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Zerulla B, Beutel D, Holzer C, Fernandez-Corbaton I, Rockstuhl C, Krstić M. A Multi-Scale Approach to Simulate the Nonlinear Optical Response of Molecular Nanomaterials. Adv Mater 2024; 36:e2311405. [PMID: 38009234 DOI: 10.1002/adma.202311405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Indexed: 11/28/2023]
Abstract
Nonlinear optics is essential for many recent photonic technologies. Here, a novel multi-scale approach is introduced to simulate the nonlinear optical response of molecular nanomaterials combining ab initio quantum-chemical and classical Maxwell-scattering computations. In this approach, the first hyperpolarizability tensor is computed with time-dependent density-functional theory and incorporated into a multi-scattering formalism that considers the optical interaction between neighboring molecules. Such incorporation is achieved by a novel object: the Hyper-Transition(T)-matrix. With this object at hand, the nonlinear optical response from single molecules and also from entire photonic devices can be computed, including the full tensorial and dispersive nature of the optical response of the molecules, as well as the optical interaction between different molecules as, for example, in the lattice of a molecular crystal. To demonstrate the applicability of the novel approach, the generation of a second-harmonic signal from a thin film of an Urea molecular crystal is computed and compared to more traditional simulations. Furthermore, an optical cavity is designed, which enhances the second-harmonic response of the molecular film up to more than two orders of magnitude. This approach is highly versatile and accurate and can be the working horse for the future exploration of nonlinear photonic molecular materials in structured photonic environments.
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Affiliation(s)
- Benedikt Zerulla
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76131, Karlsruhe, Germany
| | - Dominik Beutel
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), 76131, Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), 76131, Karlsruhe, Germany
| | - Ivan Fernandez-Corbaton
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76131, Karlsruhe, Germany
| | - Carsten Rockstuhl
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76131, Karlsruhe, Germany
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), 76131, Karlsruhe, Germany
| | - Marjan Krstić
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), 76131, Karlsruhe, Germany
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Zerulla B, Krstić M, Beutel D, Holzer C, Wöll C, Rockstuhl C, Fernandez-Corbaton I. A Multi-Scale Approach for Modeling the Optical Response of Molecular Materials Inside Cavities. Adv Mater 2022; 34:e2200350. [PMID: 35384088 DOI: 10.1002/adma.202200350] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Revised: 03/17/2022] [Indexed: 06/14/2023]
Abstract
The recent fabrication advances in nanoscience and molecular materials point toward a new era where material properties are tailored in silico for target applications. To fully realize this potential, accurate and computationally efficient theoretical models are needed for: a) the computer-aided design and optimization of new materials before their fabrication; and b) the accurate interpretation of experiments. The development of such theoretical models is a challenging multi-disciplinary problem where physics, chemistry, and material science are intertwined across spatial scales ranging from the molecular to the device level, that is, from ångströms to millimeters. In photonic applications, molecular materials are often placed inside optical cavities. Together with the sought-after enhancement of light-molecule interactions, the cavities bring additional complexity to the modeling of such devices. Here, a multi-scale approach that, starting from ab initio quantum mechanical molecular simulations, can compute the electromagnetic response of macroscopic devices such as cavities containing molecular materials is presented. Molecular time-dependent density-functional theory calculations are combined with the efficient transition matrix based solution of Maxwell's equations. Some of the capabilities of the approach are demonstrated by simulating surface metal-organic frameworks -in-cavity and J-aggregates-in-cavity systems that have been recently investigated experimentally, and providing a refined understanding of the experimental results.
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Affiliation(s)
- Benedikt Zerulla
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), D-76344, Eggenstein-Leopoldshafen, Germany
| | - Marjan Krstić
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), D-76131, Karlsruhe, Germany
| | - Dominik Beutel
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), D-76131, Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), D-76131, Karlsruhe, Germany
| | - Christof Wöll
- Institute of Functional Interfaces, Karlsruhe Institute of Technology (KIT), D-76344, Eggenstein-Leopoldshafen, Germany
| | - Carsten Rockstuhl
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), D-76344, Eggenstein-Leopoldshafen, Germany
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), D-76131, Karlsruhe, Germany
| | - Ivan Fernandez-Corbaton
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), D-76344, Eggenstein-Leopoldshafen, Germany
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Beutel D, Rockstuhl C, Fernandez-Corbaton I. T-Matrix based Scattering Analysis of Photonic Materials with Periodicity in Different Dimensions. EPJ Web Conf 2022. [DOI: 10.1051/epjconf/202226605003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
Optical devices and artificial photonic materials frequently make use of periodic arrangements of identical scatterers in 3D, 2D, and 1D, e.g. photonic crystals, meta-surfaces, or particle chains. To simplify their analysis, we present here a computational framework based on the T-matrix method that explicitly exploits spherical, cylindrical, and plane waves depending on the geometry and number of dimensions of the lattice. Due to the analytic properties of the chosen basis sets in combination with the use of Ewald’s method for the lattice summation, we obtain an efficient framework to simulate such systems. The applicability will be illustrated at the conference by means of selected examples of contemporary interest.
