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Communication modes in scalar diffraction
KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Optics. (Optik)
KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Optics.
KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Optics.ORCID iD: 0000-0003-3804-0561
KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Optics. (Optik)
2008 (English)In: Optik (Stuttgart), ISSN 0030-4026, Vol. 119, no 3, 103-111 p.Article in journal (Refereed) Published
Abstract [en]

The communication modes are a useful concept in studies of optical resolution, wave propagation, and image synthesis. We present an overview of earlier results on the communication modes in scalar diffraction theory. Besides the general theory, the modes are reviewed for the far-field and Fresnel regimes, and new eigenequations are derived for wide-angle diffraction. We prove a conjugate relationship between the transmitting and receiving modes in a general symmetric system. We also suggest an approximate method for far-field and Fresnel domain propagation, in which propagation amounts to a rotation of each mode in the complex plane. The main focus is on the near-field communication modes, where we present numerical examples of the modes and coupling strengths for a near-field geometry with a sub-wavelength size receiving domain. These results provide insights, for example, into the understanding of near-field scanning probe techniques.

Place, publisher, year, edition, pages
2008. Vol. 119, no 3, 103-111 p.
Keyword [en]
wave optics; diffraction; propagation; optical information; near fields
National Category
Atom and Molecular Physics and Optics
URN: urn:nbn:se:kth:diva-10276DOI: 10.1016/j.ijleo.2006.07.009ISI: 000253496600001ScopusID: 2-s2.0-38549134300OAI: diva2:213891
QC 20100802Available from: 2009-04-29 Created: 2009-04-29 Last updated: 2010-12-06Bibliographically approved
In thesis
1. Structural Information Content of the Optical Field
Open this publication in new window or tab >>Structural Information Content of the Optical Field
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]


The communication modes are a mathematical technique for the description of structural information in optical fields. These modes are orthogonal, optimally  connected functions characteristic of the optical system. Mathematically they are obtained by the singular value decomposition (SVD) of the operator that represents the field propagation. In this dissertation, the foundations of the technique are described, and the theory is extended and applied to a variety of specific systems.


In the Fresnel regime, the communication modes are closely related to the prolate spheroidal wavefunctions (PSWF). Within this approximation, the numerical propagation of the field in a one-dimensional optical system in terms of the PSWFs is demonstrated and the problem of assessing the best achievable realization of a given target field is addressed. Simplified equations for field propagation are presented. Approximate modes in large-aperture systems are derived and shown to agree with Gabor's theory on optics and information. The longitudinal resolution of an axicon is analyzed in terms of the communication modes. It is shown that in a generalized axicon geometry the communication modes are expressible in terms of the PSWFs, and that in usual circumstances a version of the large aperture approximation applies, resulting in quadratic waves in the aperture domain and sinc functions in the image domain


Eigenequations for the communication modes in scalar near-field diffraction are derived and applied to a simplified scanning near-field optical microscope (SNOM) geometry. It is suggested that the resolution of a SNOM system is essentially given by the width of the lowest-order communication modes. The best-connected mode is shown to effectively reduce to the Green function.


Within the context of random fluctuations the communication modes are defined for the cross-spectral density of partially coherent fields. These modes are compared to the well-known coherent modes. Expressions for the effective degree of coherence are derived, and it is demonstrated that optical fields of any state of coherence may readily be propagated through deterministic systems by means of the communication modes. Results are illustrated numerically in an optical near-field geometry.


The communication modes theory is further extended to vector diffraction on the basis of Maxwell's equations. The polarization properties of the electromagnetic communication modes as represented by the Stokes parameters are analyzed numerically for an example of a near-field geometry.

The work presented in this dissertation shows that the communication modes are an advanced, versatile tool that can be applied to deterministic and random, scalar and electromagnetic optical systems in far-field and near-field arrangements. The method is likely to find further uses in applications such as polarization microscopy.


Place, publisher, year, edition, pages
Stockholm: KTH, 2009. x, 87 p.
Trita-ICT/MAP, AVH Report 2009:02Arbete och HälsaFOU-rapport
National Category
urn:nbn:se:kth:diva-10281 (URN)978-91-7415-284-5 (ISBN)
Public defence
2009-05-22, Electrum C1, Isafjordsgatan 26, Kista, 10:15 (English)
QC 20100802Available from: 2009-05-15 Created: 2009-04-29 Last updated: 2012-03-28Bibliographically approved

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