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Ivanenko, Y., Nedic, M., Gustafsson, M., Jonsson, B. L., Luger, A. & Nordebo, S. (2020). Quasi-Herglotz functions and convex optimization. Royal Society Open Science, 7(1), 1-15, Article ID 191541.
Open this publication in new window or tab >>Quasi-Herglotz functions and convex optimization
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2020 (English)In: Royal Society Open Science, E-ISSN 2054-5703, Vol. 7, no 1, p. 1-15, article id 191541Article in journal (Refereed) Published
Abstract [en]

We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modelling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.

Place, publisher, year, edition, pages
The Royal Society Publishing, 2020
Keywords
quasi-Herglotz functions, non-passive systems, approximation, convex optimization, sum rules
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering Other Mathematics
Research subject
Physics, Waves and Signals
Identifiers
urn:nbn:se:lnu:diva-90928 (URN)10.1098/rsos.191541 (DOI)000507305300001 ()
Funder
Swedish Foundation for Strategic Research , AM13-0011
Available from: 2020-01-15 Created: 2020-01-15 Last updated: 2020-02-04Bibliographically approved
Dalarsson, M. & Nordebo, S. (2020). TE-wave propagation in graded waveguide structures. OSA Continuum, 3(1), 67-76
Open this publication in new window or tab >>TE-wave propagation in graded waveguide structures
2020 (English)In: OSA Continuum, E-ISSN 2578-7519, Vol. 3, no 1, p. 67-76Article in journal (Refereed) Published
Abstract [en]

We investigate TE-wave propagation in a hollow waveguide with a graded dielectric layer, described using a hyperbolic tangent function. General formulae for the electric field components of the TE-waves, applicable to hollow waveguides with arbitrary cross sectional shapes, are presented. We illustrate the exact analytical results for the electric field components in the special case of a rectangular waveguide. Furthermore, we derive exact analytical results for the reflection and transmission coefficients valid for waveguides of arbitrary cross sectional shapes. Finally, we show that the obtained reflection and transmission coefficients are in exact asymptotic agreement with those obtained for a very thin homogeneous dielectric layer using mode-matching and cascading. The proposed method gives analytical results that are directly applicable without the need of mode-matching, and it has the ability to model realistic, smooth transitions. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Place, publisher, year, edition, pages
Optical Society of America, 2020
National Category
Physical Sciences
Research subject
Natural Science, Physics
Identifiers
urn:nbn:se:lnu:diva-92300 (URN)10.1364/OSAC.379847 (DOI)000507977200008 ()
Available from: 2020-02-21 Created: 2020-02-21 Last updated: 2020-02-21Bibliographically approved
Shiraz, A., Khodadad, D., Nordebo, S., Yerworth, R., Frerichs, I., van Kaam, A., . . . Demosthenous, A. (2019). Compressive sensing in electrical impedance tomography for breathing monitoring. Physiological Measurement, 40(3), 1-9, Article ID 034010.
Open this publication in new window or tab >>Compressive sensing in electrical impedance tomography for breathing monitoring
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2019 (English)In: Physiological Measurement, ISSN 0967-3334, E-ISSN 1361-6579, Vol. 40, no 3, p. 1-9, article id 034010Article in journal (Refereed) Published
Abstract [en]

Objective: Electrical impedance tomography (EIT) is a functional imaging technique in which cross-sectional images of structures are reconstructed based on boundary trans-impedance measurements. Continuous functional thorax monitoring using EIT has been extensively researched. Increasing the number of electrodes, number of planes and frame rate may improve clinical decision making. Thus, a limiting factor in high temporal resolution, 3D and fast EIT is the handling of the volume of raw impedance data produced for transmission and its subsequent storage. Owing to the periodicity (i.e. sparsity in frequency domain) of breathing and other physiological variations that may be reflected in EIT boundary measurements, data dimensionality may be reduced efficiently at the time of sampling using compressed sensing techniques. This way, a fewer number of samples may be taken. Approach: Measurements using a 32-electrode, 48-frames-per-second EIT system from 30 neonates were post-processed to simulate random demodulation acquisition method on 2000 frames (each consisting of 544 measurements) for compression ratios (CRs) ranging from 2 to 100. Sparse reconstruction was performed by solving the basis pursuit problem using SPGL1 package. The global impedance data (i.e. sum of all 544 measurements in each frame) was used in the subsequent studies. The signal to noise ratio (SNR) for the entire frequency band (0 Hz-24 Hz) and three local frequency bands were analysed. A breath detection algorithm was applied to traces and the subsequent errorrates were calculated while considering the outcome of the algorithm applied to a down-sampled and linearly interpolated version of the traces as the baseline. Main results: SNR degradation was generally proportional with CR. The mean degradation for 0 Hz-8 Hz (of interest for the target physiological variations) was below similar to 15 dB for all CRs. The error-rates in the outcome of the breath detection algorithm in the case of decompressed traces were lower than those associated with the corresponding down-sampled traces for CR >= 25, corresponding to sub-Nyquist rate for breathing frequency. For instance, the mean error-rate associated with CR = 50 was similar to 60% lower than that of the corresponding down-sampled traces. Significance: To the best of our knowledge, no other study has evaluated the applicability of compressive sensing techniques on raw boundary impedance data in EIT. While further research should be directed at optimising the acquisition and decompression techniques for this application, this contribution serves as the baseline for future efforts.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2019
Keywords
breath detection, compressive sensing, electrical impedance tomography
National Category
Computer and Information Sciences Other Medical Sciences not elsewhere specified
Research subject
Computer and Information Sciences Computer Science, Computer Science
Identifiers
urn:nbn:se:lnu:diva-82046 (URN)10.1088/1361-6579/ab0daa (DOI)000463392300006 ()30844770 (PubMedID)2-s2.0-85064239164 (Scopus ID)
Available from: 2019-04-23 Created: 2019-04-23 Last updated: 2019-08-29Bibliographically approved
Ivanenko, Y. & Nordebo, S. (2019). Non-passive approximation as a tool to study the realizability of amplifying media. In: International symposium on electromagnetic theory (EMT2019): May 27-31, 2019, San Diego, CA, USA. Paper presented at URSI EM Theory Symposium, EMTS 2019, San Diego, CA, 27–31 May 2019. IEEE Press
Open this publication in new window or tab >>Non-passive approximation as a tool to study the realizability of amplifying media
2019 (English)In: International symposium on electromagnetic theory (EMT2019): May 27-31, 2019, San Diego, CA, USA, IEEE Press, 2019Conference paper, Published paper (Refereed)
Abstract [en]

