Superchiral hotspots in real chiral plasmonic structures

Light scattering from chiral plasmonic structures can create near fields with an asymmetry greater than the equivalent circularly polarised light, a property sometimes referred to as superchirality. These near fields with enhanced chiral asymmetries can be exploited for ultrasensitive detection of chiral (bio)molecules. In this combined experimental and numerical modelling study, we demonstrate that superchiral hot-spots are created around structural heterogeneities, such has protrusions and indentations, possessed by all real metal structures. These superchiral hot-spots, have chiral asymmetries greater than what would be expected from an idealised perfect structure. Our work indicates that surface morphology could play a role in determining the efficacy of a chiral structure for sensing.


Introduction
Using the tools of modern nanofabrication, periodic arrays of complex nanostructures of the same design can be routinely manufactured. Although, derived from the same idealised design, the apparently identical individual nanostructures have unique geometric variations, caused by intrinsic surface roughness or structural defects. The presence of these structural irregularities causes highly localised enhancements of EM fields within the overall near field region [1][2][3] . It has been accepted that when ensembles of nanostructures are considered within an array, the resulting linear optical response (e.g. reflection/transmission) is dependent upon the average of the individual nanostructures' morphologies. Consequently, an array of real structures can be considered a broadened version of that from an array of idealised structures 4 . However, this spatially averaging argument breaks down when one considers Raman scattering and non-linear optical responses, where observed spectroscopic responses are dominated by contributions from localised hot-spots associated with the geometric roughness and defects [5][6][7] . In addition, for complex structures that consist of multiple elements, surface roughness can alter the level of inductive coupling between elements, and hence modify optical response.
In this study we have investigated how surface roughness influences the level of the chiral asymmetries of near fields created by the optical excitation of chiral plasmonic structures.
Near fields generated by light scattering from nanostructures can, in localised regions of space, possess a greater level of chiral asymmetry than comparable circularly polarised light (CPL), a property sometimes referred to as superchirality. Such fields with enhanced chiral symmetry can be exploited for ultrasensitive detection of chiral (bio)molecules [8][9][10][11][12][13] . Numerical simulations used in previous studies to understand the chiral asymmetries of these field have relied on idealised models of the chiral structure 11,13,14 . In this study we have attempted to understand the influence of surface roughness by using a "real" model for the chiral nanostructure, a gammadion, directly derived from atomic force microscopy images, in periodic numerical simulations. The simulations are validated, by comparison with experimental circular dichroism spectra data. Simulated spectra obtained from the real model are in better agreement with the experimental data. Our study reveals that the idealised model underestimates the level of hybridisation, mediated by inductive coupling, between the arms of the gammadion structure. Significantly, surface roughness results in localised regions, close to the walls of the structure, with chiral asymmetries up to 2-3 timesgreater than those obtained from the idealised model. This suggests that surface roughness plays a role in determining the effectiveness of a chiral plasmonic structure for biodetection applications.

AFM Characterisation of structures
The gammadion structure studied has been chosen because it most closely matches those used in previous chiral sensing studies 8,11 . Representative atomic force microscopy (AFM) images of the structures are shown in figure 1 (A, B). Key parameters have been calculated by taking the mean of 5 measured values from the micrograph, these are shown on a plane view schematic of the structures in figure 1 (C). The gammadion consists of a central cross whose arms are 130 nm wide and 425 nm long and so the structure fits within a 425 × 425 nm square. The arms connected to the centre cross of the structure are thinner at 110 nm.
The spacing between the nanostructures is 375 nm.
The surface roughness of a given area is parameterised by the root-mean-square roughness (Rq). For the idealised gammadion nanostructures the Rq will be 0 as the surfaces are planar.
For the real gammadion, the Rq calculated at its top face is approximately 3.40 nm. Compare this with the glass substrate with a Rq  0.45 nm.

Real and Ideal models
The idealised model (Left handed, LH), which simplifies the geometry and morphology of the structures, is shown in figure 2  only one structure, selected arbitrarily, and the glass substrate is removed. The file is converted to a format that can be read by the numerical modelling software. This structure includes morphological defects and so it is described here as the 'real' structure.
Error! Reference source not found. (C) shows the profile of the 'real' gammadion model at 0, 50 and 100 nm above the glass substrate. The structure shows significant sloping as the height of the structure increases. Tip convolution can overestimate the lateral dimensions of the nanostructures, making protrusions from the surface appear larger and making holes appear smaller 15 . Therefore, it is likely that the micrograph overestimates the extent of the sloping.

