Electromagnetic Coherence Theory, Universality Results and Effective Degree of Coherence

Kasimir Blomstedt

Research output: ThesisDoctoral ThesisCollection of Articles


Electromagnetic coherence is central to modern optics and photonics. Three topics from classical coherence theory are considered: 1) coherence of blackbody radiation within a cavity and at a cavity aperture, 2) universality of spatial coherence of fields created by homogeneous and isotropic sources, and 3) the effective degree of coherence. Blackbody sources and fields have played a pivotal role in the development of quantum physics. The cross-spectral density (CSD) and degree-of-coherence of the blackbody field at an opening in a blackbody cavity wall and in the far field are computed, and it is shown that the aperture CSD obtained in previous works is, in fact, erroneous. The effect of the cavity wall on the CSD of the field is also studied. It is found that the wall indeed has an appreciable influence, but that this does not affect the CSD of the field in the aperture. The coherent-mode representation of the CSD function of the vector-valued blackbody field is derived for a spherical volume, and the importance of the constituent coherent modes is assessed. This expansion marks the first time that the coherent-mode representation is determined within a three-dimensional region. The blackbody results can be used to model thermal sources and propagation of natural light. In prior works it has been shown that the degree-of-coherence functions of scalar optical fields, which are produced by stochastically homogeneous and isotropic sources, all have the same universal form in lossless infinite systems. Here that result is extended to electromagnetic fields. Additionally, it is proven that for actual systems, which necessarily are finite and lossy, the universal character disappears, regardless of how negligible the losses are or how large the source region is. These considerations apply to optical media and sources of all sizes, from nanoscopic to macroscopic. It is shown that the effective degree of coherence can be extended from field representations in volumes to arbitrary (Hilbert) spaces. In addition, it is demonstrated that the effective degree of coherence is an intrinsic property of the electromagnetic field, and that it can be computed from almost any field representation. In fact, what is proven is that the effective degree of coherence is invariant to scaled unitary mappings. Finally, it is shown that of all Hilbert space functionals with this property, only the effective degree of coherence is additive.
Translated title of the contributionSähkömagneettinen koherenssiteoria, universaalisuus sekä efektiivinen koherenssiaste
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Kaivola, Matti, Supervising Professor
  • Friberg, Ari, Thesis Advisor
  • Setälä, Tero, Thesis Advisor
Print ISBNs978-952-60-5417-9
Electronic ISBNs978-952-60-5418-6
Publication statusPublished - 2013
MoE publication typeG5 Doctoral dissertation (article)


  • electromagnetic coherence theory
  • blackbody field
  • universality of spatial coherence
  • effective degree of coherence

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