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Nonradiating and minimum energy sources and their fields: Generalized source inversion theory and applications
 IEEE Trans. Antennas Propagat
, 2000
"... Abstract—A new general framework for characterizing scalar and electromagnetic (EM) nonradiating (NR) and minimum energy (ME) sources and their fields is developed that is of interest for both radiation and source reconstruction problems. NR sources are characterized in connection with the concept o ..."
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Cited by 15 (6 self)
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Abstract—A new general framework for characterizing scalar and electromagnetic (EM) nonradiating (NR) and minimum energy (ME) sources and their fields is developed that is of interest for both radiation and source reconstruction problems. NR sources are characterized in connection with the concept of reciprocity as nonreceptors. Localized ME sources are shown to be free fields truncated within the source’s support. A new source analysis tool is developed that is based on the decomposition of a source and its field into their radiating and NR components. The individual radiating and reactive energy roles of the radiating and NR parts of a source are characterized. The general theory is illustrated with a timeharmonic EM example. Index Terms—Inverse problems.
Inverse source problem with reactive power constraint
 IEEE TRANS. ANTENNAS PROPAGAT
, 2004
"... This paper reports a general Lagrangian formulation for constrained electromagnetic inverse source problems. The formulation is applicable to different forms of inverse source problems having different constraints. Two possibilities are emphasized in the paper. One yields the usual minimum energy s ..."
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Cited by 14 (9 self)
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This paper reports a general Lagrangian formulation for constrained electromagnetic inverse source problems. The formulation is applicable to different forms of inverse source problems having different constraints. Two possibilities are emphasized in the paper. One yields the usual minimum energy solution. The other establishes a new minimum energy solution with the additional constraint that the source has a prescribed reactive power (which can be zero). The latter solution incorporates the important reactive energy issues of an antenna which had not been considered before in the context of the inverse source problem. The new solution is shown to obey a homogeneous wave equation in the interior of the source volume, and expressions for the associated interior field and interaction power are also derived. The derived theory is illustrated for a canonical dipolar source and an alternative approach where the reactive power is minimized for a prescribed maximum functional energy is also presented. Advantage is taken of some of the results to briefly discuss some questions about fundamental antenna limits.
Inverse source problem in nonhomogeneous background media
 SIAM J. Appl. Math
"... The scalar wave inverse source problem (ISP) is investigated for the case where the source is embedded in a nonhomogeneous medium with known index of refraction proÞle n(r). It is shown that the solution to the ISP having minimum energy (socalled minimum energy source) can be obtained via a simple ..."
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Cited by 6 (3 self)
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The scalar wave inverse source problem (ISP) is investigated for the case where the source is embedded in a nonhomogeneous medium with known index of refraction proÞle n(r). It is shown that the solution to the ISP having minimum energy (socalled minimum energy source) can be obtained via a simple method of constrained optimization. This method is applied to the special case when the nonhomogeneous background is spherically symmetric (n(r) = n(r)) and yields the minimum energy source in terms of a series of spherical harmonics and radial wave functions that are solutions to a SturmLiouville problem. The special case of a source embedded in a spherical region of constant index that differs from the background is treated in detail and results from computer simulations are presented for this case. 1
Inverse source problem in an oblate spheroidal geometry
 IEEE Trans. Antennas Propagat
, 2006
"... The canonical inverse source problem of reconstructing an unknown source whose region of support is describable as a spheroidal (oblate or prolate) volume from knowledge of the farfield radiation pattern it generates is formulated and solved within the framework of the inhomogeneous scalar Helmholt ..."
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Cited by 6 (3 self)
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The canonical inverse source problem of reconstructing an unknown source whose region of support is describable as a spheroidal (oblate or prolate) volume from knowledge of the farfield radiation pattern it generates is formulated and solved within the framework of the inhomogeneous scalar Helmholtz equation via a linear inversion framework in Hilbert spaces. Particular attention is paid to the analysis and computer illustration of flat, aperturelike sources whose support is approximated by an oblate spheroidal volume. Key words: Inverse source problem, minimum energy source, nonradiating source, spheroidal wave. 1 1
Inverse source problem and minimum energy sources
 J. Opt. Soc. Am. A
, 2000
"... We present a new linear inversion formalism for the scalar inverse source problem in threedimensional and onedimensional (1D) spaces, from which a number of previously unknown results on minimumenergy (ME) sources and their fields readily follow. ME sources, of specified support, are shown to obe ..."
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Cited by 4 (3 self)
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We present a new linear inversion formalism for the scalar inverse source problem in threedimensional and onedimensional (1D) spaces, from which a number of previously unknown results on minimumenergy (ME) sources and their fields readily follow. ME sources, of specified support, are shown to obey a homogeneous Helmholtz equation in the interior of that support. As a consequence of that result, the fields produced by ME sources are shown to obey an iterated homogeneous Helmholtz equation. By solving the latter equation, we arrive at a new Greenfunction representation of the field produced by a ME source. It is also shown that any squareintegrable (L 2), compactly supported source that possesses a continuous normal derivative on the boundary of its support must possess a nonradiating (NR) component. A procedure based on our results on the inverse source problem and ME sources is described to uniquely decompose an L2 source of specified support and its field into the sum of a radiating and a NR part. The general theory that is developed is illustrated for the special cases of a homogeneous source in 1D space and a spherically symmetric source. © 2000 Optical
New aspects of electromagnetic information theory for wireless and antenna systems
 IEEE Trans. Antennas Propag
, 2008
"... Abstract—This paper investigates informationtheoretic characterization, via Shannon’s information capacity and number of degrees of freedom, of wave radiation (antenna) and wireless propagation systems. Specifically, the paper derives, from the fundamental physical point of view of Maxwell’s equati ..."
