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Limits of diffractive optics by communication modes
KTH, Superseded Departments, Microelectronics and Information Technology, IMIT. (Optik)ORCID iD: 0000-0003-3804-0561
KTH, Superseded Departments, Microelectronics and Information Technology, IMIT. (Optik)
KTH, Superseded Departments, Microelectronics and Information Technology, IMIT. (Optik)
2003 (English)In: Journal of Optics. A, Pure and applied optics, ISSN 1464-4258, E-ISSN 1741-3567, Vol. 5, 153-158 p.Article in journal (Refereed) Published
Abstract [en]

We apply the concept of communication modes, previously employed in information theory, to diffractive optics. The communication modes are used to study the resolution of one-dimensional optical systems in the Fresnel regime. Using the modes, which in this geometry are prolate spheroidal wavefunctions, the best achievable approximation to a given target field can be assessed. In this paper, the field propagation in terms of the communication modes is demonstrated numerically, and the results on resolution are confirmed by Fourier analysis.

Place, publisher, year, edition, pages
2003. Vol. 5, 153-158 p.
Keyword [en]
Diffraction, field propagation, resolution, communication modes
National Category
Atom and Molecular Physics and Optics
Identifiers
URN: urn:nbn:se:kth:diva-10273DOI: 10.1088/1464-4258/5/3/301ISI: 000183187500004OAI: oai:DiVA.org:kth-10273DiVA: diva2:213855
Note
QC 20100802Available from: 2009-04-29 Created: 2009-04-29 Last updated: 2010-12-07Bibliographically 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.
Series
Trita-ICT/MAP, AVH Report 2009:02Arbete och HälsaFOU-rapport
National Category
Telecommunications
Identifiers
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)
Opponent
Supervisors
Note
QC 20100802Available from: 2009-05-15 Created: 2009-04-29 Last updated: 2012-03-28Bibliographically approved

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Thaning, Anna

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