Ivan Fernandez-Corbaton

Electromagnetic Duality Symmetry and Helicity Conservation for the Macroscopic Maxwell’s Equations

In this Letter, we show that the electromagnetic duality symmetry, broken in the microscopic Maxwells equations by the presence of charges, can be restored for the macroscopic Maxwells 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.

Helicity and angular momentum: A symmetry-based framework for the study of light-matter interactions

We propose a 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 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.

Duality symmetry and Kerker conditions

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.

Role of duality symmetry in transformation optics

Maxwells 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.

Dual and chiral objects for optical activity in general scattering directions

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.

Forward and backward helicity scattering coefficients for systems with discrete rotational symmetry

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.

Objects of Maximum Electromagnetic Chirality

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.

Necessary symmetry conditions for the rotation of light

Two conditions on symmetries are identified as necessary for a linear scattering system to be able to rotate the linear polarization 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 polarization control devices at the nanoscale.

Exact dipolar moments of a localized electric current distribution

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.

An electromagnetic multipole expansion beyond the long-wavelength approximation

Abstract 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.