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Designing objects with predefined optical properties is a task of fundamental importance for nanophotonics, and chirality is a prototypical example of such a property, with applications ranging from photochemistry to nonlinear photonics. A measure of electromagnetic chirality with a well-defined upper bound has recently been proposed. Here, we optimize the shape of silver helices at discrete frequencies ranging from the far infrared to the optical band. Gaussian process optimization, taking into account also shape derivative information of the helices scattering response, is used to maximize the electromagnetic chirality. We show that the theoretical designs achieve more than 90 percent of the upper bound of em-chirality for wavelenghts \SI{3}{\micro\meter} or larger, while their performance decreases towards the optical band. We fabricate and characterize helices for operation at \SI{800}{\nano\meter}, and identify some of the imperfections that affect the performance. Our work motivates further research both on the theoretical and fabrication sides to unlock potential applications of objects with large electromagnetic chirality at optical frequencies, such as helicity filtering glasses. We show that, at \SI{3}{\micro\meter}, a thin slab of randomly oriented helices can absorb 99 percent of the light of one helicity while absorbing only 9 percent of the opposite helicity.

The T-matrix is a powerful tool that provides the complete description of the linear interaction between the electromagnetic field and a given object. In here, we generalize the usual monochromatic formalism to the case of polychromatic field-matter interaction. The group of transformations of special relativity provides the guidance for building the new formalism, which is inherently polychromatic. The polychromatic T-matrix affords the direct treatment of the interaction of electromagnetic pulses with objects, even when the objects move at constant relativistic speeds.

The evaluation of the interaction between objects arranged on a lattice requires the computation of lattice sums. A scenario frequently encountered are systems governed by the Helmholtz equation in the context of electromagnetic scattering in an array of particles forming a metamaterial, a metasurface, or a photonic crystal. While the convergence of direct lattice sums for such translation coefficients is notoriously slow, the application of Ewald's method converts the direct sums into exponentially convergent series. We present a derivation of such series for the 2D and 3D solutions of the Helmholtz equation, namely spherical and cylindrical solutions. When compared to prior research, our novel expressions are especially aimed at computing the lattice sums for several interacting sublattices in 1D lattices (chains), 2D lattices (gratings), and 3D lattices. We verify our results by comparison with the direct computation of the lattice sums.

Electronic circular dichroism is an important optical phenomenon offering insights into chiral molecular materials. On the other hand, metal-organic frameworks (MOFs) are a novel group of crystalline porous thin-film materials that provide tailor-made chemical and physical properties by carefully selecting their building units. Combining these two aspects of contemporary material research and integrating chiral molecules into MOFs promises devices with unprecedented functionality. However, considering the nearly unlimited degrees of freedom concerning the choice of materials and the geometrical details of the possibly structured films, we urgently need to complement advanced experimental methods with equally strong modeling techniques. Most notably, these modeling techniques must cope with the challenge that the material and devices thereof cover size scales from {\AA}ngstr\"oms to mm. In response to that need, we outline a computational workflow that seamlessly combines quantum chemical methods to capture the properties of individual molecules with optical simulations to capture the properties of functional devices made from these molecular materials. We concentrate on chiral properties and apply our work to UiO-67-BINOL MOFs, for which experimental results are available to benchmark the results of our simulations and explore the optical properties of cavities and metasurfaces made from that chiral material.

We introduce a systematic way to obtain expressions for computing the amount of fundamental quantities such as helicity and angular momentum contained in static matter, given its charge and magnetization densities. The method is based on a scalar product that is invariant under the 10-parameter conformal group in three-dimensional Euclidean space. Such group is obtained as the static ($\omega=0$) restriction of the symmetry group of Maxwell equations: The 15-parameter conformal group in 3+1 Minkowski spacetime. In an exemplary application, we compute the helicity and angular momentum squared stored in a Hopfion. The helicity of the Hopfion bounds the optical helicity that can be radiated from it, and also the amount of optical helicity needed in an electromagnetic beam for switching the handedness of the Hopfion upon light-matter interaction.

