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

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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}

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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}} )

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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

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Beta sheet

Alpha helix

From Chirality to Superchirality

Dipartimento di Fisica - Università di Pavia

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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

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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

Large optical chirality enhancement
Uniformity over large areas
Optical chirality switching
Broadband operation
Flat spectral response

Planar Geometries as an Ideal Candidate

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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

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

\[ \mathrm{ (\lambda_{TM},\theta_{TM})} \]

\[ \mathrm{ (\lambda_{TE},\theta_{TE})} \]

\[ \mathrm{ (\lambda_{TM},\theta_{TM})} \neq \mathrm{ (\lambda_{TE},\theta_{TE})} \]

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n_{high}

n_{low}

n_{high}

n_{low}

n_{high}

n_{low}

Aligning the Dispersion Relations

Dipartimento di Fisica - Università di Pavia

\[ \mathrm{ (\lambda_{TM},\theta_{TM})} \neq \mathrm{ (\lambda_{TE},\theta_{TE})} \]

\[ \mathrm{ (\lambda_{TM},\theta_{TM})} = \mathrm{ (\lambda_{TE},\theta_{TE})} \]

\( \mathrm{ (Wavelength)} \)

\( \mathrm{ (Angle)} \)

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A Hard Earned Solution: SiO2-Ta2O5 1PDC

Dipartimento di Fisica - Università di Pavia

Pellegrini, Giovanni, et al. "Chiral surface waves for enhanced circular dichroism." Physical Review B 95.24 (2017): 241402.
Pellegrini, Giovanni, et al. "Surface‐enhanced chiroptical spectroscopy with superchiral surface waves." Chirality 30.7 (2018): 883-889.
Pellegrini, Giovanni, et al. "Superchiral surface waves for all-optical enantiomer separation." The Journal of Physical Chemistry C 123.46 (2019): 28336-28342.

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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.

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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}