PIONEERING EXPERIMENT
COHERENT emission of light
Figure 2. a) Schematic description of the scanning IR microscope. The sample consists of gold stripes deposited on a SiC sample. The sample is not illuminated but heated up to 170 ° C so that only thermal emission can be detected in the IR. A tip oscillates vertically above the hot sample. It scatters the thermal infrared near-field which is collected by a Cassegrain objective and sent to an IR detector, b) and c) cross section of the IR signal measured through a bandpass filter( centered at 10.9 µ m, width of 1 µ m) taken for stripe widths: 12 µ m( b) and 25 µ m( c). The fringe structure reproduces the local density of states. The fringe structure illustrates the spatial coherence of the thermally excited field when only a few modes are available due to the finite width of the stripe which is on the order of the wavelength. Reproduced from ref. [ 11 ].
found that another derivation of Kirchhoff law was already available in the framework of fluctuational electrodynamics [ 9 ]. This framework is extremely powerful and enables to compute the emitted field in the framework of Maxwell equations and statistical physics. It had been used to analyse Casimir forces and thermal fields in the microwave regime. We applied it to derive the correlation function of the electric field thermally emitted close to an interface separating a material from air. We found that when a surface wave propagates along the interface, a long-range correlation( i. e. spatial coherence) exists [ 10 ]. Since spatial coherence results from the excitation of a surface wave, it can only be measured directly in the near field. Near-field optical microscopy had just been introduced and enabled to measure directly the field of surface plasmons. However, the measurement of a correlation of the field measured at two different points was more challenging. To mitigate the experimental difficulty, we briefly attempted to measure the near-field correlation in the microwave regime at the interface between water and air as surface waves may propagate along this interface. K. Joulain did experiments in collaboration with Michel Gross at Ecole Normale but we could not observe the effect. It took some years before Y. de Wilde could directly observe fringes in the structure of a thermally emitted field [ 11 ] by a gold stripe with finite width using a near-field microscope as seen in Fig. 2.
The physical mechanism
To grasp the role of spatial coherence, we use a physical picture that emerges from the fluctuational electrodynamics framework. Each volume element of the emitting body contains random currents due the thermal motion of electrons and nuclei. These currents are spatially uncorrelated. If such a volume element is chosen much smaller than a wavelength, it can be described as a random dipole. The field emitted by the dipole can be represented as a sum of plane waves. If we consider that the emitting body is a half-space separating a medium from air, each plane wave emitted in the body may be reabsorbed before reaching the interface. However, if the volume element is close enough to the interface, the radiation may be transmitted( see Fig. 3 a). For a metal or SiC, the transmission factor is low and does not depend much on the angle of incidence so that the emission is low for all directions. A directional thermal source requires an interface whose transmission factor is low for all directions but one. We now explain why a grating ruled on a SiC surface has this peculiar property. As discussed above, the emitted radiation is the sum of the intensities emitted by each volume element in the hot body. It turns out that a random
Figure 3. Sketch of the mechanism producing spatial coherence and directional emission. a) Thermal emission by a hot body. Each volume element( red disk) contains charges with random thermal motion. The corresponding current density emits light which is transmitted by the interface( red arrows). b) Thermal emission by a hot body sustaining a surface wave. In addition to the transmitted light, a surface wave( thick horizontal line) is excited. The dispersion relation of the surface wave is denoted k sw( ω). The surface wave propagates along the interface and decays exponentially due to the losses in the material. As a consequence, the field is correlated over a distance limited by the surface wave decay length. c) Coherent thermal emission. When a grating with period d is ruled on the interface, the surface wave is diffracted in a direction θ given by the grating law ω / c sin θ = k sw( ω)-2π / d.
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