The accurate and efficient computation of the electromagnetic response of objects made from artificial materials is crucial for designing photonic functionalities and interpreting experiments. Advanced fabrication techniques can nowadays produce new materials as three-dimensional lattices of scattering unit cells. Computing the response of objects of arbitrary shape made from such materials is typically computationally prohibitive unless an effective homogeneous medium approximates the discrete material. In here, we introduce a homogenization method based on the effective T-matrix. Such a matrix captures the exact response of the discrete material, is determined by the T-matrix of the isolated unit cell and the material lattice vectors, and is free of spatial dispersion. The truncation of the effective T-matrix to dipolar order determines the common bi-anisotropic constitutive relations. When combined with quantum-chemical and Maxwell solvers, the method allows one to compute the response of arbitrarily-shaped volumetric patchworks of structured molecular materials and metamaterials.

Electromagnetic waves impinging on three-dimensional helical metallic metamaterials have been shown to exhibit chiral effects of large magnitude both theoretically and in experimental realizations. Chirality here describes different responses of scatterers, materials, or metamaterials to left and right circularly polarized electromagnetic waves. These differences can be quantified in terms of electromagnetic chirality measures. In this work we consider the optimal design of thin metallic free-form nanowires that possess measures of electromagnetic chirality as large as fundamentally possible. We focus on optical frequencies and use a gradient based optimization scheme to determine the optimal shape of highly chiral thin silver and gold nanowires. The electromagnetic chirality measures of our optimized nanowires exceed that of traditional metallic helices. Therefore, these should be well suited as building blocks of novel metamaterials with an increased chiral response. We discuss a series of numerical examples, and we evaluate the performance of different optimized designs.

The electromagnetic helicity of the free electromagnetic field and the static magnetic helicity are shown to be two different embodiments of the same physical quantity, the total helicity. The total helicity is the sum of two terms: a term that measures the difference between the number of left-handed and right-handed photons of the free field, and another term that measures the screwiness of the static magnetization density in matter. Each term is the manifestation of the total helicity in different frequency regimes: $\ensuremath{\omega}g0$ and $\ensuremath{\omega}=0$, respectively. This unification establishes the theoretical basis for studying the conversion between the two embodiments of total helicity upon light-matter interaction.

The measurement of circular dichroism (CD) has widely been exploited to distinguish the different enantiomers of chiral structures. It has been applied to natural materials (e.g. molecules) as well as to artificial materials (e.g. nanophotonic structures). However, especially for chiral molecules the signal level is very low and increasing the signal-to-noise ratio is of paramount importance to either shorten the necessary measurement time or to lower the minimum detectable molecule concentration. As one solution to this problem, we propose here to use quantum states of light in CD sensing to reduce the noise below the shot noise limit that is encountered when using coherent states of light. Through a multi-parameter estimation approach, we identify the ultimate quantum limit to precision of CD sensing, allowing for general schemes including additional ancillary modes. We show that the ultimate quantum limit can be achieved by various optimal schemes. It includes not only Fock state input in direct sensing configuration but also twin-beam input in ancilla-assisted sensing configuration, for both of which photon number resolving detection needs to be performed as the optimal measurement setting. These optimal schemes offer a significant quantum enhancement even in the presence of additional system loss. The optimality of a practical scheme using a twin-beam state in direct sensing configuration is also investigated in details as a nearly optimal scheme for CD sensing when the actual CD signal is very small. Alternative schemes involving single-photon sources and detectors are also proposed. This work paves the way for further investigations of quantum metrological techniques in chirality sensing., 9 pages, 5 figures

