Polarization and coherence for vectorial electromagnetic waves and the ray picture of light propagation

Abstract

We develop a complete geometrical picture of paraxial light propagation including coherence phenomena. This approach applies both for scalar and vectorial waves via the introduction of a suitable Wigner function and can be formulated in terms of an inverted Huygens principle. Coherence is included by allowing the geometrical rays to transport generalized Stokes parameters. The degree of coherence for scalar and vectorial light can be expressed as simple functions of the corresponding Wigner function.

Synchrotron radiation representation in phase space

“…The properties of the Wigner distribution have been studied extensively in the context of quantum mechanics [15,16], wave optics [6,7,17], and signal processing [18][19][20]. To provide a suitable context for describing synchrotron radiation, the properties of the WDF are reviewed in this section.…”

“…Whereas the electric field after an aperture with transmission tðrÞ is simply EðrÞ ! EðrÞtðrÞ, the Wigner distribution is given by the convolution of the angular variables of the input Wigner function with that of the spatial filter [7]: IVAN V. BAZAROV Phys. Rev.…”

“…The Wigner distribution, or Wigner distribution function (WDF), was recognized to be a general framework to represent quantum [1] and therefore wave phenomena in phase space [2] and specifically synchrotron radiation [3][4][5]. The approach allows light characterization of arbitrary degree of coherence [6] and polarization [7] in phase space, though its application by the accelerator community has so far been mostly limited to the simplest cases of Gaussian or Gauss-Schell beams [8,9], despite the fact that the non-Gaussian nature of undulator radiation in phase space has been long recognized [4,5,8,10]. The Gaussian approximation provides a set of useful analytical expressions for quick estimates of performance of x-ray sources even though incorrect values for rms phase-space dimensions are often used (for example, the undulator radiation in the central cone is incorrectly assumed to have a diffraction limited rms emittance of !=4%).…”

“…The Wigner distribution, or Wigner distribution function (WDF), was recognized to be a general framework to represent quantum [1] and therefore wave phenomena in phase space [2,3]. The approach allows light characterization of arbitrary degree of coherence [4] and polarization [5] in phase space, though its application by the accelerator community has so far been mostly limited to simplest cases of Gaussian or Gauss-Schell beams [6,7]. This provides a set of useful analytical expressions for quick estimates of performance of modern x-ray sources with improved coherence properties.…”