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J. E. Vázquez-Lozano and A. Martínez
13.5 Conclusions and Outlook
In this chapter, we have put forward a step-by-step theoretical generalization of the
optical chirality density in arbitrary dispersive and lossy media, as well as a thorough
analysis addressing the corresponding conservation law in its most complete form.
All along the whole exposure, we have always kept in mind the classical development
for the EM energy, whose conservation is dictated by the very well-known Poynting’s theorem [28–30, 53]. Even though these matters may seem somewhat trivial at
a first glance, simply the fact of considering EM waves propagating through a dispersive medium poses a challenge, making the mathematical treatment much more
complicated, but, at the same time, enriching the physics. Good evidence of this fact
is the number of papers on this issue that still continue being published nowadays
in renowned journals [54–64], wherein there is discussed and reexamined both the
fundamentals and the interpretation of the EM energy density in dispersive media.
This renewed interest in such seemingly basic aspects has likely been fostered by
recent progresses on left-handed materials [83, 84], and metamaterial photonics in
general [85–88].
In the same vein, as for the optical chirality, the latest efforts have been focused
on the design and fabrication of metamaterials and plasmonic nanostructures [1],
aiming to boost the chiral light-matter interactions for the development of advanced
chiroptical applications [10], such as sensing, chiral spectroscopy, or enhanced enantioselectivity [5, 7, 8]. Surprisingly, however, from a theoretical point of view, contributions of material dispersion, as well as dissipation, have mostly been ignored; using
instead the original definition for the vacuum [31, 32], even when its applicability can
be questionable. Now, a decade later, we have a more comprehensive understanding
and, a general and closed formulation for the optical chirality density [46, 48], which
will not only enable us to account for such features (dispersion and dissipation) from
now on, but it also would allow a thorough reexamination of prior results in order to
check their validity as well as their accuracy, e.g., by reconsidering the widespread
presumption that surface plasmons would have a null density of optical chirality
everywhere [89]. Furthermore, by including the presence of a material system, the
analysis of the continuity equation reveals the appearance of additional source-like
terms describing the loss (or gain) rate of optical chirality. Remarkably, whatever the
dynamical property is concerned, these contributions are important because enable
one to get deeper insights into fundamental aspects of light-matter interaction [51,
52]. For example, in the familiar case of EM energy, J · E, is directly related to the
power lost (or the work exerted) by the EM fields on the sources. However, in the
optical chirality case, the physical significance of its associated source-like terms is
not so obvious, thereby limiting to some extent the concept of source (or sink) of
optical chirality and thus hindering a proper interpretation. An in-depth understanding of the meaning and the physical implications of these contributions remain as
yet unclear and would deserve further efforts [90, 91]. Finally, it is also worth to
be mentioned the controversial debate currently existing around the meaningfulness
and the differences between the EM helicity and the optical chirality [91–93]. In this
J. E. Vázquez-Lozano and A. Martínez
13.5 Conclusions and Outlook
In this chapter, we have put forward a step-by-step theoretical generalization of the
optical chirality density in arbitrary dispersive and lossy media, as well as a thorough
analysis addressing the corresponding conservation law in its most complete form.
All along the whole exposure, we have always kept in mind the classical development
for the EM energy, whose conservation is dictated by the very well-known Poynting’s theorem [28–30, 53]. Even though these matters may seem somewhat trivial at
a first glance, simply the fact of considering EM waves propagating through a dispersive medium poses a challenge, making the mathematical treatment much more
complicated, but, at the same time, enriching the physics. Good evidence of this fact
is the number of papers on this issue that still continue being published nowadays
in renowned journals [54–64], wherein there is discussed and reexamined both the
fundamentals and the interpretation of the EM energy density in dispersive media.
This renewed interest in such seemingly basic aspects has likely been fostered by
recent progresses on left-handed materials [83, 84], and metamaterial photonics in
general [85–88].
In the same vein, as for the optical chirality, the latest efforts have been focused
on the design and fabrication of metamaterials and plasmonic nanostructures [1],
aiming to boost the chiral light-matter interactions for the development of advanced
chiroptical applications [10], such as sensing, chiral spectroscopy, or enhanced enantioselectivity [5, 7, 8]. Surprisingly, however, from a theoretical point of view, contributions of material dispersion, as well as dissipation, have mostly been ignored; using
instead the original definition for the vacuum [31, 32], even when its applicability can
be questionable. Now, a decade later, we have a more comprehensive understanding
and, a general and closed formulation for the optical chirality density [46, 48], which
will not only enable us to account for such features (dispersion and dissipation) from
now on, but it also would allow a thorough reexamination of prior results in order to
check their validity as well as their accuracy, e.g., by reconsidering the widespread
presumption that surface plasmons would have a null density of optical chirality
everywhere [89]. Furthermore, by including the presence of a material system, the
analysis of the continuity equation reveals the appearance of additional source-like
terms describing the loss (or gain) rate of optical chirality. Remarkably, whatever the
dynamical property is concerned, these contributions are important because enable
one to get deeper insights into fundamental aspects of light-matter interaction [51,
52]. For example, in the familiar case of EM energy, J · E, is directly related to the
power lost (or the work exerted) by the EM fields on the sources. However, in the
optical chirality case, the physical significance of its associated source-like terms is
not so obvious, thereby limiting to some extent the concept of source (or sink) of
optical chirality and thus hindering a proper interpretation. An in-depth understanding of the meaning and the physical implications of these contributions remain as
yet unclear and would deserve further efforts [90, 91]. Finally, it is also worth to
be mentioned the controversial debate currently existing around the meaningfulness
and the differences between the EM helicity and the optical chirality [91–93]. In this