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Theoretical Generalization of the Optical Chirality to Arbitrary Optical Media

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Chirality, Magnetism and Magnetoelectricity

Part of the book series: Topics in Applied Physics ((TAP,volume 138))

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Abstract

Chiroptical light-matter interaction is largely boosted in the surroundings of complex-shaped metallic nanostructures. Multiple enhancement schemes have been proposed, from twisted structures, such as spirals or helices, arrays of chiral and even achiral plasmonic nanostructures, to stacked planar metasurfaces. Furthermore, there is a steadily growing trend in using assemblies of high-index dielectric nanostructures, which are actually revealing promising results in terms of the enhancement of chiroptical effects. At any rate, whatever the type of material is, the effects of dispersion and absorption need to be accounted for, with the only exception of the vacuum. These considerations are often neglected, presuming media with an ideal lossless and dispersionless behavior. However, when matter is nanostructured to achieve more complex behaviors, as for the case of metamaterials or plasmonic nanostructures, the effects of dispersion and losses in chiroptical interactions cannot be disregarded at all. Hence, as with the energy, the optical chirality should also be generalized to the case of arbitrary dispersive and lossy optical media. This is the matter of the present chapter; namely, a thorough derivation of the optical chirality, extending it so as to include both dispersive and dissipative effects. For simplicity, as well as for constructiveness, we shall elaborate this theoretical analysis upon the basis of the most complete form of the conservation law for the optical chirality.

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Notes

  1. 1.

    It is worth pointing out that, superchirality (or superchiral light), is well defined only in the case of plane-wave propagation in free space, because it is actually defined with respect to the chirality of circularly polarized light. Notice that, for example, in the case of waveguiding systems, the term of superchirality may be misunderstood, as it would depend on the specific structure [18]. So, in lieu of superchirality, henceforth we shall refer to it simply as the enhanced chirality. In any case, it is noteworthy to mention that there exists a subtle controversy regarding superchiral fields and its apparent unlimited enhancement factor (for further details on this issue see, e.g., [19]).

  2. 2.

    In this regard, it is noteworthy to mention the so-called Abraham-Minkowski dilemma, a long-standing problem concerning with an ambiguity that arises from the real definition of the linear and angular momentum for optical radiation in media [34]. Even though there are a number of influential papers claiming to have solved it (see, e.g., [35, 36]), this challenging problem still remains as a subject of current interest and debate [37, 38].

  3. 3.

    Notice that, strictly speaking, dispersion is necessarily tied to dissipation. This connection is well established by the so-called Kramers-Kronig relations [28], according to which the real and imaginary parts of the material parameters, i.e., the electric permittivity and the magnetic permeability (\(\varepsilon (\omega )=\varepsilon '+i\varepsilon ''\) and \(\mu (\omega )=\mu '+i\mu ''\)), appear to be coupled together. In addition, it has been demonstrated that Kramers-Kronig relations underpin the fundamental principle of causality [45], and hence, initial assumptions regarding dispersion and dissipation have to be carefully considered, otherwise they may lead to misleading outcomes. Still, one can find many cases where is assumed a dispersive medium neglecting the losses.

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  1. Nanophotonics Technology Center, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, Spain

    J. Enrique Vázquez-Lozano & Alejandro Martínez

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    Eugene Kamenetskii

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Vázquez-Lozano, J.E., Martínez, A. (2021). Theoretical Generalization of the Optical Chirality to Arbitrary Optical Media. In: Kamenetskii, E. (eds) Chirality, Magnetism and Magnetoelectricity. Topics in Applied Physics, vol 138. Springer, Cham. https://doi.org/10.1007/978-3-030-62844-4_13

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