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Structural Information Content of the Optical Field
KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Optics. (Optik)
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: urn:nbn:se:kth:diva-10281ISBN: 978-91-7415-284-5 (print)OAI: oai:DiVA.org:kth-10281DiVA: diva2:213907
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
List of papers
1. Limits of diffractive optics by communication modes
Open this publication in new window or tab >>Limits of diffractive optics by communication modes
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.

Keyword
Diffraction, field propagation, resolution, communication modes
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-10273 (URN)10.1088/1464-4258/5/3/301 (DOI)000183187500004 ()
Note
QC 20100802Available from: 2009-04-29 Created: 2009-04-29 Last updated: 2017-12-13Bibliographically approved
2. Communication modes in scalar diffraction
Open this publication in new window or tab >>Communication modes in scalar diffraction
2008 (English)In: Optik (Stuttgart), ISSN 0030-4026, E-ISSN 1618-1336, 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.

Keyword
wave optics; diffraction; propagation; optical information; near fields
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-10276 (URN)10.1016/j.ijleo.2006.07.009 (DOI)000253496600001 ()2-s2.0-38549134300 (Scopus ID)
Note
QC 20100802Available from: 2009-04-29 Created: 2009-04-29 Last updated: 2017-12-13Bibliographically approved
3.
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4. Communication modes with partially coherent fields
Open this publication in new window or tab >>Communication modes with partially coherent fields
2007 (English)In: Journal of the Optical Society of America A, ISSN 0740-3232, Vol. 24, no 10, 3336-3342 p.Article in journal (Refereed) Published
Abstract [en]

We develop a theory for the description of partially coherent wave fields in linear optical systems in terms of the so-called communication modes. The communication modes are the singular functions and singular values of the appropriate propagation kernels. In particular, we show that optical fields of any state of coherence may be readily propagated through deterministic systems using the modal representation based on the system properties. The relation of the communication modes to the conventional coherent-mode representation is discussed, and expressions for the effective degree of coherence in the optical system are derived. The results are illustrated by numerical examples in optical near-field geometry.

Keyword
Coherent light; Light propagation; Modal analysis
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-10278 (URN)10.1364/JOSAA.24.003336 (DOI)000250682300048 ()2-s2.0-36949039170 (Scopus ID)
Note
QC 20100802Available from: 2009-04-29 Created: 2009-04-29 Last updated: 2017-12-13Bibliographically approved
5. Scanning optical near-field resolution analyzed in terms of communication modes
Open this publication in new window or tab >>Scanning optical near-field resolution analyzed in terms of communication modes
2006 (English)In: Optics Express, ISSN 1094-4087, E-ISSN 1094-4087, Vol. 14, no 23, 11392-11401 p.Article in journal (Refereed) Published
Abstract [en]

We present an analysis of scanning near-field optical microscopy in terms of the so-called communication modes using scalar wave theory. We show that the number of connected modes increases when the scanning distance is decreased, but the number of modes decreases when the size of the scanning aperture is decreased. In the limit of small detector aperture the best-connected mode reduces effectively to the Green function, evaluated at the center of the scanning aperture. We also suggest that the resolution of a scanning optical near-field imaging system is essentially given by the width of the lowest-order communication mode.

Keyword
microscope; freedom; limits; waves
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-10277 (URN)10.1364/OE.14.011392 (DOI)000242325400049 ()2-s2.0-33751117215 (Scopus ID)
Note
QC 20100802Available from: 2009-04-29 Created: 2009-04-29 Last updated: 2017-12-13Bibliographically approved
6. Communication modes applied to axicons
Open this publication in new window or tab >>Communication modes applied to axicons
2004 (English)In: Optics Express, ISSN 1094-4087, E-ISSN 1094-4087, Vol. 12, no 3, 377-383 p.Article in journal (Refereed) Published
Abstract [en]

The communication modes, which constitute a convenient method for the propagation and information analysis of optical fields, are formulated in the generalized axicon geometry. The transmitting region is the axicon’s annular aperture, and the observation domain is the optical axis containing the focal line segment. We show that in rotational symmetry one may employ the prolate spheroidal wave functions to represent the communication modes. Further, in usual circumstances the modes can be approximated by quadratic waves in the aperture domain and by sinc functions in the image domain. Both the exact communication modes and the approximate technique are confirmed numerically, with linear axicons as examples.

Keyword
spheroidal wave-functions; in-depth resolution; fourier-analysis; fresnel zone; beams; uncertainty; limits; fields; optics; range
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-10275 (URN)10.1364/OPEX.12.000377 (DOI)000188830500004 ()2-s2.0-2942726415 (Scopus ID)
Note
QC 20100802Available from: 2009-04-29 Created: 2009-04-29 Last updated: 2017-12-13Bibliographically approved
7. Communication modes in large-aperture approximation
Open this publication in new window or tab >>Communication modes in large-aperture approximation
2007 (English)In: Optics Letters, ISSN 0146-9592, E-ISSN 1539-4794, Vol. 32, no 6, 611-613 p.Article in journal (Refereed) Published
Abstract [en]

Simplified versions of the communication modes in the Fresnel domain are derived when the system apertures are large. The approximate modes, which are in the form of spherical waves and sinc functions with a spherical curvature, give physical insight into the communication modes approach and the basic limits of free-space optical communication systems. They also show that Gabor's information theory is readily derived from the communication modes.

Keyword
optics; limits; zone
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-10274 (URN)10.1364/OL.32.000611 (DOI)000244726900010 ()2-s2.0-33847611214 (Scopus ID)
Note
QC 20100802Available from: 2009-04-29 Created: 2009-04-29 Last updated: 2017-12-13Bibliographically approved
8. Communication modes in vector diffraction
Open this publication in new window or tab >>Communication modes in vector diffraction
2010 (English)In: Optik (Stuttgart), ISSN 0030-4026, E-ISSN 1618-1336, Vol. 121, no 22, 2087-2093 p.Article in journal (Refereed) Published
Abstract [en]

The communication modes, which mathematically correspond to singular value decomposition, have proven a useful concept in optical scalar-field diffraction, with applications in resolution studies, image synthesis, and wave propagation. For optical near-field geometries the communication modes have to be extended to electromagnetic field accounting for the polarization properties. In this paper we present the vector-valued communication modes method based on the rigorous electric-field diffraction integral. As a special case the transverse-electric scalar field modes are obtained. The intensity and polarization properties of the leading electromagnetic communication modes in near-field arrangements with rectangular apertures are discussed in terms of the Stokes parameters. For small separations between the transmitting and receiving apertures the fundamental mode possesses a ring-shaped hollow structure. The polarization properties of the near-field modes show features on spatial scales smaller than the wavelength of light. The system symmetries lead to degenerate communication modes.

Keyword
Wave optics, Diffraction, Propagation, Optical information, Near fields
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-30252 (URN)10.1016/j.ijleo.2009.07.016 (DOI)000285530000017 ()2-s2.0-78049329657 (Scopus ID)
Funder
Swedish Research Council
Note
QC 20110222Available from: 2011-02-22 Created: 2011-02-21 Last updated: 2017-12-11Bibliographically approved

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