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Abstract
We outline a methodology for efficiently computing the electromagnetic response of molecular ensembles. The methodology is based on the link that we establish between quantum‐chemical simulations and the transfer matrix (T‐matrix) approach, a common tool in physics and engineering. We exemplify and analyze the accuracy of the methodology by using the time‐dependent Hartree‐Fock theory simulation data of a single chiral molecule to compute the T‐matrix of a cross‐like arrangement of four copies of the molecule, and then computing the circular dichroism of the cross. The results are in very good agreement with full quantum‐mechanical calculations on the cross. Importantly, the choice of computing circular dichroism is arbitrary: Any kind of electromagnetic response of an object can be computed from its T‐matrix. We also show, by means of another example, how the methodology can be used to predict experimental measurements on a molecular material of macroscopic dimensions. This is possible because, once the T‐matrices of the individual components of an ensemble are known, the electromagnetic response of the ensemble can be efficiently computed. This holds for arbitrary arrangements of a large number of molecules, as well as for periodic or aperiodic molecular arrays. We identify areas of research for further improving the accuracy of the method, as well as new fundamental and technological research avenues based on the use of the T‐matrices of molecules and molecular ensembles for quantifying their degrees of symmetry breaking. We provide T‐matrix‐based formulas for computing traditional chiro‐optical properties like (oriented) circular dichroism, and also for quantifying electromagnetic duality and electromagnetic chirality. The formulas are valid for light‐matter interactions of arbitrarily‐high multipolar orders.
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Affiliation(s)
- Ivan Fernandez-Corbaton
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), P.O. Box 3640, 76021, Karlsruhe, Germany
| | - Dominik Beutel
- Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, 76049, Karlsruhe, Germany
| | - Carsten Rockstuhl
- Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, 76049, Karlsruhe, Germany.,Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), P.O. Box 3640, 76021, Karlsruhe, Germany
| | - Ansgar Pausch
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, 76049, Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, 76049, Karlsruhe, Germany.,Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), P.O. Box 3640, 76021, Karlsruhe, Germany
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Kosik M, Burlayenko O, Rockstuhl C, Fernandez-Corbaton I, Słowik K. Interaction of atomic systems with quantum vacuum beyond electric dipole approximation. Sci Rep 2020; 10:5879. [PMID: 32246018 PMCID: PMC7125098 DOI: 10.1038/s41598-020-62629-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2020] [Accepted: 03/09/2020] [Indexed: 11/17/2022] Open
Abstract
The photonic environment can significantly influence emission properties and interactions among atomic systems. In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. While this holds true for many canonical systems, it ceases to be applicable for more contemporary nanophotonic structures. To go beyond the electric dipole approximation, we propose and develop in this article an analytical framework to describe the impact of the photonic environment on emission and interaction properties of atomic systems beyond the electric dipole approximation. Particularly, we retain explicitly magnetic dipolar and electric quadrupolar contributions to the light-matter interactions. We exploit a field quantization scheme based on electromagnetic Green’s tensors, suited for dispersive materials. We obtain expressions for spontaneous emission rate, Lamb shift, multipole-multipole shift and superradiance rate, all being modified with dispersive environment. The considered influence could be substantial for suitably tailored nanostructured photonic environments, as demonstrated exemplarily.
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Affiliation(s)
- Miriam Kosik
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100, Torun, Poland.
| | - Oleksandr Burlayenko
- Department of Physics and Technology, V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
| | - Carsten Rockstuhl
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, 76131, Karlsruhe, Germany.,Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany
| | | | - Karolina Słowik
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100, Torun, Poland.
