The van Cittert-Zernike theorem for electromagnetic fields

Abstract

The van Cittert-Zernike theorem, well known for the scalar optical fields, is generalized for the case of vector electromagnetic fields. The deduced theorem shows that the degree of coherence of the electromagnetic field produced by the completely incoherent vector source increases on propagation whereas the degree of polarization remains unchanged. The possible application of the deduced theorem is illustrated by an example of optical simulation of partially coherent and partially polarized secondary source with the controlled statistical properties.

3D polarisation speckle as a demonstration of tensor version of the van Cittert-Zernike theorem for stochastic electromagnetic beams

“…(21) and (22). The degree of polarization of this propagated field is independent of the location ′ ρ and invariable during propagation, and this property of consistent polarization state is in accordance with earlier discussions for free space propagation 18,19 . Especially, in the case of z → ∞ , denoting a far propagation distance, In metrology, the 3D speckle shape is usually the parameter in which we are interested.…”

“…(18) and (19) thus facilitate the calculation of the spatial coherence and degree of polarization for a given depolarizer illuminated with linearly polarized light.…”

“…(18) and (19), the propagated coherence matrix for such system could be calculated to assess the evolution of the degree of polarization and the degree of coherence during free space propagation. Based on this, we obtain the expression for the degree of coherence and degree of polarization for the resultant field: …”

“…Relevant researches like recent hot spot of the vectorial extension of conventional Van Cittert-Zernike theorem 18,19 also raise demands of describing this incoherent field with spatially non-uniformly distributed polarization state. The matrix form, tensor version extension of the conventional Van Cittert-Zernike theorem is first described by Gori 8,20 in the temporal domain, and then similar work in the spectral domain by Ostrovsky 19 .…”

“…The matrix form, tensor version extension of the conventional Van Cittert-Zernike theorem is first described by Gori 8,20 in the temporal domain, and then similar work in the spectral domain by Ostrovsky 19 . Further research work about the variation of the degree of coherence and degree of polarization within this field was developed both theoretically 18,21,22 and experimentally 23 soon after.…”