Spatial coherence of thermal fields in far-and near-field zones generated by heated half-space into vacuum is studied at essentially different thermodynamical conditions. It is shown that correlation lengths of fields in any field zone are different in equilibrium and out of equilibrium systems. In wide range of distances from sample surface correlation functions are should be calculated using a total sum of evanescent and propagating contributions due to their mutual compensation at some conditions because of anticorrelations. It is demonstrated that correlation lengths as calculated with a proposed formula are in agreement with a behavior of correlation functions of thermal fields in spectral range of surface excitations
1.IntroductionThe study of the time and spatial coherence properties of spontaneous fields is an important part of modern science. Correlation properties of free thermal electromagnetic fields in equilibrium with surrounding matter are described in detail; see for example [1][2][3][4]. Correlation tensors of the fields at any distances from bodies with arbitrary geometric shapes can be theoretically calculated both in equilibrium and in out of equilibrium when heated body radiates into a cold surrounding [5][6][7][8]. It should be emphasized that in accordance with the theoretic analysis thermal fields are formally divided into the propagating and evanescent fields with different spectral and correlation properties, see for numerous examples [9][10][11]. We recall that the correlation radius of propagating waves of the black body field is on the order of the Wien wavelength in case of non-equal time correlation functions, and is on the order of a wavelength of interest in case of equal time correlation functions. The spatial correlation scale of fields nearby heated bodies depends on electrodynamic properties of materials and other parameters of the problem under study. An analysis of properties of thermally stimulated fields in a vicinity of interfaces is extremely important for a description of dynamics of near surface processes. There has been a vast amount of scientific activity in the study of the coherence properties of thermal fluctuations at frequencies of the surface excitations and waveguide modes [12][13][14][15][16]. The prominent result here is the increase of the spatial correlation at the surface eigenfrequencies. The increase can reach tens of wavelengths nearby an interface which is substantially larger than the correlation scale of the equilibrium radiation in free space [12]. Furthermore, it was shown in [11,15] that the length of correlation is determined by the dispersion characteristic for surface polaritons. The physical grounding is that the collective coherent excitation of surface charges or surface oscillations of the lattice at the interface becomes as the source of fields at corresponding eigenfrequencies transferring the spatial coherence to the fluctuating electromagnetic fields. Obviously, a study the coherence of spontaneous fields in the frequency range of res...