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Feis J, Beutel D, Köpfler J, Garcia-Santiago X, Rockstuhl C, Wegener M, Fernandez-Corbaton I. Helicity-Preserving Optical Cavity Modes for Enhanced Sensing of Chiral Molecules. Phys Rev Lett 2020; 124:033201. [PMID: 32031847 DOI: 10.1063/5.0025006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Accepted: 11/13/2020] [Indexed: 05/20/2023]
Abstract
Researchers routinely sense molecules by their infrared vibrational "fingerprint" absorption resonances. In addition, the dominant handedness of chiral molecules can be detected by circular dichroism (CD), the normalized difference between their optical response to incident left- and right- handed circularly polarized light. Here, we introduce a cavity composed of two parallel arrays of helicity-preserving silicon disks that allows one to enhance the CD signal by more than 2 orders of magnitude for a given molecule concentration and given thickness of the cell containing the molecules. The underlying principle is first-order diffraction into helicity-preserving modes with large transverse momentum and long lifetimes. In sharp contrast, in a conventional Fabry-Perot cavity, each reflection flips the handedness of light, leading to large intensity enhancements inside the cavity, yet to smaller CD signals than without the cavity.
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Affiliation(s)
- Joshua Feis
- Institute of Applied Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Dominik Beutel
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Julian Köpfler
- Institute of Applied Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
- Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - Xavier Garcia-Santiago
- Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
- JCMWave GmbH, 14050 Berlin, Germany
| | - Carsten Rockstuhl
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
- Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - Martin Wegener
- Institute of Applied Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
- Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
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7
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Feis J, Beutel D, Köpfler J, Garcia-Santiago X, Rockstuhl C, Wegener M, Fernandez-Corbaton I. Helicity-Preserving Optical Cavity Modes for Enhanced Sensing of Chiral Molecules. Phys Rev Lett 2020; 124:033201. [PMID: 32031847 DOI: 10.1103/physrevlett.124.033201] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Indexed: 05/20/2023]
Abstract
Researchers routinely sense molecules by their infrared vibrational "fingerprint" absorption resonances. In addition, the dominant handedness of chiral molecules can be detected by circular dichroism (CD), the normalized difference between their optical response to incident left- and right- handed circularly polarized light. Here, we introduce a cavity composed of two parallel arrays of helicity-preserving silicon disks that allows one to enhance the CD signal by more than 2 orders of magnitude for a given molecule concentration and given thickness of the cell containing the molecules. The underlying principle is first-order diffraction into helicity-preserving modes with large transverse momentum and long lifetimes. In sharp contrast, in a conventional Fabry-Perot cavity, each reflection flips the handedness of light, leading to large intensity enhancements inside the cavity, yet to smaller CD signals than without the cavity.
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Affiliation(s)
- Joshua Feis
- Institute of Applied Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Dominik Beutel
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Julian Köpfler
- Institute of Applied Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
- Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - Xavier Garcia-Santiago
- Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
- JCMWave GmbH, 14050 Berlin, Germany
| | - Carsten Rockstuhl
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
- Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
| | - Martin Wegener
- Institute of Applied Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
- Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
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8
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Fernandez-Corbaton I, Rockstuhl C, Ziemke P, Gumbsch P, Albiez A, Schwaiger R, Frenzel T, Kadic M, Wegener M. New Twists of 3D Chiral Metamaterials. Adv Mater 2019; 31:e1807742. [PMID: 30790363 DOI: 10.1002/adma.201807742] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2018] [Indexed: 06/09/2023]
Abstract
Rationally designed artificial materials, called metamaterials, allow for tailoring effective material properties beyond ("meta") the properties of their bulk ingredient materials. This statement is especially true for chiral metamaterials, as unlocking certain degrees of freedom necessarily requires broken centrosymmetry. While the field of chiral electromagnetic/optical metamaterials has become rather mature, the field of elastic/mechanical metamaterials is just emerging and wide open. This research news reviews recent theoretical and experimental progress concerning 3D chiral mechanical and optical metamaterials, with special emphasis on work performed at KIT.
