Partial polarization and electromagnetic spatial coherence of blackbody radiation emanating from an aperture

We consider, within the classical theory of electromagnetic coherence, the spectral coherence properties of a field emanating from an aperture in a blackbody cavity. Spatial coherence and polarization are assessed both in the aperture and in its far zone. We derive an expression for the full $3\times 3$ cross-spectral density matrix of the field in the opening and discuss the validity of some related results given in the literature. The aperture field serves as a finite, planar secondary source whose transverse coherence length is found to be of the order of the wavelength and which is unpolarized in the three-dimensional sense. The far field is obtained by propagating each of the three source-field components separately, resulting in the evaluation of the far-field spatial coherence in any pair of directions, paraxial or nonparaxial. We show that in the paraxial case, the coherence properties coincide with those obtained for a planar, secondary source which is spatially $\delta$-correlated and unpolarized. The results can find applications in the modeling of thermal sources and in the propagation of natural light fields.

Figure 1

Blackbody radiation inside a cavity can be regarded as a superposition of plane waves which is isotropic within the full $4\pi$ solid angle, whereas radiation emanating from the aperture is isotropic within the $2\pi$ solid angle. The aperture is at the $z=0$ plane. The figure illustrates the situation in two dimensions.

Figure 2

Illustration of notation.

Figure 3

Illustration of the electromagnetic degree of coherence as a function of $k\rho$, with $\rho =|{\rho }_2-{\rho }_1|$, in the aperture of a blackbody cavity.

Figure 4

Illustration of the far-field electromagnetic degree of coherence as a function of ${\theta }_1$ (in units of $\pi$) when (a) ${\theta }_2=0$ and (b) ${\theta }_2=3\pi /8$. In both cases ${\phi }_1={\phi }_2=0$, corresponding to the $xz$ plane, while the dashed (blue) and solid (red) curves refer to $k\varepsilon =100$ and $k\varepsilon =400$, respectively. The peak values are $1/\sqrt{2}$.