances in both space and frequency on the Kerker-like condition, which combined lead to maximized optical chirality.35−39
Figure 1. (a) Schematic of silicon nanodisk metasurface illuminated by CPL with enantiospecific absorption. (b) Transmission spectrum of CPL through an array of disks with a height of 200 nm, radius of 280 nm, and refractive index of 3.5. (c) Electric field magnitude and direction maps of disk cross-section at the electric and magnetic dipolar modes. (d) Transmission spectra of arrays with h = 200 nm and radius 150−350 nm with a 2.5 nm step size. Dashed lines indicate peak intensity of the electric or magnetic field at the disk center.
the Kerker-like condition emerges, and we see the largest enhancements in C. Finally, as the radius is increased past the Kerker-like condition, enhancements in C decrease and begin C
DOI: 10.1021/acsphotonics.8b01365 ACS Photonics XXXX, XXX, XXX−XXX
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Figure 3. (a) Spatial maximum in g around the outside of a silicon metasurface with varying disk radii and incident wavelengths. Black dotted lines mark the peak locations of electric and magnetic field within the two dipolar modes. (b) Normalized electric field amplitude, magnetic field amplitude, cos(βiE,H), and enhancement in Kuhn’s dissymmetry factor, plotted for a disk with r = 255 nm and incident wavelength λ = 1297 nm. (c) Field distributions for a metasurface producing large spatial enhancements in g with r = 280 nm and λ = 1363.
Together, these conditions result in an enhanced region around each disk in the metasurface that is exclusively of one sign. The Kerker condition in this metasurface generates a maximum, local enhancement in C of 138-fold, as well as a 30fold global enhancement when averaged throughout a 100 nm shell around each single disk (see Supporting Information, Figure 6). In addition to the conservation of chirality, this large volume enhancement is further enabled by the low spatial variation in the lowest order dipolar modes, which gives rise to a consistent field distribution across the surface of the disk. At smaller radii, where the dipolar modes are partially overlapped, the enhancements in C follow the magnetic dipolar mode because the combined electric and magnetic field amplitude is higher at the magnetic dipolar mode than at the electric dipolar mode (see Supporting Information, Figure 7). However, the enhancements in C begin to track the electric mode as the radius is increased. Here, the electric field amplitude at the magnetic resonance decreases as the two modes move apart (see Supporting Information, Figures 7 and 8), while both field amplitudes remain high at the electric resonance. Overall, the design rules for high C enhancement are high electric and magnetic field strength, in addition to a π/2 phase lag between the two. This scenario occurs when an electric and magnetic mode peak at the same frequency, resulting in overlapping electric and magnetic fields in space and thus enhancement of a single-handedness. Unlike C, the condition for the external point enhancement in g is slightly shifted from the overlap of the resonances. As seen in Figure 3a, there is no enhancement when the resonances coincide, primarily due to the high electric field strength. As denoted by eq 7, g is instead enhanced when the magnetic field strength is high, the electric field strength is near unity (i.e., the field strength of the incident CPL), and the phase difference between the electric and magnetic field is near π/2. Therefore, g is enhanced at aspect ratios on either side of the Kerker-like condition. Additionally, enhancements track the electric dipolar mode, which exhibits a strong external magnetic field, but more modest external electric field. We also note that the highest enhancements occur just off the resonant wavelength, with the largest positive values blue-shifted and the largest negative values red-shifted. On the resonance itself, however, the enhancement in g drops to zero, while switching
from positive to negative with the phase lag of the radiated fields. While there is enhancement for radii both larger and smaller than 230 nm, the ideal condition occurs at a larger radius-to-height aspect ratio, with the absolute local maximum occurring at r = 255 nm and λ = 1297 nm. Due to the larger aspect ratio, here the magnetic field induced by the electric dipole resides more largely outside of the disk. However, as the radius approaches 300 nm, the spatial region with overlapped magnetic field enhancements and the appropriate relative phase of the fields decreases, producing more modest enhancements in g. To visualize the design rules for enhancement in g, Figure 3b plots the electric and magnetic field amplitude, cos(βiE,H) and the enhancement in g at the ideal condition of λ = 1297 nm for a disk of radius equal to 255 nm. In the electric field, we see three local maxima around the disk, while a region approximately 100 nm in diameter on top of the disk maintains an electric field strength near that of incident CPL. In the magnetic field, we see a region of enhancement that extends over the surface both above and below the cylinder. As the two modes are not simultaneously resonant and thus do not maintain the phase lag of the incident light, the differences in spatial enhancement of electric and magnetic fields is a crucial component of enhancement in g. This result is clear through consideration of cos(βiE,H), which reaches its maximum absolute values in regions where either the magnetic or the electric field is enhanced, but not both. This is in contrast to the Kerker condition, which saw cos(βiE,H) enhanced alongside both electric and magnetic fields. As expected, the enhancement in g is seen in the region centered above the disk, where the magnitude of cos(βiE,H) is near 1, and normalized electric field amplitude remains near, but not below, ∥E0∥. At this wavelength, the 255 nm radius disk reaches a maximum enhancement of 15-fold, though only in a small localized region. Similar to the enhancments in C, the observed enhancements in g are all enantiopure (that is, of uniform sign) for a given wavelength and radius. Due to the difficulty of localizing molecules specifically within one region of enhancement and their propensity for diffusion, this signconsistent enhancement is crucial for experimental enantiomeric separation. D