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Affiliation(s)
- I Fernandez-Corbaton
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
| | - C Rockstuhl
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
| | - P Ziemke
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
| | - P Gumbsch
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
- Institute for Applied Materials, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
- Fraunhofer IWM, Wöhlerstr. 11, 79108, Freiburg, Germany
| | - A Albiez
- Institute for Applied Materials, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
| | - R Schwaiger
- Institute for Applied Materials, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
| | - T Frenzel
- Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
| | - M Kadic
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
- Institut FEMTO-ST, UMR 6174, CNRS, Université de Bourgogne Franche-Comté, 25000, Besançon, France
| | - M Wegener
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
- Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany
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9
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Vaskin A, Mashhadi S, Steinert M, Chong KE, Keene D, Nanz S, Abass A, Rusak E, Choi DY, Fernandez-Corbaton I, Pertsch T, Rockstuhl C, Noginov MA, Kivshar YS, Neshev DN, Noginova N, Staude I. Manipulation of Magnetic Dipole Emission from Eu 3+ with Mie-Resonant Dielectric Metasurfaces. Nano Lett 2019; 19:1015-1022. [PMID: 30605616 DOI: 10.1021/acs.nanolett.8b04268] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Mie-resonant high-index dielectric nanoparticles and metasurfaces have been suggested as a viable platform for enhancing both electric and magnetic dipole transitions of fluorescent emitters. While the enhancement of the electric dipole transitions by such dielectric nanoparticles has been demonstrated experimentally, the case of magnetic-dipole transitions remains largely unexplored. Here, we study the enhancement of spontaneous emission of Eu3+ ions, featuring both electric and magnetic-dominated dipole transitions, by dielectric metasurfaces composed of Mie-resonant silicon nanocylinders. By coating the metasurfaces with a layer of an Eu3+ doped polymer, we observe an enhancement of the Eu3+ emission associated with the electric (at 610 nm) and magnetic-dominated (at 590 nm) dipole transitions. The enhancement factor depends systematically on the spectral proximity of the atomic transitions to the Mie resonances as well as their multipolar order, both controlled by the nanocylinder size. Importantly, the branching ratio of emission via the electric or magnetic transition channel can be modified by carefully designing the metasurface, where the magnetic dipole transition is enhanced more than the electric transition for cylinders with radii of about 130 nm. We confirm our observations by numerical simulations based on the reciprocity principle. Our results open new opportunities for bright nanoscale light sources based on magnetic transitions.
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Affiliation(s)
- Aleksandr Vaskin
- Institute of Applied Physics, Abbe Center of Photonics , Friedrich Schiller University Jena , 07745 Jena , Germany
| | - Soheila Mashhadi
- Center for Materials Research , Norfolk State University , Norfolk , Virginia 23504 , United States
| | - Michael Steinert
- Institute of Applied Physics, Abbe Center of Photonics , Friedrich Schiller University Jena , 07745 Jena , Germany
| | - Katie E Chong
- Nonlinear Physics Centre, Research School of Physics and Engineering , The Australian National University , Canberra , ACT 2601 , Australia
| | - David Keene
- Center for Materials Research , Norfolk State University , Norfolk , Virginia 23504 , United States
| | - Stefan Nanz
- Institute of Theoretical Solid State Physics , Karlsruhe Institute of Technology , 76131 Karlsruhe , Germany
| | - Aimi Abass
- Institute of Nanotechnology , Karlsruhe Institute of Technology , 76021 Karlsruhe , Germany
| | - Evgenia Rusak
- Nonlinear Physics Centre, Research School of Physics and Engineering , The Australian National University , Canberra , ACT 2601 , Australia
- Institute of Theoretical Solid State Physics , Karlsruhe Institute of Technology , 76131 Karlsruhe , Germany
| | - Duk-Yong Choi
- Laser Physics Centre, Research School of Physics and Engineering , The Australian National University , Canberra , ACT 2601 , Australia
| | | | - Thomas Pertsch
- Institute of Applied Physics, Abbe Center of Photonics , Friedrich Schiller University Jena , 07745 Jena , Germany
| | - Carsten Rockstuhl
- Institute of Theoretical Solid State Physics , Karlsruhe Institute of Technology , 76131 Karlsruhe , Germany
- Institute of Nanotechnology , Karlsruhe Institute of Technology , 76021 Karlsruhe , Germany
| | - Mikhail A Noginov
- Center for Materials Research , Norfolk State University , Norfolk , Virginia 23504 , United States
| | - Yuri S Kivshar
- Nonlinear Physics Centre, Research School of Physics and Engineering , The Australian National University , Canberra , ACT 2601 , Australia
| | - Dragomir N Neshev
- Nonlinear Physics Centre, Research School of Physics and Engineering , The Australian National University , Canberra , ACT 2601 , Australia
| | - Natalia Noginova
- Center for Materials Research , Norfolk State University , Norfolk , Virginia 23504 , United States
| | - Isabelle Staude
- Institute of Applied Physics, Abbe Center of Photonics , Friedrich Schiller University Jena , 07745 Jena , Germany
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Fruhnert M, Fernandez-Corbaton I, Yannopapas V, Rockstuhl C. Correction: Computing the T-matrix of a scattering object with multiple plane wave illuminations. Beilstein J Nanotechnol 2018; 9:953. [PMID: 29600155 PMCID: PMC5870158 DOI: 10.3762/bjnano.9.88] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/27/2018] [Accepted: 03/09/2018] [Indexed: 06/08/2023]
Abstract
[This corrects the article DOI: 10.3762/bjnano.8.66.].
