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Olohan BJ, Petronijevic E, Kilic U, Wimer S, Hilfiker M, Schubert M, Argyropoulos C, Schubert E, Clowes SR, Pantoş GD, Andrews DL, Valev VK. Chiroptical Second-Harmonic Tyndall Scattering from Silicon Nanohelices. ACS NANO 2024; 18:16766-16775. [PMID: 38881465 PMCID: PMC11223486 DOI: 10.1021/acsnano.4c02006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2024] [Revised: 04/15/2024] [Accepted: 05/08/2024] [Indexed: 06/18/2024]
Abstract
Chirality is omnipresent in the living world. As biomimetic nanotechnology and self-assembly advance, they too need chirality. Accordingly, there is a pressing need to develop general methods to characterize chiral building blocks at the nanoscale in liquids such as water─the medium of life. Here, we demonstrate the chiroptical second-harmonic Tyndall scattering effect. The effect was observed in Si nanohelices, an example of a high-refractive-index dielectric nanomaterial. For three wavelengths of illumination, we observe a clear difference in the second-harmonic scattered light that depends on the chirality of the nanohelices and the handedness of circularly polarized light. Importantly, we provide a theoretical analysis that explains the origin of the effect and its direction dependence, resulting from different specific contributions of "electric dipole-magnetic dipole" and "electric dipole-electric quadrupole" coupling tensors. Using numerical simulations, we narrow down the number of such terms to 8 in forward scattering and to a single one in right-angled scattering. For chiral scatterers such as high-refractive-index dielectric nanoparticles, our findings expand the Tyndall scattering regime to nonlinear optics. Moreover, our theory can be broadened and adapted to further classes where such scattering has already been observed or is yet to be observed.
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Affiliation(s)
- Ben J. Olohan
- Centre
of Photonics and Photonic Materials, University
of Bath, Bath BA2 7AY, U.K.
- Centre
of Nanoscience and Nanotechnology, University
of Bath, Bath BA2 7AY, U.K.
| | | | - Ufuk Kilic
- Department
of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States
| | - Shawn Wimer
- Department
of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States
| | - Matthew Hilfiker
- Department
of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States
| | - Mathias Schubert
- Department
of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States
- Solid
State Physics and NanoLund, Lund University, Box 118, Lund, Skane 22100, Sweden
| | - Christos Argyropoulos
- Department
of Electrical Engineering, The Pennsylvania
State University, University Park, Pennsylvania 16803, United States
| | - Eva Schubert
- Department
of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States
| | | | - G. Dan Pantoş
- Department
of Chemistry, University of Bath, Bath BA2 7AY, U.K.
| | - David L. Andrews
- Centre
for Photonics and Quantum Science, University
of East Anglia, Norwich NR4 7TJ, U.K.
| | - Ventsislav K. Valev
- Centre
of Photonics and Photonic Materials, University
of Bath, Bath BA2 7AY, U.K.
- Centre
of Nanoscience and Nanotechnology, University
of Bath, Bath BA2 7AY, U.K.
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Bonvicini A. Irreducible Cartesian tensor decomposition: A computational approach. J Chem Phys 2024; 160:224105. [PMID: 38856057 DOI: 10.1063/5.0208846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2024] [Accepted: 05/22/2024] [Indexed: 06/11/2024] Open
Abstract
Cartesian tensors are widely used in physics and chemistry, especially for the formulation of linear and nonlinear spectroscopies as well as for molecular response properties. In this work, we review the problem of irreducible Cartesian tensor (ICT) decomposition of a generic Cartesian tensor of rank n into its irreducible parts, each characterized by a specific symmetry. The matrix formulation of the ICT decomposition is structurally similar to the problem of rotational averaging using isotropic Cartesian tensors. Analogously to the latter, the ICT decomposition can be considered as a problem of selecting a set of permutations of n indices that provides a linearly independent set of mappings between Cartesian tensor subspaces. This selection can be performed using a simple computational approach based on the reduced row echelon form (rref) algorithm. This protocol has been implemented in a computer code used to re-derive the already known ICT decomposition for 2 ≤ n ≤ 4. Finally, for the first time, we performed the explicit ICT decomposition of a Cartesian tensor of rank n = 5.
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Affiliation(s)
- Andrea Bonvicini
- Departement of Chemistry, Theoretical Chemistry Laboratory, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, Rue de Bruxelles 61, 5000 Namur, Belgium
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Cameron RP, Alexakis EI, Arnold AS, McArthur D. Theory of Rayleigh-Brillouin optical activity light scattering applicable to chiral liquids. Phys Chem Chem Phys 2024; 26:11641-11648. [PMID: 38546720 DOI: 10.1039/d3cp05109a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/18/2024]
Abstract
It has long been understood that dilute samples of chiral molecules such as rarefied gases should exhibit Rayleigh optical activity. We extend the existing theory by accounting for molecular dynamics and correlations, thus obtaining a more general theory of Rayleigh-Brillouin optical activity applicable to dense samples such as neat liquids.
