From Chirality to Superchirality, from Molecules to Light
J. Barolak, G. Pellegrini, and P. Biagioni
Chirality (In Nature)
Dipartimento di Fisica - Università di Pavia
Molecules
DNA
Proteins
Left Enantiomer
Right Enantiomer
Spiral Meeting, 30-31 October 2024, Rome, Italy
Chirality and Light
Dipartimento di Fisica - Università di Pavia
Horizontal Polarization: TE
Vertical Polarization: TM
\begin{cases}
\mathbf{E}_{\mathrm{TE}} = \mathbf{E}^{0}_{\mathrm{TE}} * e^{i(kz-\omega t)} \\
\mathbf{E}^{0}_{\mathrm{TE}} = \{E_{x},0,0\}
\end{cases}
\begin{cases}
\mathbf{E}_{\mathrm{TM}} = \mathbf{E}^{0}_{\mathrm{TM}} * e^{i(kz-\omega t)} \\
\mathbf{E}^{0}_{\mathrm{TM}} = \{0,E_{y},0\}
\end{cases}
Spiral Meeting, 30-31 October 2024, Rome, Italy
Chirality and Light
Dipartimento di Fisica - Università di Pavia
Circular Polarization: Right (R)
\mathbf{E}_{\mathrm{L}} = \frac{1}{\sqrt{2}} ( \mathbf{E}_{\mathrm{TE}} + i*\mathbf{E}_{\mathrm{TM}} )
Circular Polarization: Left (L)
\mathbf{E}_{\mathrm{R}} = \frac{1}{\sqrt{2}} ( \mathbf{E}_{\mathrm{TE}} - i*\mathbf{E}_{\mathrm{TM}} )
Spiral Meeting, 30-31 October 2024, Rome, Italy
Chirality and Light
Dipartimento di Fisica - Università di Pavia
From Circular to Linear
\begin{cases}
\mathbf{E}_{\mathrm{TE}} = \frac{1}{\sqrt{2}} ( \mathbf{E}_{\mathrm{L}} + \mathbf{E}_{\mathrm{R}} ) \\
\mathbf{E}_{\mathrm{TM}} = -\frac{i}{\sqrt{2}} ( \mathbf{E}_{\mathrm{L}} - \mathbf{E}_{\mathrm{R}} ) \\
\end{cases}
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Chirality and Light: Circular Dichroism and Ellipticity
Dipartimento di Fisica - Università di Pavia
\begin{cases}
\mathrm{CD} = A_{R}-A_{L} \\
\mathrm{CD}_{L \, Enant.} = -\mathrm{CD}_{R \, Enant.}
\end{cases}
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Chirality and Light: Optical Rotation
Dipartimento di Fisica - Università di Pavia
\begin{cases}
\psi = \Delta \theta \\
\psi_{L \, Enant.} = -\psi_{R \, Enant.}
\end{cases}
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Chirality and Light: from Spectra to Structures
Dipartimento di Fisica - Università di Pavia
Spiral Meeting, 30-31 October 2024, Rome, Italy
Beta sheet
Alpha helix
From Chirality to Superchirality
Dipartimento di Fisica - Università di Pavia
Spiral Meeting, 30-31 October 2024, Rome, Italy
Molecule
Light
C = - \frac{\varepsilon_{0} \omega}{2} \mathrm{Im} (\mathbf{E}^{*} \cdot \mathbf{B})
g=-\left(\frac{G^{\prime \prime}}{\alpha^{\prime \prime}}\right)\left(\frac{2 C}{\omega U_e}\right)
Optical Chirality
Circular Dichroism
From Chirality to Superchirality: Focusing on \( \mathbf{E} \)
Dipartimento di Fisica - Università di Pavia
Spiral Meeting, 30-31 October 2024, Rome, Italy
Superchiral Light: Enhancing Chiral Light-Matter Interaction
Dipartimento di Fisica - Università di Pavia
Finazzi, Marco, et al. "Quasistatic limit for plasmon-enhanced optical chirality." Physical Review B 91.19 (2015): 195427.
Schäferling, Martin. "Chiral nanophotonics." Springer Series in Optical Sciences 205 (2017): 159.