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Affiliation(s)
- Martin Fruhnert
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, Wolfgang-Gaede-Strasse 1, 76131 Karlsruhe, Germany
| | - Ivan Fernandez-Corbaton
- Institute of Nanotechnology, Karlsruhe Institute of Technology, P.O. Box 3640, 76021 Karlsruhe, Germany
| | - Vassilios Yannopapas
- Department of Physics, National Technical University of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece
| | - Carsten Rockstuhl
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, Wolfgang-Gaede-Strasse 1, 76131 Karlsruhe, Germany
- Institute of Nanotechnology, Karlsruhe Institute of Technology, P.O. Box 3640, 76021 Karlsruhe, Germany
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11
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Garcia-Santiago X, Burger S, Rockstuhl C, Fernandez-Corbaton I. Measuring the electromagnetic chirality of 2D arrays under normal illumination. Opt Lett 2017; 42:4075-4078. [PMID: 29028016 DOI: 10.1364/ol.42.004075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2017] [Accepted: 09/05/2017] [Indexed: 06/07/2023]
Abstract
We present an electromagnetic chirality measure for 2D arrays of subwavelength periodicities under normal illumination. The calculation of the measure uses only the complex reflection and transmission coefficients from the array. The measure allows the ordering of arrays according to their electromagnetic chirality, which further allows a quantitative comparison of different design strategies. The measure is upper bounded, and the extreme properties of objects with high values of electromagnetic chirality make them useful in both near- and far-field applications. We analyze the consequences that different possible symmetries of the array have on its electromagnetic chirality. We use the measure to study four different arrays. The results indicate the suitability of helices for building arrays of high electromagnetic chirality, and the low effectiveness of a substrate for breaking the transverse mirror symmetry.
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Fernandez-Corbaton I, Nanz S, Rockstuhl C. On the dynamic toroidal multipoles from localized electric current distributions. Sci Rep 2017; 7:7527. [PMID: 28790393 PMCID: PMC5548821 DOI: 10.1038/s41598-017-07474-4] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2016] [Accepted: 06/29/2017] [Indexed: 11/09/2022] Open
Abstract
We analyze the dynamic toroidal multipoles and prove that they do not have an independent physical meaning with respect to their interaction with electromagnetic waves. We analytically show how the split into electric and toroidal parts causes the appearance of non-radiative components in each of the two parts. These non-radiative components, which cancel each other when both parts are summed, preclude the separate determination of each part by means of measurements of the radiation from the source or of its coupling to external electromagnetic waves. In other words, there is no toroidal radiation or independent toroidal electromagnetic coupling. The formal meaning of the toroidal multipoles is clear in our derivations. They are the higher order terms of an expansion of the multipolar coefficients of electric parity with respect to the electromagnetic size of the source.
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Affiliation(s)
| | - Stefan Nanz
- Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology, 76131, Karlsruhe, Germany
| | - Carsten Rockstuhl
- Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany.,Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology, 76131, Karlsruhe, Germany
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13
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Fruhnert M, Fernandez-Corbaton I, Yannopapas V, Rockstuhl C. Computing the T-matrix of a scattering object with multiple plane wave illuminations. Beilstein J Nanotechnol 2017; 8:614-626. [PMID: 28462063 PMCID: PMC5372708 DOI: 10.3762/bjnano.8.66] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2016] [Accepted: 02/22/2017] [Indexed: 05/04/2023]
Abstract
Given an arbitrarily complicated object, it is often difficult to say immediately how it interacts with a specific illumination. Optically small objects, e.g., spheres, can often be modeled as electric dipoles, but which multipole moments are excited for larger particles possessing a much more complicated shape? The T-matrix answers this question, as it contains the entire information about how an object interacts with any electromagnetic illumination. Moreover, a multitude of interesting properties can be derived from the T-matrix such as the scattering cross section for a specific illumination and information about symmetries of the object. Here, we present a method to calculate the T-matrix of an arbitrary object numerically, solely by illuminating it with multiple plane waves and analyzing the scattered fields. Calculating these fields is readily done by widely available tools. The finite element method is particularly advantageous, because it is fast and efficient. We demonstrate the T-matrix calculation at four examples of relevant optical nanostructures currently at the focus of research interest. We show the advantages of the method to obtain useful information, which is hard to access when relying solely on full wave solvers.
