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Introduction To Electrodynamics

Chirality arises universally across many different fields. Recent advancements in artificial nanomaterials have demonstrated chiroptical responses that far exceed those found in natural materials. Chiroptical phenomena are complicated processes that involve transitions between states with opposite parities, and solid interpretations of these observations are yet to be clearly provided. In this review, we present a comprehensive overview of the theoretical aspects of chirality in light, nanostructures, and nanosystems and their chiroptical interactions. Descriptions of observed chiroptical phenomena based on these fundamentals are intensively discussed. We start with the strong intrinsic and extrinsic chirality in plasmonic nanoparticle systems, followed by enantioselective sensing and optical manipulation, and then conclude with orbital angular momentum-dependent responses. This review will be helpful for understanding the mechanisms behind chiroptical phenomena based on underlying chiral properties and useful for interpreting chiroptical systems for further studies. Strengthening the theoretical understanding of chirality is necessary for developing applications based on its phenomena. Junsuk Rho of Korea’s Pohang University of Science and Technology (POSTECH) reviewed with colleagues the theoretical aspects of chirality, a symmetry property that describes mirror-image objects or systems that cannot be superimposed. Chiral materials have attracted much attention due to their interesting interactions. Scientists are familiar with how geometrically chiral objects and systems interact with light. However, such ‘chiroptical effects’ can also be found in achiral systems, Rho and his colleagues explain. Also, globally achiral light can be locally chiral near nanostructures. Scientists need to extend their concepts and theoretical understandings of chiroptical systems in order to be able to further develop applications based on their phenomena, such as in metamaterials, sensing, spintronics and stereochemistry.

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Electromagnetic chirality: from fundamentals to nontraditional chiroptical phenomena

Der speziellen Relativitatstheorie liegt folgendes Postulat zugrunde, welchem auch durch die Galilei-Newtonsche Mechanik Genuge geleistet wird: Wird ein Koordinatensystem K so gewahlt, das in bezug auf dasselbe die physikalischen Gesetze in ihrer einfachsten Form gelten, so gelten dieselben Gesetze auch in Bezug auf jedes andere Koordinatensystem K′, das relativ zu K in gleichformiger Translationsbewegung begriffen ist. Dieses Postulat nennen wir „spezielles Relativitatsprinzip“. Durch das Wort „speziell“ soll angedeutet werden, das das Prinzip auf den Fall beschrankt ist, das K′ eine gleichformige Translationsbewegung gegen K ausfuhrt, das sich aber die Gleichwertigkeit von K′ und K nicht auf den Fall ungleichformiger Bewegung von K′ gegen K erstreckt.

Die Grundlage der allgemeinen Relativitätstheorie

On the Light from the Sky, its Polarization and Colour (1871)

Optical activity is conventionally understood as a natural difference in the optical responses of chiral materials with opposite handedness. It stems from the quantised spin angular momentum ±ħ per photon, with the ± representing either left- or right-handed circular polarisations. Less well known, until recently, was the possibility that matter might also respond in a similar, discriminatory way to the handedness of twisted light, or ‘optical vortices’, whose orbital angular momentum (OAM) is quantised as ℓℏ per photon, where ℓ is the topological charge whose sign determines a wavefront twist to the left or right. Initial studies focusing on whether, in spectroscopic applications, chiral matter might respond differently to the vortex handedness of +ℓ and −ℓ beams, failed to identify any viable mechanism. However, in the last few years, theory and experiment have both supplied ample evidence that, under certain conditions, such forms of interaction do exist—and as a result, the field of chirality and optical OAM is beginning to flourish at a pace. This topical review presents a survey of this new field, working up from a description of those initial studies to the cutting-edge experiments now taking place. Analysing the fundamental mechanisms provides for a revision of previous precepts, broadening their scope in the light of recent advances in understanding, and highlighting a vibrant synergy between the fields of optical activity and twisted light.

https://iopscience.iop.org/article/10.1088/2515-7647/abdb06/pdf

Orbital angular momentum of twisted light: chirality and optical activity

We consider the helicity and chirality of the free electromagnetic field, and advocate the
former as a means of characterising the interaction of chiral light with matter. This is in view of the
intuitive quantum form of the helicity density operator, and of the dual symmetry transformation
generated by its conservation. We go on to review the form of the helicity density and its associated
continuity equation in free space, in the presence of local currents and charges, and upon interaction
with bulk media, leading to characterisation of both microscopic and macroscopic sources of helicity.

Optical Helicity and Chirality: Conservation and Sources

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 ±\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 symmetry condition of a chiral medium with a constant value of e/μ. Extending the results to arbitrary order in β establishes an exact relationship between the energy and helicity densities in a chiral medium.

https://iopscience.iop.org/article/10.1088/2040-8986/ab387c/pdf

On the conservation of helicity in a chiral medium

We consider the energy and helicity densities of circularly polarised light within a lossless chiral medium, characterised by the chirality parameter $\beta$. A form for the helicity density is introduced, valid to first order in $\beta$, 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 symmetry condition of a chiral medium with a constant value of ${\epsilon}/{\mu}$. Extending the results to arbitrary order in $\beta$ establishes an exact relationship between the energy and helicity densities in a chiral medium.

We extend the usual multipolar theory of linear Rayleigh and Raman scattering to include the second-order correction. These terms promise a wealth of information about the shape of a scatterer and yet are insensitive to the scatterer's chirality. Our extended theory might prove especially useful for analyzing samples in which the scatterers have nontrivial shapes but no chiral preference overall, as the zeroth-order theory offers little information about shape and the first-order correction is often quenched for such samples. A basic estimate suggests that our extended theory can be applied to a scatterer as large as ${k}_{0}d\ensuremath{\sim}1/10$ with less than $\ensuremath{\sim}0.1%$ error resulting from the neglect of the third- and higher-order corrections. Our results are entirely analytical.

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Linear Rayleigh and Raman scattering to the second order : analytical results for light scattering by any scatterer of size k0d ≲ 1/10

Locally conserved quantities of the electromagnetic field in lossless chiral media are derived from Noether's theorem, including helicity, chirality, momentum, and angular momentum, as well as the separate spin and orbital components of this last quantity. We discuss sources and sinks of each in the presence of current densities within the material, and in some cases, as also generated by inhomogeneity of the medium. A previously obtained result connecting sources of helicity and energy within chiral materials is explored, revealing that association between the two quantities is not restricted to chiral media alone. Rather, it is analogous to the connection between the momentum, and the spin and orbital components of the total angular momentum. The analysis reveals a new quantity, appearing as the "orbital" counterpart of the helicity density in classical electromagnetism.

/pdf/continuous-symmetries-and-conservation-laws-in-chiral-media-386hpi4wia.pdf

Neel Mackinnon

Papers

Optical Helicity and Chirality: Conservation and Sources

On the conservation of helicity in a chiral medium

On the conservation of helicity in a chiral medium

Linear Rayleigh and Raman scattering to the second order : analytical results for light scattering by any scatterer of size k0d ≲ 1/10

Continuous symmetries and conservation laws in chiral media