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Affiliation(s)
- Robert P Cameron
- SUPA and Department of Physics, University of Strathclyde, Glasgow, G4 0NG, UK.
| | | | - Aidan S Arnold
- SUPA and Department of Physics, University of Strathclyde, Glasgow, G4 0NG, UK.
| | - Duncan McArthur
- SUPA and Department of Physics, University of Strathclyde, Glasgow, G4 0NG, UK.
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Andrews DL. Fundamental symmetry origins in the chiral interactions of optical vortices. Chirality 2023; 35:899-913. [PMID: 37403618 DOI: 10.1002/chir.23604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Revised: 05/24/2023] [Accepted: 06/14/2023] [Indexed: 07/06/2023]
Abstract
Recently, a variety of mechanisms have been discovered that extend the range of optical techniques for identifying and characterizing molecular chirality, beyond those associated with optical polarization. It is now evident that beams of light with a twisted wavefront, known as optical vortices, can also interact with chiral matter with a specificity determined by relative handedness. Exploring this chiral sensitivity of vortex light in its interactions with matter requires careful consideration of the symmetry properties that engage in such processes. Most of the familiar measures of chirality are directly applicable to either matter, or to light itself-but only to one or the other. To elicit the principles that determine the viability of distinctly optical vortex-based forms of chiral discrimination invites a more universal approach to symmetry analysis, as is afforded by the common, fundamental physics of CPT symmetry. Taking this approach supports a comprehensive and straightforward analysis to identify the mechanistic origins of vortex chiroptical interactions. Careful inspection of selection rules for absorption also elicits the principles governing any identifiable engagement with vortex structures, providing a reliable basis to ascertain the viability of other forms of enantioselective vortex interaction.
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Affiliation(s)
- David L Andrews
- Centre for Photonics and Quantum Science, School of Chemistry, University of East Anglia, Norwich, UK
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Bonvicini A, Champagne B. Third-harmonic scattering optical activity: QED theory, symmetry considerations, and quantum chemistry applications in the framework of response theory. J Chem Phys 2023; 159:114107. [PMID: 37712789 DOI: 10.1063/5.0165425] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Accepted: 08/28/2023] [Indexed: 09/16/2023] Open
Abstract
In this work, expressions for the third-harmonic scattering optical activity (THS-OA) spectroscopic responses are derived by combining molecular quantum electrodynamics (QED) and response theory, allowing their computational implementation. The QED theory of THS-OA presented here is meant to be an extension of a previous study by Andrews [Symmetry 12, 1466 (2020)]. In particular, the THS-OA phenomena are described within the Power-Zienau-Woolley multipolar Hamiltonian by including the electric-dipole, magnetic-dipole, and electric-quadrupole interactions for the absorption as well as the emission processes between the dynamic electromagnetic field (the photons) and matter. Moreover, we derive the expressions for the differential scattering ratios as a function of the scattering angle defined by the wavevectors of the incident and scattered photons. We show how the pure and mixed second hyperpolarizabilities can be obtained in the framework of response theory as specific cases of a generic cubic response function, thus enabling the computational implementation of THS-OA spectroscopy. We prove the origin-independence of the theory for exact wavefunctions. Preliminary computations on a prototype chiral molecule (methyloxirane) are considered together with an analysis of the basis set convergence and of the origin-dependence.
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Affiliation(s)
- Andrea Bonvicini
- Theoretical Chemistry Laboratory, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, B-5000 Namur, Belgium
| | - Benoît Champagne
- Theoretical Chemistry Laboratory, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, B-5000 Namur, Belgium
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Andrews DL. Symmetry-based identification and enumeration of independent tensor properties in nonlinear and chiral optics. J Chem Phys 2023; 158:034101. [PMID: 36681645 DOI: 10.1063/5.0129636] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
For many laser-based methods of material characterization and analysis, a tensor formulation of theory is necessary, especially in techniques that exploit nonlinear or chiral optics. The fundamental interactions that underpin such methods offer various levels of approach to theory, but the most rigorous often lead to equations of considerable complexity. To compute the values for individual material parameters frequently demands making assumptions of extreme simplicity, overly dependent on calculational method, yet still providing unsatisfactory results. A pragmatic and entirely rigorous symmetry-based approach to the irreducible tensorial structures circumvents many of these problems, securing reliable results and guiding the pathway to applications. Instead of focusing on individual tensor components, such an approach can rapidly determine the number of linearly independent quantities-and hence the number of operationally different setups necessary for full characterization. By such means, one can directly ascertain how variations of optical polarization and beam geometry can reliably capture the response of any material system. The use of an irreducible tensor method operates independently of any means that might be chosen to calculate material properties. It removes the need for common simplifying assumptions, such as the approximation of tensorial structure by a scalar representation, adoption of a two-state model, or disregarding near-resonance damping. It also obviates any dependence on a choice of simulation package or quantum-calculational software. In this paper, the principles are set down and illustrated by application to experiments of varying degrees of complexity, including interactions of growing significance in the realm of chiral nonlinear optics. Limitations of this approach are also critically assessed.
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Affiliation(s)
- David L Andrews
- School of Chemistry, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, United Kingdom
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