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Affiliation(s)
- Martin Fruhnert
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, Wolfgang-Gaede-Strasse 1, 76131 Karlsruhe, Germany
| | - Ivan Fernandez-Corbaton
- Institute of Nanotechnology, Karlsruhe Institute of Technology, P.O. Box 3640, 76021 Karlsruhe, Germany
| | - Vassilios Yannopapas
- Department of Physics, National Technical University of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece
| | - Carsten Rockstuhl
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, Wolfgang-Gaede-Strasse 1, 76131 Karlsruhe, Germany
- Institute of Nanotechnology, Karlsruhe Institute of Technology, P.O. Box 3640, 76021 Karlsruhe, Germany
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Fernandez-Corbaton I, Nanz S, Alaee R, Rockstuhl C. Exact dipolar moments of a localized electric current distribution. Opt Express 2015; 23:33044-33064. [PMID: 26831974 DOI: 10.1364/oe.23.033044] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The multipolar decomposition of current distributions is used in many branches of physics. Here, we obtain new exact expressions for the dipolar moments of a localized electric current distribution. The typical integrals for the dipole moments of electromagnetically small sources are recovered as the lowest order terms of the new expressions in a series expansion with respect to the size of the source. All the higher order terms can be easily obtained. We also provide exact and approximated expressions for dipoles that radiate a definite polarization handedness (helicity). Formally, the new exact expressions are only marginally more complex than their lowest order approximations.
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Fernandez-Corbaton I. Forward and backward helicity scattering coefficients for systems with discrete rotational symmetry. Opt Express 2013; 21:29885-29893. [PMID: 24514539 DOI: 10.1364/oe.21.029885] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The forward and backward scattering off linear systems with discrete rotational symmetries R(z)(2π/n) with n ≥ 3 are shown to be restricted by symmetry reasons. Along the symmetry axis, forward scattering can only be helicity preserving and backward scattering can only be helicity flipping. These restrictions do not exist for n < 3. If, in addition to the n ≥ 3 discrete rotational symmetry, the system has duality symmetry (obeys the helicity conservation law), it will exhibit zero backscattering. The results pinpoint the underlying symmetry reasons for some notable scattering properties of R(z)(2π/4) symmetric systems that have been reported in the metamaterials and radar literature. Applications to planar metamaterials and solar cells are briefly discussed.
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Fernandez-Corbaton I, Zambrana-Puyalto X, Tischler N, Vidal X, Juan ML, Molina-Terriza G. Electromagnetic duality symmetry and helicity conservation for the macroscopic Maxwell's equations. Phys Rev Lett 2013; 111:060401. [PMID: 23971539 DOI: 10.1103/physrevlett.111.060401] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2013] [Indexed: 05/13/2023]
Abstract
In this Letter, we show that the electromagnetic duality symmetry, broken in the microscopic Maxwell's equations by the presence of charges, can be restored for the macroscopic Maxwell's equations. The restoration of this symmetry is shown to be independent of the geometry of the problem. These results provide a tool for the study of light-matter interactions within the framework of symmetries and conservation laws. We illustrate its use by determining the helicity content of the natural modes of structures possessing spatial inversion symmetries and by elucidating the root causes for some surprising effects in the scattering off magnetic spheres.
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Affiliation(s)
- Ivan Fernandez-Corbaton
- Department of Physics and Astronomy, Macquarie University, North Ryde, New South Wales 2109, Australia
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Abstract
We unveil the relationship between two anomalous scattering processes known as Kerker conditions and the duality symmetry of Maxwell equations. We generalize these conditions and show that they can be applied to any particle with cylindrical symmetry, not only to spherical particles as the original Kerker conditions were derived for. We also explain the role of the optical helicity in these scattering processes. Our results find applications in the field of metamaterials, where new materials with directional scattering are being explored.
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Affiliation(s)
- X Zambrana-Puyalto
- Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia.
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