We derive a set of design requirements that lead to structures suitable for molecular circular dichroism (CD) enhancement. Achirality of the structure and two suitably selected sequentially incident beams of opposite helicity ensures that the CD signal only depends on the chiral absorption properties of the molecules, and not on the achiral ones. Under this condition, a helicity preserving structure, which prevents the coupling of the two polarization handednesses, maximizes the enhancement of the CD signal for a given ability of the structure to enhance the field. When the achirality and helicity preservation requirements are met, the enhancement of the CD signal is directly related to the enhancement of the field. Next, we design an exemplary structure following the requirements. The considered system is a planar array of silicon cylinders under normally incident plane-wave illumination. Full-wave numerical calculations show that the enhancement of the transmission CD signal is between 6.5 and 3.75 for interaction lengths between 1.25 and 3 times the height of the cylinders., Comment: This document is the unedited Authors version of a Submitted Work that was subsequently accepted for publication in ACS Photonics, copyright American Chemical Society after peer review. To access the final edited and published work see 10.1021/acsphotonics.8b01454. The corrections published in 10.1021/acsphotonics.0c00113 are included in this arxiv document

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., Comment: 2 figures + supplementary material, 21 pages altogether

The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The multipole moments of the source. These numbers are frequently computed with expressions obtained after the long-wavelength approximation. Here, we derive exact expressions for the multipole moments of dynamic sources that resemble in their simplicity their approximate counterparts. We validate our new expressions against analytical results for a spherical source, and then use them to calculate the induced moments for some selected sources with a non-trivial shape. The comparison of the results to those obtained with approximate expressions shows a considerable disagreement even for sources of subwavelength size. Our expressions are relevant for any scientific area dealing with the interaction between the electromagnetic field and material systems., Comment: 21 pages, 3 figures

Recent experiments demonstrated strongly directional coupling of light into waveguide modes. We identify here the mechanisms behind this effect. We consider emitters near a waveguide, either centered on the median plane of the waveguide, or displaced from such plane. We show that, independently of the displacement, the directionality is mostly due to a mirror symmetry breaking caused by the axial character of the angular momentum of the emitted light. The sign of the angular momentum along an axis transverse to the waveguide determines the preferential coupling direction. The degree of directionality grows exponentially as the magnitude of such transverse angular momentum increases linearly. We trace this exponential dependence back to a property of the evanescent angular spectrum of the emissions. A binary and less pronounced directional coupling effect due to the chiral character of the handedness of the emission is possible when the displacement of the emitter breaks another of the mirror symmetries of the waveguide. We find a selection rule that allows or prevents the coupling of centered electric(magnetic) multipolar emissions onto the waveguide modes. We also show that the selection of a different angular momentum axis made in some experiments causes significant differences in the way in which directionality depends on angular momentum. We then use these differences to propose an experiment featuring a transverse magnetic bias that allows to aggregate the directional emissions from quantum dots on top of waveguides. Our symmetry-based results apply to any emitted multipolar order, clarify the spin-momentum locking concept, and generalize it to an exponentially-strong locking between the transverse angular momentumand the preferential coupling direction.

Predicting the optical response of macroscopic arrangements of individual scatterers is a computational challenge because the problem involves length scales across multiple orders of magnitude. We present a full-wave optical method to efficiently compute the scattering of light at objects that are arranged in biperiodic arrays. Multiple arrays or homogeneous thin films can be stacked to build up an entire multicomposite material in the third dimension. The scattering properties of the individual objects in each array are described by the T-matrix formalism. Therefore, arbitrarily shaped objects and even molecules can be the basic constituent of the arrays. Taking the T-matrix of the individual scatterer as the point of departure we can explain the optical properties of the bulk material from the scattering properties of its constituents. We use solutions of Maxwell’s equations with well-defined helicity. Therefore, chiral media are particularly easy to consider as materials for both scatterers and embedding media. We exemplify the efficiency of the algorithm with an exhaustive parametric study of anti-reflective coatings for solar cells made from cylinders with a high degree of helicity preservation. The example shows a speed-up factor of about 500 with respect to finite-element computations. A second example specifically exploits the use of helicity modes to investigate the enhancement of the circular dichroism signal in a chiral material.

