8 Controlling Thermal Radiation with Surface Waves
289
8.1.1.6 Partially Coherent Sources: Emissivity as a Filter
In this section, we introduce a simple picture of the partially coherent emission by a
single interface separating an opaque medium from vacuum. In order to derive this
simple picture, we use two simple arguments introduced above. First, we have seen
that the emissivity can be interpreted as the transmissivity of the interface. Second,
we have seen that at local thermodynamic equilibrium all the modes are populated
according to the Bose-Einstein distribution. In particular, radiation impinging on the
interface from the emitter side is characterized by the emitter temperature as the
body is in local thermodynamic equilibrium. Finally, we have seen that controlling
the coherence amounts to control the direction of emission for spatial coherence and
the emission spectrum for temporal coherence. Summarizing, we see that if we can
design the angular and spectral dependence of the interface transmissivity, we can
fully control the coherence of the thermally emitted field. For instance, a temporally
coherent source requires a transmission factor (i.e. emissivity) which is zero almost
everywhere and close to one in a narrow spectrum.
8.1.1.7 Early Results
A corner stone result is the first demonstration of total absorption by a shallow gold
grating due to the resonant excitation of a surface plasmon. It has been predicted by
D. Maystre and observed by Maystre and Hutley [81] in the 1970s. It is a remarkable
result as the reflectivity of this shallow grating is essentially either 1 (as one would
expect for a gold mirror) or zero (for a very limited range of frequencies and angle
corresponding to the excitation of the surface plasmon). Later on, Hesketh and his
group showed spectral measurements on doped-silicon deep gratings with varying
periods heated at 400 ◦ C [51]. They showed that the behavior of the emission in
p-polarization depended strongly on the period, while in s-polarization the spectra
did not change significantly. Since then, it has been shown that this was related to the
surface plasmon thermally excited on doped silicon. In the late 1990s works were
conducted on doped-silicon V-grooved gratings showing antireflection properties in
p-polarization [5, 49]. In 1999, The first experiment on thermal emission by a metallic
lamellar grating has been performed by Kreiter and coworkers [62]. A gold grating
was heated at 700 ◦ C and the angular emission at two wavelengths (710 and 810 nm)
was observed. They showed a purely p-polarized peak emission for well-defined
angles, attributed to surface plasmons.
Of particular relevance for thermal sources are surface phonon polaritons. Indeed,
surface plasmons of common metals are in the near UV so that they cannot be effectively thermally excited close to the plasma frequency for achievable temperatures.
Of course, the part of the dispersion relation that lies close to the light line at lower
frequencies (see Fig. 8.1) can always be excited. By contrast, the surface phonon
polaritons exist in the so-called reststrahlen region where optical phonon exists, in the
infrared. This region exist between the so-called longitudinal optical frequency and
transverse optical frequency. The polaritons are coupled electromagnetic and vibra-
289
8.1.1.6 Partially Coherent Sources: Emissivity as a Filter
In this section, we introduce a simple picture of the partially coherent emission by a
single interface separating an opaque medium from vacuum. In order to derive this
simple picture, we use two simple arguments introduced above. First, we have seen
that the emissivity can be interpreted as the transmissivity of the interface. Second,
we have seen that at local thermodynamic equilibrium all the modes are populated
according to the Bose-Einstein distribution. In particular, radiation impinging on the
interface from the emitter side is characterized by the emitter temperature as the
body is in local thermodynamic equilibrium. Finally, we have seen that controlling
the coherence amounts to control the direction of emission for spatial coherence and
the emission spectrum for temporal coherence. Summarizing, we see that if we can
design the angular and spectral dependence of the interface transmissivity, we can
fully control the coherence of the thermally emitted field. For instance, a temporally
coherent source requires a transmission factor (i.e. emissivity) which is zero almost
everywhere and close to one in a narrow spectrum.
8.1.1.7 Early Results
A corner stone result is the first demonstration of total absorption by a shallow gold
grating due to the resonant excitation of a surface plasmon. It has been predicted by
D. Maystre and observed by Maystre and Hutley [81] in the 1970s. It is a remarkable
result as the reflectivity of this shallow grating is essentially either 1 (as one would
expect for a gold mirror) or zero (for a very limited range of frequencies and angle
corresponding to the excitation of the surface plasmon). Later on, Hesketh and his
group showed spectral measurements on doped-silicon deep gratings with varying
periods heated at 400 ◦ C [51]. They showed that the behavior of the emission in
p-polarization depended strongly on the period, while in s-polarization the spectra
did not change significantly. Since then, it has been shown that this was related to the
surface plasmon thermally excited on doped silicon. In the late 1990s works were
conducted on doped-silicon V-grooved gratings showing antireflection properties in
p-polarization [5, 49]. In 1999, The first experiment on thermal emission by a metallic
lamellar grating has been performed by Kreiter and coworkers [62]. A gold grating
was heated at 700 ◦ C and the angular emission at two wavelengths (710 and 810 nm)
was observed. They showed a purely p-polarized peak emission for well-defined
angles, attributed to surface plasmons.
Of particular relevance for thermal sources are surface phonon polaritons. Indeed,
surface plasmons of common metals are in the near UV so that they cannot be effectively thermally excited close to the plasma frequency for achievable temperatures.
Of course, the part of the dispersion relation that lies close to the light line at lower
frequencies (see Fig. 8.1) can always be excited. By contrast, the surface phonon
polaritons exist in the so-called reststrahlen region where optical phonon exists, in the
infrared. This region exist between the so-called longitudinal optical frequency and
transverse optical frequency. The polaritons are coupled electromagnetic and vibra-