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Spatial Correlations and Partial Polarization in Electromagnetic Optical Fields: Effects of Evanescent Waves

Tero Setälä

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics for public examination and debate in Auditorium S4 at Helsinki University of Technology (Espoo, Finland) on the 28th of March, 2003, at 12 noon.

Overview in PDF format (ISBN 951-22-6402-1)   [537 KB]
Dissertation is also available in print (ISBN 951-22-6401-3)

Abstract

In this thesis, partial polarization and spatial correlation properties of electromagnetic optical fields are investigated. The emphasis is on near fields which exist only within the distance of the light wavelength from the emitting or scattering object. In the near-field region, the contribution of the evanescent (non-radiating) waves is overwhelming compared to the propagating waves that can be observed far from the source.

Certain fundamental issues related to the optical near-fields are studied. The decomposition of the free-space Green tensor into its evanescent and propagating parts is performed. This issue is of importance in near-field optics and it has attracted considerable attention in the recent literature. Another fundamental issue investigated in the thesis concerns the three-dimensional degree of polarization needed to characterize of electromagnetic fields having arbitrary planar or non-planar wave structures. The physical interpretation of the concept is presented, and its differences in comparison with the conventional two-dimensional formulation of the degree of polarization are brought out. The theory is applied to investigate the effects of evanescent waves and resonant surface waves on the polarization state of the near fields generated by some thermal half-space sources.

The thesis also includes a study of the partial polarization and spatial correlation properties of homogeneous free electromagnetic fields. The fields are modelled as an isotropic distribution of angularly uncorrelated and, in the 2D-sense, unpolarized plane waves propagating within a solid angle. When the solid angle extends over the full space, the spatial correlations are found to be determined by the imaginary part of the associated Green tensor, and the field is fully unpolarized in the 3D-sense. These results are the same as for black-body fields, although here no thermal equilibrium is assumed. The same behavior is discovered for any electromagnetic field generated by a statistically homogeneous and isotropic current distribution, which fluctuates within a medium having a vanishingly small absorption. For the fields whose electric cross-spectral density tensor is proportional to the imaginary part of the Green tensor, the degree of coherence has a universal form given by the sinc law.

This thesis consists of an overview and of the following 5 publications:

  1. Setälä T., Kaivola M. and Friberg A. T., 1999. Decomposition of the point-dipole field into homogeneous and evanescent parts. Physical Review E 59, pages 1200-1206. © 1999 American Physical Society. By permission.
  2. Setälä T., Shevchenko A., Kaivola M. and Friberg A. T., 2002. Degree of polarization for optical near fields. Physical Review E 66, 016615. © 2002 American Physical Society. By permission.
  3. Setälä T., Kaivola M. and Friberg A. T., 2002. Degree of polarization in near fields of thermal sources: effects of surface waves. Physical Review Letters 88, 123902. © 2002 American Physical Society. By permission.
  4. Setälä T., Kaivola M. and Friberg A. T., Spatial correlations and degree of polarization in homogeneous electromagnetic fields. Optics Letters, submitted.
  5. Setälä T., Blomstedt K., Kaivola M. and Friberg A. T., 2003. Universality of electromagnetic-field correlations within homogeneous and isotropic sources. Physical Review E 67, 026613. © 2003 American Physical Society. By permission.

Keywords: optical near field, polarization, coherence

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© 2003 Helsinki University of Technology

Last update 2011-05-26