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Cited by 3 (0 self)
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Abstract—This paper investigates informationtheoretic characterization, via Shannon’s information capacity and number of degrees of freedom, of wave radiation (antenna) and wireless propagation systems. Specifically, the paper derives, from the fundamental physical point of view of Maxwell’s equations describing electromagnetic fields, the Shannon information capacity of spacetime wireless channels formed by electromagnetic sources and receivers in a known background medium. The theory is developed first for the case of sources working at a fixed frequency (timeharmonic case) and is expanded later to the more general case of temporally bandlimited systems (timedomain fields). In the bandlimited case we consider separately the two cases of timelimited and essentially bandlimited systems and of purely bandlimited systems. The developments take into account the physical radiated power constraint in addition to a constraint in the source L 2 norm which acts to avoid antenna superdirectivity. Based on such radiated power and current L 2 norm constraints we derive the Shannon information capacity of canonical wireless and antenna systems in free space, for a given additive Gaussian noise level, as well as an associated number of degrees of freedom resulting from such capacity calculations. The derived results also illustrate, from a new informationtheoretic point of view, the transition from near to far fields. Index Terms—Antenna, degrees of freedom, electromagnetic information, information capacity, wave information, wireless. I.
SOURCE SYNTHESIS IN SUBSTRATE MEDIA: FUNDAMENTAL BOUNDS
"... Abstract: A mathematical inverse source theory in substrate media is derived, with applications to analysis, sourcesynthesis and characterization of antennas embedded in substrates. The developed theory, which is based on optimization theory, and the associated computer illustrations, shed basic un ..."
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Cited by 2 (2 self)
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Abstract: A mathematical inverse source theory in substrate media is derived, with applications to analysis, sourcesynthesis and characterization of antennas embedded in substrates. The developed theory, which is based on optimization theory, and the associated computer illustrations, shed basic understanding, from first principles, of radiation enhancements due to substrates, such as reduction of required physical resources (size, current level, tuning to resonance, and so on) for the launching of given fields. The derived results are fundamental, in particular, deviceindependent, and thus constitute a formal benchmark, clarifying fundamental bounds in performance with given resources, or in the minimal resources for given performance, in the context of antennaembedding media.
Transformation formulas for spherical and spheroidal multipole fields
 Int. J. Electron. Commun. (AE Ü
, 2007
"... A transformation linking spherical multipole fields with generalized spheroidal multipole fields is derived. Applications including the inverse diffraction problem for sphericallyscanned near field data for sources that due to conformal considerations are efficiently described using spheroidal (eit ..."
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Cited by 1 (1 self)
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A transformation linking spherical multipole fields with generalized spheroidal multipole fields is derived. Applications including the inverse diffraction problem for sphericallyscanned near field data for sources that due to conformal considerations are efficiently described using spheroidal (either oblate or prolate) volume support regions are discussed with the aid of numerical illustrations. Keywords: spherical multipole fields, spheroidal multipole fields, field transformation, near field scanning. 1
AN INVERSE RANDOM SOURCE PROBLEM FOR THE HELMHOLTZ EQUATION
"... Abstract. This paper is concerned with an inverse random source problem for the onedimensional stochastic Helmholtz equation, which is to reconstruct the statistical properties of the random source function from boundary measurements of the radiating random electric field. Although the emphasis of ..."
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Abstract. This paper is concerned with an inverse random source problem for the onedimensional stochastic Helmholtz equation, which is to reconstruct the statistical properties of the random source function from boundary measurements of the radiating random electric field. Although the emphasis of the paper is on the inverse problem, we adapt a computationally more efficient approach to study the solution of the direct problem in the context of the scattering model. Specifically, the direct model problem is equivalently formulated into a twopoint spatially stochastic boundary value problem, for which the existence and uniqueness of the pathwise solution is proved. In particular, an explicit formula is deduced for the solution from an integral representation by solving the twopoint boundary value problem. Based on this formula, a novel and efficient strategy, which is entirely done by using the fast Fourier transform, is proposed to reconstruct the mean and the variance of the random source function from measurements at one boundary point, where the measurements are assumed to be available for many realizations of the source term. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed method. 1.
Measurements for Antenna NearField Imaging Problems
, 2016
"... Citation for published version (APA): Nordebo, S., & Gustafsson, M. (2006). On the design of optimal measurements for antenna nearfield imaging problems. (Technical Report LUTEDX/(TEAT7142)/117/(2006); Vol. TEAT7142). [Publisher information missing]. General rights Copyright and moral right ..."
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Citation for published version (APA): Nordebo, S., & Gustafsson, M. (2006). On the design of optimal measurements for antenna nearfield imaging problems. (Technical Report LUTEDX/(TEAT7142)/117/(2006); Vol. TEAT7142). [Publisher information missing]. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profitmaking activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.