Experimental and simulated CD spectra
Both experimental and simulated spectra for both gammadion enantiomorphs are displayed in figure 3. As expected, both measured and simulated, spectra for LH and RH structures are equal in magnitude but opposite in sign: they are mirrored around the 0 millidegree line of the plot. The experimental data has four pronounced resonances, labelled I-IV in order of increasing wavelength, that have corresponding features in the simulated spectra derived from both models. The positions of these band for measured and simulated spectra are given in table 1.
The level of CD observed in the simulated spectra are approximately an order of magnitude larger than those observed experimentally. A reduction by a factor of 2 can be attributed to the 'chessboard' fabrication strategy, which reduces the writing time of the lithography tool by patterning only half of the substrate (see supplementary information). Further reductions must be due to fabrication defects such as missing nanostructures, or missing parts of the structure which are not accounted for in either the ideal or real models.
It is readily apparent that, predictably, the simulations based on the real model provide the best qualitative agreement with the experimental data. However, while both the real and ideal models replicate the position of IV equally well, only the real model provides good qualitative agreement for bands I, II and III. In particular, the idealised model does not replicate the relative intensities of the three resonances, it also under-estimates the wavelength separation between resonances I and II

Simulated 3-D field plots
To rationalise the differences between ideal and real models requires an understanding of the origins of the resonances, which can in part be gained from maps of electric field magnitude | | and chiral asymmetries. The chiral asymmetry of a field can be conveniently parameterised using optical chirality density (C) [16][17][18][19][20] where is the displacement field, the magnetic induction and ̇ and ̇ are their respective timederivatives.
Three dimensional plots of the | | and C have been generated to aid interpretation. Mapping the entire ranges for the | | and C is ineffective for 3-D visualisation, as then only the field at the boundaries of the simulation are visible. By limiting the mapped fields to only those above a certain threshold, allows localised "hot -spot" regions of both | | and C to be easily observed. Analogous 2-D plots are shown in supplementary information.

Discussion
It is unsurprising that the simulations based on the real structure are in closer agreement with the overall measured experimental spectra. However, the ideal and real models do both replicate mode IV, the lattice mode, equally well. This can be attributed to the fact that the lattice mode will be predominately controlled by the periodicity and This symmetry reducing perturbation would be expected to cause a broadening of the CD resonances.
The differences in the positions and line shapes of modes I -II predicted by ideal and real models cannot be solely justified using the symmetry reducing perturbation argument.
Specifically, since surface roughness modifies both the intensities and chiral asymmetries of the near fields, creating hot-spots, one would expect that this would alter the level of inductive coupling between the rod elements of the gammadion structure. Intuitively, one would assume that the presence of hot-spots would enhance inductive coupling between the consistent rods. In previous work 21 it has been shown that the wavelength separation between modes I and III (subsequently labelled SI-III) scales with increasing coupling between neighbouring rod elements. The value of SI-III derived from the ideal model (78 nm) is smaller than that observed experimentally (92.7 nm), implying that it underestimates the magnitude of the inductive coupling. In contrast the SI-III obtained using the real model (107.9 nm) is larger than the experimental value.
To summarise the current study illustrates the advantages of using realistic structural models for the numerical modelling of the optical properties of metamaterials. Field maps derived from these "realistic" models reveal the presence of localised regions, or hot-spots, of enhanced | | and C which have a greater magnitude than the maximum values obtained from idealised models. An important implication of structural heterogeneity creating enhanced "superchiral" hot-spot in the vicinity of nanostructure, is that surfaces roughness could enhance the enantiomeric sensing ability of chiral nanostructures.

Numerical modelling
Numerical simulations of electromagnetic fields were performed using the COMSOL The material properties of the structure can then be implemented. To replicate the experimental CD work from the previous section, the gammadion nanostructure is placed onto the glass substrate with a refractive index equal to 1.5 then covered with water with refractive index 1.33.

Gammadion Sample Fabrication
The gammadia structures were fabricated using an electron beam lithography process. Quartz glass slides were cleaned under ultrasonic agitation in acetone, methanol and isopropyl alcohol (AMI) for 5 minutes each, dried under N2 flow and exposed to O2 plasma for 5 minutes