The differential response of chiral molecules to incident left- and right- handed circularly polarized light is used for sensing the handedness of molecules. Currently, significant effort is directed towards enhancing weak differential signals from the molecules, with the goal of extending the capabilities of chiral spectrometers to lower molecular concentrations or small analyte volumes. Previously, optical cavities for enhancing vibrational circular dichroism have been introduced. Their enhancements are mediated by helicity-preserving cavity modes which maintain the handedness of light due to their degenerate TE and TM components. In this article, we simplify the design of the cavity, and numerically compare it with the previous one using an improved model for the response of chiral molecules. We use parameters of molecular resonances to show that the cavities are capable of bringing the vibrational circular dichroism signal over the detection threshold of typical spectrometers for concentrations that are one to three orders of magnitude smaller than those needed without the cavities, for a fixed analyte volume. Frequency resolutions of current spectrometers result in enhancements of more than one order (two orders) of magnitude for the new (previous) design. With improved frequency resolution, the new design achieves enhancements of three orders of magnitude. We show that the TE/TM degeneracy in perfectly helicity preserving modes is lifted by factors that are inherent to the cavities. More surprisingly, this degeneracy is also lifted by the molecules themselves due to their lack of electromagnetic duality symmetry, that is, due to the partial change of helicity during the light-molecule interactions., This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Applied Physics Reviews 7, 041413 (2020) and may be found at https://aip.scitation.org/doi/abs/10.1063/5.0025006

Manipulating the excitation of resonant electric and magnetic multipole moments in structured dielectric media has unlocked many sophisticated electromagnetic functionalities. This article demonstrates the experimental realization of a broadband Huygens' source. This Huygens' source consists of a spherical particle that exhibits a well-defined forward-scattering pattern across more than an octave-spanning spectral band at GHz frequencies, where the scattering in the entire backward hemisphere is suppressed. Two different low-index nonmagnetic spheres are studied that differ in their permittivity. This causes them to offer a different shape for the forward-scattering pattern. The theoretical understanding of this broadband feature is based on the approximate equality of the resonant electric and magnetic multipole moments in both amplitude and phase in low permittivity spheres. This is a key condition to approximate the electromagnetic duality symmetry which, together with the spherical symmetry, suppresses the backscattering. With such a configuration, broadband Huygens' sources can be designed even if magnetic materials are unavailable. This article provides guidelines for designing broadband Huygens' sources using low-index spheres that could be valuable to a plethora of applications., Comment: 14 pages, 6 figures

Decomposing the field scattered by an object into vector spherical wave functions (VSWF) is a useful tool when discussing its optical properties on more analytical grounds. Thus far, it was frequently required in the decomposition that the scattered field is available on a spherical surface enclosing the scatterer. This requirement is adapted to the spatial dependency of the VSWFs but is rather incompatible with many numerical solvers. To mitigate this problem, we propose an orthogonal expression for the decomposition that holds for any surface that encloses the scatterer, independently of its shape. We also show that the orthogonal relations remain unchanged when the radiative VSWF used for the expansion of the scattered field are substituted by the regular VSWF used for the expansion of the incident illumination as test functions. This is a key factor for the numerical stability of our decomposition. As an example, we use a finite-element based solver to compute the multipole response of a nanorod illuminated by a plane wave and study its convergence properties.

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., We outline a methodology for efficiently computing the electromagnetic response of molecular ensembles. Instead of performing quantum‐mechanical simulations of the entire ensemble, we combine the quantum‐mechanical simulations of single molecules with the transfer matrix (T‐matrix) approach, a common tool in physics and engineering. We show that the T‐matrix calculations agree very well with the full quantum‐mechanical calculations. We also show how the methodology can be used to predict experimental measurements on a molecular material of macroscopic dimensions.

Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination of "how much a system breaks a symmetry" allows to reach beyond this binary situation and is a necessary step towards the quantitative connection between symmetry breaking and its effects. We introduce measures of symmetry breaking for a system interacting with external fields (particles). They can be computed from measurements of the system-mediated coupling strengths between subspaces of incoming and outgoing fields (particles) that transform in a definite way under the symmetry. The generality of these symmetry breaking measures and their tight connection to experimental measurements make them applicable to a very wide range of physics, like quantification of phase transitions, constraints in dynamical evolution, and the search for hidden symmetries., Link to published article: http://iopscience.iop.org/article/10.1088/2399-6528/aada25

The scattering cancellation technique is a powerful tool to reduce the scattered field from electrically small objects in a specific frequency window. The technique relies on covering the object of interest with a shell that scatters light into the far field of equal strength as the object, but $\pi$ out-of-phase. The resulting destructive interference prohibits its detection in measurements that probe the scattered light. Whereas at radio or microwave frequencies feasible designs have been proposed that allow to tune the operational frequency upon request, similar capabilities have not yet been explored in the visible. However, such ability is decisive to capitalize on the technique in many envisioned applications. Here, we solve the problem and study the use of small metallic nanoparticles with an ellipsoidal shape as the material from which the shell is made to build an isotropic geometry. Changing the aspect ratio of the ellipsoids allows to change the operational frequency. The basic functionality is explored with two complementary analytical approaches. Additionally, we present a powerful multiscattering algorithm that can be used to perform full wave simulations of clusters of arbitrary particles. We utilize this method to analyze the scattering of the presented designs numerically. Hereby we provide useful guidelines for the fabrication of this cloak with self-assembly methods by investigating the effects of disorder., Comment: 23 Pages, 7 Figures, Accepted at PRB

We propose a novel scheme to normalize scattering modes of the electromagnetic field. By relying on analytical solutions for Maxwell's equations in the homogenous medium outside the scatterer, we derive normalization conditions that only depend on the electromagnetic field on the surface of a sphere containing the scatterer. We pay special attention to the important cases of plane wave illumination and illumination with a multipolar field, for which an explicit and easy to use normalization condition is derived. We demonstrate the versatility of our method by normalizing scattering modes of some selected metallic and dielectric scatterers of different geometries in the context of different application scenarios. Since every quantum mechanical treatment of light-matter interaction requires the proper normalization of electromagnetic fields, we deem our proposed normalization scheme broadly applicable independent of the scatterer involved., 16 pages, 5 figures

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.

Material electromagnetic duality symmetry requires a system to have equal electric and magnetic responses. Electromagnetic duality enables technologically important effects like artificial optical activity and zero back-scattering, is a requirement for metamaterials in transformation optics, Huygens wave-front control, and maximal electromagnetic chirality, and appears in topological photonic systems. Intrinsically dual materials that meet the duality conditions at the level of the constitutive relations do not exist in many frequency bands. Nevertheless, discrete objects like metallic helices and homogeneous dielectric spheres can be engineered to approximate the dual behavior. The discrete objects can then be used as building blocks with the objective of obtaining composite systems with high duality symmetry. Here, we exploit the extra degrees of freedom of a core-shell dielectric sphere to obtain a particle whose duality symmetry is more than one order of magnitude better than previously reported non-magnetic objects. We show that the improvement is transferred onto the duality symmetry of composite objects when the core-shell particle is used as a building block instead of homogeneous spheres., Comment: 5 pages, 3 figures, 1 table

We present a unified theory to treat conservation laws in light-matter interactions. It can be used to describe and engineer the transfer of any measurable property from the electromagnetic field to any object. The theory allows to explicitly characterize and separately compute the transfer due to asymmetry of the object and the transfer due to field absorption by the object. It also allows to compute the upper bound of the transfer rate of any given property to any given object, together with the corresponding most efficient illumination which achieves the bound. Due to its algebraic nature, the approach is inherently suited for computer implementation., Small title modification. Some figures have changed after fixing an error in the calculations. Some more discussion on the asymmetry and absorption mediated transfers has been added just before Sec. III A

