Tailoring Enhanced Optical Chirality: Design Principles for Chiral Plasmonic Nanostructures

Electromagnetic fields with strong optical chirality can be formed in the near field of chiral plasmonic nanostructures. We calculate and visualize the degree of chirality to identify regions with relatively high values. This analysis leads to design principles for a simple utilization of chiral fields. We investigate planar geometries, which offer a convenient way to access the designated fields, as well as three-dimensional nanostructures, which show a very high local optical chirality.

Popular Summary

Many molecules encountered in chemistry and biology are “chiral,” in that they come in two structural enantiomers: the left- and the right-handed. Each is the mirror image of the other but cannot be superimposed onto its own mirror image through any rotation. The two enantiomers may taste different, as in the case of sugars. And they may behave differently, as in the case of chiral drugs interacting with the human body. Detecting the handedness of a chiral molecule is, therefore, crucial to understanding and controlling many biological or chemical processes.

The method that is currently used most commonly explores the fortunate fact that the two versions of a chiral molecule interact differently with circularly polarized light. But there is still a fundamental snag: The differences are usually small, and they need to be amplified for detection. A recent advent in chiral-molecule detection put forward a new concept of amplifying the differences through enhanced optical chirality: Nanoscaled metallic structures, onto which molecules are adsorbed or attached, are used to turn spatially uniform incident probing light into “superchiral” hot spots, where the light is either right- or left-circularly polarized and with enhanced intensity. How should one design structures for such tasks? In this paper, we answer this important open question.

There are a number of goals for a good design. Not only are high values of optical chirality needed, but large, continuous “hot“ regions with the enhanced optical chirality that are easily accessible for the chiral species are also most desirable. Easier fabrication is yet another goal. We have investigated different designs and compared their usefulness for practical chiral applications. We’ve discovered a number of basic design rules. For example, nanoscale elements with strong twist but without sharp corners lead to the best results, and three-dimensional chiral elements generate notably stronger optical chirality than two-dimensional ones. A superstructure that is composed of both handed species of a chiral metallic element should be used for simultaneous sensing of both species of a chiral molecule.

We believe that our investigation provides timely and vital insights needed for the further development of the new chirality-sensing approach.

Figure 1

To calculate the enantioselectivity in presence of chiral plasmonic structures, a modified dissymmetry factor $g^{*}$ is used. The definition requires a superstructure composed of both of the enantiomers of the single chiral nanostructure. Chiral probe molecules of one handedness (sketched as red spheres) are placed at corresponding positions at each of the enantiomers where the near fields differ only in the sign of optical chirality when the incident polarization is switched.

Figure 2

Optical chirality enhancement for (a) a left-handed helix with left-handed circularly polarized light and (b) a right-handed helix with right-handed circularly polarized light at a wavelength of $2.03\mu \mathrm{m}$. Diameter and height of the helix are 400 nm with a gold thickness of 80 nm. Both combinations show enhanced optical chirality where the values of maximum and minimum enhancement are denoted by the black horizontal lines across the color bars. The regions with enhanced optical chirality are located at corresponding positions of the respective helix, but their signs flip. The pictures addressing the polarization state are taken from the detector’s view; hence, the direction of the arrow indicates the handedness of the field vectors in space at a fixed time.

Figure 3

(a) Enhancement of dissymmetry factor ${\widehat{g}}^{*}$ near a plasmonic helix structure with respect to circularly polarized light. Superchiral light fields with up to 7 times higher enantioselectivity could be obtained. This value does not follow the enhancement of optical chirality directly, as (b) the enhancement of electric energy density $\widehat{U_e}$ also enters the calculation. The electric energy density shows similar distributions as optical chirality, leading to more complicated shapes of the superchiral light fields. Note the different scale of the color bar related to the plot of ${\widehat{g}}^{*}$ compared to the plots of $\widehat{C}$ in Fig. 2.

Figure 4

Optical chirality enhancement by a planar gammadion structure illuminated with (a) LCP and (b) RCP at a wavelength of $2.01\mu \mathrm{m}$. The structure exhibits similar shapes for the regions with enhanced chirality for both polarizations; only the values differ (as best seen in the two-dimensional slice views).

Figure 5

Enhancement of the electric energy density $\widehat{U_e}$ by the planar gammadion structure illuminated with right-handed circularly polarized light at a wavelength of $2.01\mu \mathrm{m}$. As for the optical chirality, the electric energy density has been normalized by the value obtained for RCP without the presence of the nanostructure. Strongest enhancement can be found at the end of each arm and the nearby gaps. For LCP, the enhancement is similar in shape.

Figure 6

Optical chirality enhancement by a two-armed gold nanospiral with (a) LCP and (b) RCP as incident polarizations at a wavelength of $1.84\mu \mathrm{m}$. The two polarizations differ significantly in their near-field response. The smaller pictures on the bottom of (a) and (b) show the scenario from different angles. The enhancement of the optical chirality for the nanospiral is up to 50% higher than for the gammadion, which can be understood by the fact that the spiral is bent everywhere.

Figure 7

Current distributions inside the nanospiral for incident (a) LCP and (b) RCP light at wavelength $1.84\mu \mathrm{m}$. The two polarizations excite different modes. The current distributions correspond to the regions with enhanced optical chirality as identified in Fig. 6.

Figure 8

Difference $\Delta \widehat{C}={\widehat{C}}_{+}-{\widehat{C}}_{-}$ of the chirality enhancement of the nanospiral. (a) The side view shows that the distribution of the enhanced regions is continuous, while the structure separates the parts with different signs. (b) In the presence of a substrate, the access is automatically limited to one polarity. Note that this picture is only a sketch, as the calculation was performed without the substrate.

Figure 9

Sketch of the chiral plasmonic oligomer. The arrangement of the gold disks mimics the chiral structure of a left-handed helix.

Figure 10

Optical chirality enhancement of the chiral oligomer for incident (a),(d) LCP and (b),(e) RCP light at a wavelength of 900 nm. The spatial points with strongest enhancement can be found on similar spatial locations but exhibit different signs, which leads to (c),(f) a very strong difference $\Delta \widehat{C}$. (d)–(f) Slices through the point between the top and bottom left disk of the front layer show that the region with strongest enhancement is located in the gap between these two disks.

Figure 11

Optical chirality enhancement induced by the stereometamaterial with (a) LCP and (b) RCP as incident polarizations at wavelength $1.34\mu \mathrm{m}$. Note that the enhancement is strongest when the handedness of the light is opposite to the handedness of the structure. The strongest enhancement can be observed in the middle of the layer between the two split-ring resonators.