DOI: 10.1021/acsphotonics.8b01365 ACS Photonics XXXX, XXX, XXX−XXX
ACS Photonics
Letter
We also consider external enhancements in g over a larger, experimentally relevant volume. Specifically, we average the enhancement in g over a cylindrical volume 100 nm in height and 100 nm in radius centered above one disk within the array. By performing this calculation for the same radius range as in our local enhancement calculation, we find that the trend for maximum average enhancement closely follows that of the local point maximum (see Supporting Information, Figure 5). However, we find the ideal condition for this volume enhancement to be slightly shifted from the ideal position for a local point enhancement. While the highest point enhancement was seen with a 255 nm radius disk, the ideal condition for volume enhancements is a 280 nm radius disk or a 1.4:1 radius to height ratio. Referring back to the transmission map in Figure 1d, this result means that the most significant volume enhancement occurs when the electric and magnetic mode are resonant at more distinct frequencies than for the point enhancement. Figure 3c highlights the distinctions between the two cases. We first note that the spatial distribution of the magnetic field remains nearly the same between the two radii. The electric field, however, differs when comparing local versus large-area g enhancements. In particular, the enhanced region remains closer to the corners of the disk, and a large region directly above the disk remains at the amplitude of incident CPL. This result means that while the values of electric field, magnetic field, and cos(βiE,H) are of similar values to those in the r = 255 nm case, the ideal conditions for each overlap in different regions. Specifically, as can be seen in Figure 3b, this region occurs largely inside the disk in the 255 nm case, while it is pushed out into the region above the disk for the larger 280 nm radius disk. Thus, in the 280 nm radius case, the enhancement in g reaches its maximum absolute value approximately 75 nm above the disk rather than on the surface, occurring almost entirely outside of the disk. Therefore, while the maximum external enhancement is lower in the 280 nm radius disk at 8-fold compared to 15-fold, g is enhanced over a much larger external area. In particular, for these two cases, the average enhancement is 4.2-fold compared to 2.1-fold, respectively. To investigate the effect of optical loss on the system, enhancements in g were also calculated for metasurfaces at visible wavelengths where silicon becomes significantly absorptive.40 The 280 nm radius disk array, which produced the greatest volume enhancements in g, was scaled to achieve resonant modes in the visible. Disks with a 112 nm radius, 80 nm height, and 400 nm pitch produced a maximum point enhancement of 8-fold at 600 nm and an average enhancement (similarly scaled down in volume) of 4.2-fold at a wavelength of 614 nm. Since the magnetic and electric dipole modes that are interacting in this system have a low quality factor (Qm ≈ 9, Qe ≈ 16), the resonances are only weakly affected by material losses. The maximum g enhancement is also not significantly affected by the presence of a substrate (see SI for more details). Finally, we analyze the potential of the single-handed enhancement in the optimized metasurfaces to separate racemic chemical mixtures. The impact of these enhancements on a chiral photoseparation process can be determined from first-order photodecomposition kinetics8 ÄÅ É 1/2 − 1/ g −1/2 − 1/ g Ñ Å ÑÑ ÑÑ 1 ÅÅÅÅjij 1 + y zyz jij 1 + y zyz ÑÑ x = 1 − ÅÅjj + jj zz zz ÑÑ j z j z Å 2 ÅÅk 1 − y { 1 y − ÑÑ k { (8) ÅÇ ÑÖ
where x is the extent of reaction, y is the enantiomeric excess, and g is the effective dissymmetry factor of a chiral molecule present in a volume above a disk. For our example experimental system, we use the molecule thiocamphor, which exhibits gmolecule = 0.04 at 520 nm.41 This molecule is among several chiral molecules that exhibit resonant electronic transitions in the visible, including chiral fluorophores and biomolecules such as hemoglobin and bacteriorhodopsin.42−46 For this model system, we consider a metasurface of GaP, a high-index lossless material for most visible wavelengths, with disks of radius 110 nm and height 80 nm spaced by 400 nm. As shown in the schematic in Figure 4a, largest enhancements in g
Figure 4. (a) Enantiomeric excess plotted against percent yield in a photoionization reaction based on thiocamphor with gmolecule = 0.04, for three different volume regions above a disk with fixed height (H = 40 nm) and varying radii (R = 110, 80, 40 nm) vs CPL illumination. Inset schematic shows volumetric g enhancement above a GaP metasurface with a cylinder radius of 110 nm and height 80 nm. (b) Enantiomeric excess plotted against percent yield in a photoionization reaction based on thiocamphor for no enhancement, the maximum point enhancement for a silicon sphere,24 and that for the GaP disk metasurface (7- and 15-fold, respectively). (c) Percent yield plotted against absolute g for enantiomeric excesses (ee) of 10%, 20%, and 50%. Vertical lines mark values of g for thiocamphor with no enhancement (0.040), considering the enhancement in the smallest cylindrical region considered (0.126) and with the maximum enhancement (0.600).
occur in a spatial volume above the disks. We calculate a volume averaged enhancement when irradiated at λ = 520 nm (Figure 4a). For cylindrical volumes with radii 110, 80, and 40 nm and a height of 40 nm, the dissymmetry factor is increased 1.5-, 2.3-, and 4.2-fold, respectively. For this system, a 4.2-fold enhancement in g would increase the effective dissymmetry factor to gmolecule = 0.168. This enhancement would produce a mixture with [10%, 20%, 50%] enantiomeric excesses with a product yield (1 − x) of [30.45%, 9.11%, 0.17%] versus only [0.66%, 0.004%,