We present an approach to study the interaction between matter and evanescent fields. The approach is based on the decomposition of evanescent plane waves into multipoles of well-defined angular momentum transverse to both decay and propagation directions. We use the approach to identify the origin of the recently observed directional coupling of emitters into guided modes, and of the opposite Zeeman state excitation of atoms near a fiber. We explain how to rigorously quantify both effects, and show that the directionality and the difference in excitation rates grow exponentially with the multipolar order of the light-matter interaction. We also use the approach to study and maximize the transverse torque exerted by an evanescent plane wave onto a given spherical absorbing particle. The maximum occurs at the quadrupolar order of the particle, and for a particular polarization of the plane wave. All the obtained physical insights can be traced back to the two main features of the decomposition of evanescent plane waves into transverse multipolar modes: A polarization independent exponential dominance of modes with large transverse angular momentum, and a polarization controlled parity selection rule., Last version with slight changes in the figures and text

Optical force and torque provide unprecedented control on the spatial motion of small particles. A valid scientific question, that has many practical implications, concerns the existence of fundamental upper bounds for the achievable force and torque exerted by a plane wave illumination with a given intensity. Here, while studying isotropic particles, we show that different light-matter interaction channels contribute to the exerted force and torque; and analytically derive upper bounds for each of the contributions. Specific examples for particles that achieve those upper bounds are provided. We study how and to which extent different contributions can add up to result in the maximum optical force and torque. Our insights are important for applications ranging from molecular sorting, particle manipulation, nanorobotics up to ambitious projects such as laser-propelled spaceships., 5 pages, 5 figures, 2 tables, Supplemental Material (27 pages, 6 figures)

On the one hand, electromagnetic dual particles preserve the helicity of light upon interaction. On the other hand, chiral particles respond differently to light of opposite helicity. These two properties on their own constitute a source of fascination. Their combined action, however, is less explored. Here, we study on analytical grounds the force and torque as well as the optical cross sections of dual chiral particles in the dipolar approximation exerted by a particular wave of well-defined helicity: A circularly polarized plane wave. We put emphasis on particles that possess a maximally electromagnetic chiral and hence dual response. Besides the analytical insights, we also investigate the exerted optical force and torque on a real particle at the example of a metallic helix that is designed to approach the maximal electromagnetic chirality condition. Various applications in the context of optical sorting but also nanorobotics can be foreseen considering the particles studied in this contribution., Comment: 7 pages, 5 figures

We introduce a definition of the electromagnetic chirality of an object and show that it has an upper bound. Reciprocal objects attain the upper bound if and only if they are transparent for all the fields of one polarization handedness (helicity). Additionally, electromagnetic duality symmetry, i.e., helicity preservation upon interaction, turns out to be a necessary condition for reciprocal objects to attain the upper bound. We use these results to provide requirements for the design of such extremal objects. The requirements can be formulated as constraints on the polarizability tensors for dipolar objects or on the material constitutive relations for continuous media. We also outline two applications for objects of maximum electromagnetic chirality: a twofold resonantly enhanced and background-free circular dichroism measurement setup, and angle-independent helicity filtering glasses. Finally, we use the theoretically obtained requirements to guide the design of a specific structure, which we then analyze numerically and discuss its performance with respect to maximal electromagnetic chirality., Comment: This version contains an example of how to use the theoretically derived constraints for designing realistic structures. It also contains a discussion related to the optical chirality density

Optically active artificial structures have attracted tremendous research attention. Such structures must meet two requirements: Lack of spatial inversion symmetries and, a condition usually not explicitly considered, the structure shall preserve the helicity of light, which implies that there must be a vanishing coupling between the states of opposite polarization handedness among incident and scattered plane waves. Here, we put forward and demonstrate that a unit cell made from chiraly arranged electromagnetically dual scatterers serves exactly this purpose. We prove this by demonstrating optical activity of such unit cell in general scattering directions., Comment: This document is the unedited Authors version of a Submitted Work that was subsequently accepted for publication in ACS Photonics, copyright American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/articlesonrequest/AOR-3yvzAibCIU6wdTuzx9cE

