# Numerical Modeling of 3D Chiral Metasurfaces for Sensing Applications

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

**E**|/

**E ${}_{0}$**) on the helix surface at the three resonance peaks. A significant enhancement of the electric field can be appreciated for the absorbance peak at 792 nm (≈9), at 957 nm (≈6), and 1173 nm (≈6).

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

SPP | Surface Plasmon Polaritons |

LSPR | Localized Surface Plasmon Resonances |

SERS | Surface Enhanced Raman Spectroscopy |

LCP | Left Circular Polarized |

RCP | Right Circular Polarized |

CD | Circular Dichroism |

UV | Ultraviolet |

IR | Infrared |

FOM | Figure of Merit |

EWFD | Electromagnetic Waves, Frequency Domain |

PDEs | Partial Differential Equations |

FEM | Finite Element Method |

PBCs | Periodic Boundary Conditions |

PMLs | Perfect Matched Layers |

TM | Transverse Magnetic |

R | Reflectance |

T | Transmittance |

A | Absorbance |

FWHM | Full Width at Half Maximum |

E | Electric Field |

RIU | Refractive Index Unit |

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**Figure 1.**(

**a**) The geometry of one lateral unit cell of the out-of-plane chiral structure composed of a right-handed Au helix on a glass substrate with the relevant structure parameters illustrated: the wire radius (r), helix radius (R), axial pitch (p), and the lattice constant (a). The out-of-plane periodicity is indicated by N. The geometry of the chiral metasurface for (

**b**) a = 100 nm and (

**c**) a = 250 nm.

**Figure 2.**Normalized absorbance map of the plasmonic metasurface as a function of (

**a**) the in-plane periodicity a in the range 100–250 nm and (

**b**) the out-of-plane periodicity N in the range 1–4. (

**c**) The angle of incidence in the range 40–60${}^{\circ}$.

**Figure 3.**(

**a**) Spectral characterization of the plasmonic metasurface: absorbance spectra calculated for different concentrations of 1,2,3-Propantriol for a = 250 nm; (

**b**) linear fit of the peak wavelength plotted versus the refractive index of the medium for the three resonant modes. The fitting equation is ${\lambda}_{p}$ = ${\lambda}_{0}$ + Sn; the correlation coefficient is R = 0.99 for the three fits.

**Figure 4.**Electric field enhancement on the helix surface at the three ${\lambda}_{p}$: 792 nm, 957 nm, and 1173 nm.

**Figure 5.**Absorbance and transmittance spectra of the plasmonic metasurface for (

**a**) Right-Circular Polarized (RCP) and (

**b**) Left-Circular Polarized (LCP) light. (

**c**) CD spectra calculated in a 1,2,3-Propantriol–water solution at different molar concentrations ranging from 0% (corresponding to water (n = 1.333)) to 82% 1,2,3-Propantriol in water (n = 1.467). (

**d**) Linear fit of the peak wavelength plotted versus the refractive index of the medium.

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**MDPI and ACS Style**

Guglielmelli, A.; Nicoletta, G.; Valente, L.; Palermo, G.; Strangi, G.
Numerical Modeling of 3D Chiral Metasurfaces for Sensing Applications. *Crystals* **2022**, *12*, 1804.
https://doi.org/10.3390/cryst12121804

**AMA Style**

Guglielmelli A, Nicoletta G, Valente L, Palermo G, Strangi G.
Numerical Modeling of 3D Chiral Metasurfaces for Sensing Applications. *Crystals*. 2022; 12(12):1804.
https://doi.org/10.3390/cryst12121804

**Chicago/Turabian Style**

Guglielmelli, Alexa, Giuseppe Nicoletta, Liliana Valente, Giovanna Palermo, and Giuseppe Strangi.
2022. "Numerical Modeling of 3D Chiral Metasurfaces for Sensing Applications" *Crystals* 12, no. 12: 1804.
https://doi.org/10.3390/cryst12121804