C = -\frac{\varepsilon_{0} \omega}{2} Im(\mathrm{\mathbf{E}}^{*} \cdot \mathrm{\mathbf{B}})
Mattioli, F. et al. Plasmonic Superchiral Lattice Resonances in the Mid-Infrared. ACS Photonics 7, 2676–2681 (2020)
Local optical chirality
Optical chirality enhancement
\frac{C}{C_{\mathrm{CPL}}}
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Superchiral Light with a Planar Geometry
Dipartimento di Fisica - Università di Pavia
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Large optical chirality enhancement
-
Uniformity over large areas
-
Optical chirality switching
-
Broadband operation
-
Flat spectral response
Planar Geometries as an Ideal Candidate
Spiral Meeting, 30-31 October 2024, Rome, Italy
Leveraging Total Internal Reflection (TIR)
Dipartimento di Fisica - Università di Pavia
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A Planar Geometry for Superchiral Light: Take 1
Dipartimento di Fisica - Università di Pavia
TE ± i*TM
TE ± i*TM
Surface Plasmon
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A Planar Geometry for Superchiral Light: Take 2
Dipartimento di Fisica - Università di Pavia
Bloch Surface Waves (BSW)
TE ± i*TM
TE ± i*TM
\[ \mathrm{ (\lambda_{TM},\theta_{TM})} \]
\[ \mathrm{ (\lambda_{TE},\theta_{TE})} \]
\[ \mathrm{ (\lambda_{TM},\theta_{TM})} \neq \mathrm{ (\lambda_{TE},\theta_{TE})} \]
Spiral Meeting, 30-31 October 2024, Rome, Italy
n_{high}
n_{low}
n_{high}
n_{low}
n_{high}
n_{low}
Aligning the Dispersion Relations
Dipartimento di Fisica - Università di Pavia
\[ \mathrm{ (\lambda_{TM},\theta_{TM})} \neq \mathrm{ (\lambda_{TE},\theta_{TE})} \]
\[ \mathrm{ (\lambda_{TM},\theta_{TM})} = \mathrm{ (\lambda_{TE},\theta_{TE})} \]
\( \mathrm{ (Wavelength)} \)
\( \mathrm{ (Angle)} \)
Spiral Meeting, 30-31 October 2024, Rome, Italy
A Hard Earned Solution: SiO2-Ta2O5 1PDC
Dipartimento di Fisica - Università di Pavia
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Pellegrini, Giovanni, et al. "Chiral surface waves for enhanced circular dichroism." Physical Review B 95.24 (2017): 241402.
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Pellegrini, Giovanni, et al. "Surface‐enhanced chiroptical spectroscopy with superchiral surface waves." Chirality 30.7 (2018): 883-889.
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Pellegrini, Giovanni, et al. "Superchiral surface waves for all-optical enantiomer separation." The Journal of Physical Chemistry C 123.46 (2019): 28336-28342.
Spiral Meeting, 30-31 October 2024, Rome, Italy
Towards Surface Mode Polarization Control
Dipartimento di Fisica - Università di Pavia
Mogni, Erika, et al. "One‐Dimensional Photonic Crystal for Surface Mode Polarization Control." Advanced Optical Materials (2022): 2200759.
Spiral Meeting, 30-31 October 2024, Rome, Italy
The Lazy Man Solution: Multi Objective Optimization
Dipartimento di Fisica - Università di Pavia
\omega_1 \, (\lambda_1)
\omega_2 \, (\lambda_2)
\begin{cases}
C(\omega_1) = -\frac{\varepsilon_{0} \omega_1}{2} Im(\mathrm{\mathbf{E}}^{*} \cdot \mathrm{\mathbf{B}}) \\
C(\omega_2) = -\frac{\varepsilon_{0} \omega_2}{2} Im(\mathrm{\mathbf{E}}^{*} \cdot \mathrm{\mathbf{B}})
\end{cases}
Maximize \(C \)
@ \(\omega_1\) and \(\omega_2\)
@ the 1DPC Surface
SIMULTANEOUSLY!!!
Band Alignement
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Genetically Evolved (NSGAII) SiO2-Ta2O5 1PDC
Dipartimento di Fisica - Università di Pavia
SiO\(_{2}\)
Ta\(_{2}\)O\(_{5}\)
Vilfredo Pareto
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Genetically Evolved Cellulose-Polystyrene 1PDC
Dipartimento di Fisica - Università di Pavia
Polystyrene
Cellulose
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Genetically Evolved Low Contrast 1PDC
Dipartimento di Fisica - Università di Pavia
High Contrast
Ta\(_{2}\)O\(_{5}\)
SiO\(_{2}\)
SiO\(_{2}\)
SiO\(_{x}\)
Low Contrast
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High vs Low Dielectric Contrast: Zooming in the Bands
Dipartimento di Fisica - Università di Pavia
High Contrast
Ta\(_{2}\)O\(_{5}\)
SiO\(_{2}\)
SiO\(_{2}\)
SiO\(_{x}\)
Low Contrast
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High vs Low Dielectric Contrast: Reflection Maps for 1DPCs
Dipartimento di Fisica - Università di Pavia
High Contrast
Ta\(_{2}\)O\(_{5}\)
SiO\(_{2}\)
SiO\(_{2}\)
SiO\(_{x}\)
Low Contrast
Spiral Meeting, 30-31 October 2024, Rome, Italy
High vs Low Dielectric Contrast: CD Enhancement
Dipartimento di Fisica - Università di Pavia
High Contrast
Ta\(_{2}\)O\(_{5}\)
SiO\(_{2}\)
SiO\(_{2}\)
SiO\(_{x}\)
Low Contrast
Spiral Meeting, 30-31 October 2024, Rome, Italy