In my thesis, I first develop the theoretical basis and tools for the use of helicity and duality in the study, understanding and engineering of interactions between electromagnetic radiation and material systems. Then, within the general framework of symmetries and conservation laws, I apply the theoretical results to several different problems: Optical activity, zero backscattering, metamaterials for transformation optics and nanophotonics phenomena involving the electromagnetic angular momentum. The tool has provided new insights and design guidelines in all these cases., Comment: PhD Thesis, Department of Physics and Astronomy, Macquarie University. Fixed a very slow figure from the previous version

Gravitational waves, as predicted by Einstein's general relativity theory, appear as ripples in the fabric of spacetime traveling at the speed of light. We prove that the propagation of small amplitude gravitational waves in a curved spacetime is equivalent to the propagation of a subspace of electromagnetic states. We use this result to propose the use of entangled photons to emulate the evolution of gravitational waves in curved spacetimes by means of experimental electromagnetic setups featuring metamaterials., 10 pages, 2 figures

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.

The forward and backward scattering off linear systems with discrete rotational symmetries R_z (2{\pi} /n) with n $\ge$ 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 $\ge$ 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 (2{\pi} /4) symmetric systems that have been reported in the metamaterials and radar literature. Applications to planar metamaterials and solar cells are briefly discussed., Comment: 9 pages, 3 figures, http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-21-24-29885

Maxwell's equations in curved space-time are invariant under electromagnetic duality transformations. We exploit this property to constraint the design parameters of metamaterials used for transformations optics. We show that a general transformation must be implemented using a dual-symmetric metamaterial. This can be accomplished constraining the polarisability tensors of their individual constituents, i.e. the meta atoms. We obtain explicit expressions for these constraints. We also show that the spatial part of the coordinate transformation depends only on the electric-electric tensorial coupling of the polarisability tensor, while the spatio-temporal part depends only on the electric-magnetic tensorial coupling. In our derivations, we find that two dipoles located at the same point, one electric (p) and one magnetic (m), are needed to produce a total field with well defined helicity equal to +1 or -1, and that they must be related as p=im/c or p=-im/c, respectively.

We propose a new theoretical and practical framework for the study of light-matter interactions and the angular momentum of light. Our proposal is based on helicity, total angular momentum, and the use of symmetries. We compare the new framework to the current treatment, which is based on separately considering spin angular momentum and orbital angular momentum and using the transfer between the two in physical explanations. In our proposal, the fundamental problem of spin and orbital angular momentum separability is avoided, predictions are made based on the symmetries of the systems, and the practical application of the concepts is straightforward. Finally, the framework is used to show that the concept of spin to orbit transfer applied to focusing and scattering is masking two completely different physical phenomena related to the breaking of different fundamental symmetries: transverse translational symmetry in focusing and electromagnetic duality symmetry in scattering., 34 pages, 4 figures, http://link.aps.org/doi/10.1103/PhysRevA.86.042103. v4: corrected typo (loose bracket) in formulas 15 and B13, which are actually the same formulas. Replaced Fig 3a and 3b to correct wrong labels of the horizontal axis

Modern physics is largely devoted to study conservation laws, such as charge, energy, linear momentum or angular momentum, because they give us information about the symmetries of our universe. Here, we propose to add the relationship between electromagnetic duality and helicity to the toolkit. Generalized electromagnetic duality symmetry, broken in the microscopic Maxwell's equations by the empirical absence of magnetic 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 simple and powerful tool for the study of light-matter interactions within the framework of symmetries and conservation laws. We apply such framework to the experimental investigation of helicity transformations in cylindrical nanoapertures, and we find that the transformation is significantly enhanced by the coupling to surface modes, where electromagnetic duality is strongly broken., Comment: 26 pages, 4 figures

