286
P. Ben-Abdallah et al.
mary, this simple qualitative discussion shows that emissivity and absorptivity are
two sides of the same coin: transmission by an interface. This discussion provides
some physical ideas justifying Kirchhoff’s law that states the equality between the
emissivity and the absorptivity. Here, we do not elaborate any further on the foundations of Kirchhoff’s law. We only note that it is valid for directional monochromatic
polarized fields. A rigorous derivation of Kirchhoff’s law can be found in Ref. [44].
It is based on the definition of the specific intensity (the fundamental radiometric
quantity) in the framework of statistical electrodynamics (i.e. coherence theory). Let
us also point out that a generalized form of Kirchhoff’s law has been derived for
non isothermal sources. This generalized relation establishes a link between local
absorption rate and local emission rate. The local emission rate then depends on the
local temperature [48, 125].
Kirchhoff’s law is thus the corner stone of the modelling of thermal emission.
We emphasize that it establishes a connection between the emissivity that characterizes the emission process by random currents with the absorptivity which can be
computed using a coherent incident wave. This is important from a practical point
of view as emissivity is a concept that belongs to radiometry and thermodynamics
whereas absorptivity or transmissivity belong to coherent optics. Kirchhoff’s law
establishes a link between the two worlds. In summary, designing a thermal emitter
with specific directional or spectral properties amounts to design an absorber with
the same properties. The latter can be done using standard electromagnetic tools.
When designing absorbers, it is useful to design structures that can excite resonantly surface waves. Indeed, it is well known that absorption can be drastically
modified when surface waves can be excited. It is the purpose of this section to review
the potential applications to control the design of thermal sources.
8.1.1.4 Characteristics of Usual Thermal Sources, Limitations and Prospects
Incandescent sources relying on thermal emission have been the most commonly
way of lighting with the tungsten filament bulb. Yet this type of radiation source
suffers from a number of limitations.
It is usually taken for granted that thermal emission is incoherent as opposed to
a laser which is coherent. More specifically, thermal radiation is usually temporally
incoherent because the emitted spectrum is very broad. This is basically because all
the available modes are thermally populated according to Bose-Einstein distribution.
As shown by the fluctuation-dissipation theorem, the spectrum of the random currents
is only limited by the absorption spectrum given by the imaginary part of the dielectric
constant. In what follows, we will see that the emission spectrum can be changed
dramatically by microstructuring the interface. Indeed, it is the absorptivity of the
interface that matters, not the intrinsic absorption spectrum of the material.
It is also usually taken for granted that thermal sources are spatially incoherent.
This amounts to say that they emit over many angles as opposed to a laser that can
emit in a well-defined direction (or over a small area that can be located at the focus of
a lens). This appears to be a reasonable assumption as the fluctuating current densities
P. Ben-Abdallah et al.
mary, this simple qualitative discussion shows that emissivity and absorptivity are
two sides of the same coin: transmission by an interface. This discussion provides
some physical ideas justifying Kirchhoff’s law that states the equality between the
emissivity and the absorptivity. Here, we do not elaborate any further on the foundations of Kirchhoff’s law. We only note that it is valid for directional monochromatic
polarized fields. A rigorous derivation of Kirchhoff’s law can be found in Ref. [44].
It is based on the definition of the specific intensity (the fundamental radiometric
quantity) in the framework of statistical electrodynamics (i.e. coherence theory). Let
us also point out that a generalized form of Kirchhoff’s law has been derived for
non isothermal sources. This generalized relation establishes a link between local
absorption rate and local emission rate. The local emission rate then depends on the
local temperature [48, 125].
Kirchhoff’s law is thus the corner stone of the modelling of thermal emission.
We emphasize that it establishes a connection between the emissivity that characterizes the emission process by random currents with the absorptivity which can be
computed using a coherent incident wave. This is important from a practical point
of view as emissivity is a concept that belongs to radiometry and thermodynamics
whereas absorptivity or transmissivity belong to coherent optics. Kirchhoff’s law
establishes a link between the two worlds. In summary, designing a thermal emitter
with specific directional or spectral properties amounts to design an absorber with
the same properties. The latter can be done using standard electromagnetic tools.
When designing absorbers, it is useful to design structures that can excite resonantly surface waves. Indeed, it is well known that absorption can be drastically
modified when surface waves can be excited. It is the purpose of this section to review
the potential applications to control the design of thermal sources.
8.1.1.4 Characteristics of Usual Thermal Sources, Limitations and Prospects
Incandescent sources relying on thermal emission have been the most commonly
way of lighting with the tungsten filament bulb. Yet this type of radiation source
suffers from a number of limitations.
It is usually taken for granted that thermal emission is incoherent as opposed to
a laser which is coherent. More specifically, thermal radiation is usually temporally
incoherent because the emitted spectrum is very broad. This is basically because all
the available modes are thermally populated according to Bose-Einstein distribution.
As shown by the fluctuation-dissipation theorem, the spectrum of the random currents
is only limited by the absorption spectrum given by the imaginary part of the dielectric
constant. In what follows, we will see that the emission spectrum can be changed
dramatically by microstructuring the interface. Indeed, it is the absorptivity of the
interface that matters, not the intrinsic absorption spectrum of the material.
It is also usually taken for granted that thermal sources are spatially incoherent.
This amounts to say that they emit over many angles as opposed to a laser that can
emit in a well-defined direction (or over a small area that can be located at the focus of
a lens). This appears to be a reasonable assumption as the fluctuating current densities