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J. E. Vázquez-Lozano and A. Martínez
[46]. Notice that just as much the energy, linear momentum, angular momentum, or
helicity, optical chirality is also a conserved quantity for free-space EM fields [31,
32, 47]. Upon this basis, in Sect. 13.2 we will recall some general aspects on conservation laws, particularizing to the simplest case of EM energy. In Sect. 13.3 we will
elaborate on the most complete form of the continuity equation for the optical chirality, without any restrictions on the nature of the medium. From this, and building
on previous approaches addressing the EM energy density considering dispersion as
well as dissipation, in Sect. 13.4, we will put forward an alternative derivation for the
optical chirality density in dispersive media, distinguishing between the lossless and
lossy cases [46]. Remarkably, our description will be completely general, i.e., it will
be valid for arbitrarily varying radiation fields, and will be applicable to any kind of
medium, including dielectrics, semiconductors, as well as highly dispersive material
systems such as metals (or plasmonic structures) and metamaterials [48]. Finally, in
Sect. 13.5, we will summarize the main results of this chapter and conclude with a
general outlook towards possible lines of future research.
13.2 Electromagnetic Energy Density in Dispersive and
Lossy Media: A General Approach from the
Continuity Equation
Aiming to provide a comprehensive and easy-to-follow guideline for generalizing
the optical chirality (and any other dynamical property), we will start by revisiting
basic aspects on the conservation laws focusing upon the most well-known dynamical
property: the EM energy. As will be seen below, this will enable a straightforward
procedure for obtaining a general expression of the EM energy density valid in any
kind of medium, either non-dispersive or dispersive, and, concerning this latter case,
extending it to both the lossless and the lossy approaches.
13.2.1 Poynting’s Theorem and Energy Density in
Non-Dispersive Media
Like Maxwell’s equations and the conservation of charge, the EM energy conservation law, often referred to as the Poynting’s theorem, is a fundamental piece of
classical electrodynamics. It is in fact a recurring matter all over the main textbooks
on electromagnetism [28, 30], optics [49], nano-optics [29], and photonics [50]. For
our purposes, it will serve as a guideline for mathematics and also for the interpretation when addressing the optical chirality density, specially those regarding
the source-like contributions, since its physical meaning in such a case may not be
so obvious [51, 52]. Notice that, even though it could seem quite burdensome, for
J. E. Vázquez-Lozano and A. Martínez
[46]. Notice that just as much the energy, linear momentum, angular momentum, or
helicity, optical chirality is also a conserved quantity for free-space EM fields [31,
32, 47]. Upon this basis, in Sect. 13.2 we will recall some general aspects on conservation laws, particularizing to the simplest case of EM energy. In Sect. 13.3 we will
elaborate on the most complete form of the continuity equation for the optical chirality, without any restrictions on the nature of the medium. From this, and building
on previous approaches addressing the EM energy density considering dispersion as
well as dissipation, in Sect. 13.4, we will put forward an alternative derivation for the
optical chirality density in dispersive media, distinguishing between the lossless and
lossy cases [46]. Remarkably, our description will be completely general, i.e., it will
be valid for arbitrarily varying radiation fields, and will be applicable to any kind of
medium, including dielectrics, semiconductors, as well as highly dispersive material
systems such as metals (or plasmonic structures) and metamaterials [48]. Finally, in
Sect. 13.5, we will summarize the main results of this chapter and conclude with a
general outlook towards possible lines of future research.
13.2 Electromagnetic Energy Density in Dispersive and
Lossy Media: A General Approach from the
Continuity Equation
Aiming to provide a comprehensive and easy-to-follow guideline for generalizing
the optical chirality (and any other dynamical property), we will start by revisiting
basic aspects on the conservation laws focusing upon the most well-known dynamical
property: the EM energy. As will be seen below, this will enable a straightforward
procedure for obtaining a general expression of the EM energy density valid in any
kind of medium, either non-dispersive or dispersive, and, concerning this latter case,
extending it to both the lossless and the lossy approaches.
13.2.1 Poynting’s Theorem and Energy Density in
Non-Dispersive Media
Like Maxwell’s equations and the conservation of charge, the EM energy conservation law, often referred to as the Poynting’s theorem, is a fundamental piece of
classical electrodynamics. It is in fact a recurring matter all over the main textbooks
on electromagnetism [28, 30], optics [49], nano-optics [29], and photonics [50]. For
our purposes, it will serve as a guideline for mathematics and also for the interpretation when addressing the optical chirality density, specially those regarding
the source-like contributions, since its physical meaning in such a case may not be
so obvious [51, 52]. Notice that, even though it could seem quite burdensome, for