The spectral expansion of the Green's tensor for a planar multilayered structure allows us to semi analytically obtain the angular spectrum representation of the field scattered by an arbitrary dielectric perturbation present in the structure. In this paper we present a method to find the expansion coefficients of the scattered field, given that the electric field inside the perturbation is available. The method uses a complete set of orthogonal vector wave functions to solve the structure's vector wave equation. In the two semi-infinite bottom and top media, those vector wave functions coincide with the plane-wave basis vectors, including both propagating and evanescent components. The technique is used to obtain the complete angular spectrum of the field scattered by a nanohole in a metallic film under Gaussian illumination. We also show how the obtained formalism can easily be extended to spherically and cylindrically multilayered media. In those cases, the expansion coefficients would multiply the spherical and cylindrical vector wave functions., 9 pages, 5 figures

We present a study of the properties of the transversal "spin angular momentum" and "orbital angular momentum" operators. We show that the "spin angular momentum" operators are generators of spatial translations which depend on helicity and frequency and that the "orbital angular momentum" operators generate transformations which are a sequence of this kind of translations and rotations. We give some examples of the use of these operators in light matter interaction problems. Their relationship with the helicity operator allows to involve the electromagnetic duality symmetry in the analysis. We also find that simultaneous eigenstates of the three "spin" operators and parity define a type of standing modes which has been recently singled out for the interaction of light with chiral molecules. With respect to the relationship between "spin angular momentum", polarization, and total angular momentum, we show that, except for the case of a single plane wave, the total angular momentum of the field is decoupled from its vectorial degrees of freedom even in the regime where the paraxial approximation holds. Finally, we point out a relationship between the three "spin" operators and the spatial part of the Pauli-Lubanski four vector.

Two conditions on symmetries are identified as necessary for a linear scattering system to be able to rotate the linear polarisation of light: Lack of at least one mirror plane of symmetry and electromagnetic duality symmetry. Duality symmetry is equivalent to the conservation of the helicity of light in the same way that rotational symmetry is equivalent to the conservation of angular momentum. When the system is a solution of a single species of particles, the lack of at least one mirror plane of symmetry leads to the familiar requirement of chirality of the individual particle. With respect to helicity preservation, according to the analytical and numerical evidence presented in this paper, the solution preserves helicity if and only if the individual particle itself preserves helicity. However, only in the particular case of forward scattering the helicity preservation condition on the particle is relaxed: We show that the random orientation of the molecules endows the solution with an effective rotational symmetry; at its turn, this leads to helicity preservation in the forward scattering direction independently of any property of the particle. This is not the case for a general scattering direction. These results advance the current understanding of the phenomena of molecular optical activity and provide insight for the design of polarisation control devices at the nanoscale., 17 pages, 3 figures

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.

Suppressing the reflection from material interfaces or entire layer stacks across an extended spectral range is important for various applications. While many approaches have been described for this purpose, we look at the problem here from the perspective of helicity preservation. Specifically, the anti-reflection performance of nano-particle arrays on top of solar cell stacks is related to two conditions: a high enough degree of discrete rotational symmetry and the ability of the system to suppress cross-talk between the two handednesses (helicities) of the electromagnetic field upon light-matter interaction. For particle-lattice systems with high enough degree of discrete rotational symmetry ($2��/n$ for $n>2$), our numerical studies link the suppression of backscattering to the ability of the system to avoid the mixing between the two helicity components of the incident field. In an exemplary design, we use an array of TiO$_2$ disks placed on top of a flat heterojunction solar cell stack, and analyze the helicity preservation properties of the system. We show numerically that a hexagonal array lattice, featuring a higher degree of discrete rotational symmetry, can improve over the anti-reflection performance of a square lattice. Importantly, the disks are introduced in an electrically decoupled manner such that the passivation and electric properties of the device are not disturbed., 23 pages, 4 figures

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.