We present a new approach to the definition of optical helicity in a medium. Our approach resolves the problem that duality transformations which simultaneously combine $\mathbf{E}$ with $\mathbf{H}$ and $\mathbf{D}$ with $\mathbf{B}$ are incompatible with linear constitutive relations. We find that the helicity density in a medium, as the conserved quantity associated with duality transforms, must contain an explicit contribution associated with the polarisation and magnetisation of the matter, and that it can be expressed naturally in terms of the elementary polarised excitations of the system. In media for which the helicity is conserved, each circular excitation carries a well-defined helicity. However, in a medium for which the helicity is not conserved, we find that the time-varying helicity can be viewed in terms of oscillations between different helicity eigenstates, analogous to neutrino oscillations. Here we explicitly study the helicity in homogeneous and lossless media but we believe that, differently to other choices, this helicity is readily generalisable to media that may be inhomogeneous, lossy, chiral or nonreciprocal.
We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum (OAM) in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.
Optical helicity density is usually discussed for monochromatic electromagnetic fields in free space. It plays an important role in the interaction with chiral molecules or nanoparticles. Here we introduce the optical helicity density in a dispersive isotropic medium. Our definition is consistent with biorthogonal Maxwell electromagnetism in optical media, the Brillouin energy density, as well as with the recently-introduced canonical momentum and spin of light in dispersive media. We consider a number of examples, including electromagnetic waves in dielectrics, negative-index materials, and m…
In this Letter, it is claimed that, in addition to the Chiao-Wu geometric phase and optical Aharonov-Carmi geometric phase, there exists a new interesting geometric phase caused by the helicity inversion of photons in the optical fiber composed periodically of left- and right- handed (LRH) media. By making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, we calculate this geometric phase. It is emphasized that this geometric phase should not been neglected when considering the anomalous refraction on the interfaces between left- and rig…
We present a method, based on Feynman path integrals, to describe the propagation and properties of the quantised electromagnetic field in an arbitrary, nonlinear medium. We provide a general theory, valid for any order of optical nonlinearity, and we then specialise the the case of second order nonlinear processes. In particular, we show, that second-order nonlinear processes in arbitrary media, under the undepleted pump approximation, can be described by an effective free electromagnetic field, propagating in a vacuum, dressed by the medium itself. Moreover, we show,that the probability of s…
We consider the energy and helicity densities of circularly polarised light within a lossless chiral medium, characterised by the chirality parameter $β$. A form for the helicity density is introduced, valid to first order in $β$, that produces a helicity of $\pm\hbar$ per photon for right and left circular polarisation, respectively. This is in contrast to the result obtained if we use the form of the helicity density employed for linear media. We examine the helicity continuity equation, and show that this modified form of the helicity density is required for consistency with the dual symmet…
Maxwell electromagnetism, describing the wave properties of light, was formulated 150 years ago. More than 60 years ago it was shown that interfaces between optical media (including dielectrics, metals, negative-index materials) can support surface electromagnetic waves, which now play crucial roles in plasmonics, metamaterials, and nano-photonics. Here we show that surface Maxwell waves at interfaces between homogeneous, isotropic media described by real permittivities and permeabilities have a purely topological origin explained by the bulk-boundary correspondence. Importantly, the topologic…
The backscattering of circularly polarized light at normal incidence to a half-space of scattering particles is studied using the Electric Field Monte Carlo (EMC) method. The spatial distribution of the backscattered light intensity is examined for both the time-resolved and continuous-wave cases for large particles with anisotropy factor, g, in the range 0.8 to 0.97. For the time-resolved case, the backscattered light with the same helicity as that of the incident beam (co-polarized) is found to form a ring centered on the point of incidence. The ring expands and simultaneously grows weak as …
We demonstrate experimentally an optical process in which the spin angular momentum carried by a circularly polarized light beam is converted into orbital angular momentum, leading to the generation of helical modes with a wavefront helicity controlled by the input polarization. This phenomenon requires the interaction of light with matter that is both optically inhomogeneous and anisotropic. The underlying physics is also associated with the so-called Pancharatnam-Berry geometrical phases involved in any inhomogeneous transformation of the optical polarization.
Time-resolved imaging reveals that the helicity dependent all-optical switching (HD-AOS) of Co/Pt ferromagnetic multilayers proceeds by two stages. First one involves the helicity independent and stochastic nucleation of reversed magnetic domains. At the second stage circularly polarized light breaks the degeneracy between the magnetic domains and promotes the preferred direction of domain wall (DW) motion. The growth of the reversed domain from the nucleation cite, for a particular helicity, leads to full magnetic reversal. This study demonstrates a novel mechanism of HD-AOS mediated by the d…
We report that the classical phenomena of optical activity and circular dichroism, which are traditionally associated with chirality (helicity) of organic molecules, proteins and inorganic structures, can be observed in non-chiral artificial media. Intriguingly, our metamaterial structure yields exceptionally strong resonant optical activity, which also leads to the appearance of a backward wave, a characteristic sign of negative-index media.
Spin and orbital angular momenta (AM) of light are well studied for free-space electromagnetic fields, even nonparaxial. One of the important applications of these concepts is the information transfer using AM modes, often via optical fibers and other guiding systems. However, the self-consistent description of the spin and orbital AM of light in optical media (including dispersive and metallic cases) was provided only recently [K.Y. Bliokh et al., Phys. Rev. Lett. 119, 073901 (2017)]. Here we present the first accurate calculations, both analytical and numerical, of the spin and orbital AM, a…
Several dynamical properties such as energy, momentum, angular momentum, and optical helicity have been recently reexamined in dispersive and lossless media. Here, we address a parallel derivation for the optical chirality, extending it so as to include dissipative effects as well. To this end, we first elaborate on the most complete form of the conservation law for the optical chirality, without any restrictions on the nature of the medium. As a result we find a general expression for the optical chirality density both in lossless and lossy dispersive media. Our definition is perfectly consis…
Electric magnetic duality symmetry is well understood in vacuum. For light propagating through a medium this symmetry is typically broken. We investigate under what conditions duality transformation is preserved in a linear medium and employ these conditions to generalise the definition of optical helicity to a general linear medium. We will discuss some unique properties duality symmetric media possess, provided they exist and reformulate Maxwell's equation in such a way that they explicitly show the decoupling of opposite helicities. The feasibility of constructing a duality symmetric medium…
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 t…
The paper develops a modified geometrical optics (GO) of smoothly inhomogeneous isotropic medium, which takes into account two topological phenomena: Berry phase and the optical Magnus effect. By using the analogy between a quasi-classical motion of a quantum particle with a spin and GO of an electromagnetic wave in smoothly inhomogeneous media, we have introduced the standard gauge potential associated with the degeneracy in the wave momentum space. This potential corresponds to the Dirac-monopole-like field (Berry curvature), which causes the topological spin (polarization) transport of phot…
