COHERENT emission of light
PIONNERING EXPERIMENT wavelength range 10-12 µ m. Hence, thermal emission could be observed by increasing the temperature by only 100 or 200 ° C if Kirchhoff ' s law is applicable. As the angular position of the peak depends on the frequency, directional emission is only observed when detecting at a given frequency. The first design of the grating led to the fabrication of a grating that did not produce the expected directional peaks [ 5 ] neither in reflection nor in emission. This was due to the use of a perturbative model to design the surface. Total absorption is a non-perturbative resonant phenomenon that requires an accurate numerical simulation for the design and an accurate nanofabrication of the sample. We designed the surface profile in the team at Ecole Centrale. The team of Yong Chen did the fabrication of the samples at L2M / CNRS using optical lithography and reactive ion-etching. The measurements were made at CESTA / CEA by S. Mainguy in 2002 [ 6 ]. The reflectivity measurements displayed the expected total absorption as seen in Fig. 1. The sample was then installed on a heater and emission spectra were taken for different emission angles. As predicted by Kirchhoff ' s law, we observed highly directional emission by a hot body( see Fig. 1 lower panel). In this first experiment, the angular resolution was limited by the detection system. A second setup was later developed by F. Marquier to study in detail the measured coherence length and to improve the agreement with theory by accounting for the dependence of the refractive index on the temperature [ 7 ].
Discussion
At that point, it was clear that Kirchhoff law prediction was confirmed by the experiments. That result raised the question of the origin of the spatial coherence. It also suggested that Kirchhoff law could be derived without making the geometrical optics approximation. We managed to derive Kirchhoff’ s law beyond the geometrical optics approximation by using a wave equation framework [ 8 ]. We also
Figure 1. Upper panel: reflectivity of a grating ruled on a SiC sample. A total absorption peak is observed at 11.36 µ m for a 45 ° incidence. Lower panel, emissivity measurement for three different wavelengths( blue: 11.04 µ m, green: 11.86 µ m, red: 11.36 µ m). The experimental data are given by the circles, the theoretical results( solid line) are convoluted to account for the experimental angular resolution. The emissivity is given by the ratio of the emitted power by the power emitted by a blackbody at the same temperature.( reproduced from ref. [ 6 ]).
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