Non-passive approximation is presented as a tool to study the realizability of amplifying media. As an interesting physical example, we derive first a suitable approximation of the plasmonic singularity of a dielectric sphere with respect to a hypothetical amplifying background medium. A non-passive approximation based on convex optimization is then employed to investigate the necessary bandwidth requirements to achieve the approximate pole singularity.

Place, publisher, year, edition, pages
IEEE Press, 2019
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering Other Mathematics
Research subject
Physics, Waves and Signals
Identifiers
urn:nbn:se:lnu:diva-90222 (URN)10.23919/URSI-EMTS.2019.8931480 (DOI)978-1-946815-06-4 (ISBN)978-1-5386-5593-1 (ISBN)
Conference
URSI EM Theory Symposium, EMTS 2019, San Diego, CA, 27–31 May 2019
Funder
Swedish Foundation for Strategic Research , AM13-0011
Available from: 2019-11-21 Created: 2019-11-21 Last updated: 2020-03-09Bibliographically approved
Nordebo, S., Mirmoosa, M. & Tretyakov, S. (2019). On the quasistatic optimal plasmonic resonances in lossy media. Journal of Applied Physics, 125(10), 1-11, Article ID 103105.
Open this publication in new window or tab >>On the quasistatic optimal plasmonic resonances in lossy media
2019 (English)In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 125, no 10, p. 1-11, article id 103105Article in journal (Refereed) Published
Abstract [en]

This paper discusses and analyzes the quasistatic optimal plasmonic dipole resonance of a small dielectric particle embedded in a lossy surrounding medium. The optimal resonance at any given frequency is defined by the complex valued dielectric constant that maximizes the absorption of the particle under the quasistatic approximation and a passivity constraint. In particular, for an ellipsoid aligned along the exciting field, the optimal material property is given by the complex conjugate of the pole position associated with the polarizability of the particle. In this paper, we employ the classical Mie theory to analyze this approximation for spherical particles in a lossy surrounding medium. It turns out that the quasistatic optimal plasmonic resonance is valid, provided that the electrical size of the particle is sufficiently small at the same time as the external losses are sufficiently large. Hence, it is important to note that this approximation cannot be used for a lossless medium, and which is also obvious, since the quasistatic optimal dipole absorption becomes unbounded for this case. Moreover, it turns out that the optimal normalized absorption cross sectional area of the small dielectric sphere has a very subtle limiting behavior and is, in fact, unbounded even in full dynamics when both the electrical size and the exterior losses tend to zero at the same time. A detailed analysis is carried out to assess the validity of the quasistatic estimation of the optimal resonance, and numerical examples are included to illustrate the asymptotic results.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2019
National Category
Condensed Matter Physics
Research subject
Physics, Condensed Matter Physics
Identifiers
urn:nbn:se:lnu:diva-81700 (URN)10.1063/1.5085721 (DOI)000461370200005 ()2-s2.0-85062904957 (Scopus ID)
Available from: 2019-04-05 Created: 2019-04-05 Last updated: 2019-08-29Bibliographically approved
Ivanenko, Y., Gustafsson, M. & Nordebo, S. (2019). Optical theorems and physical bounds on absorption in lossy media. Optics Express, 27(23), 34323-34342
Open this publication in new window or tab >>Optical theorems and physical bounds on absorption in lossy media
2019 (English)In: Optics Express, ISSN 1094-4087, E-ISSN 1094-4087, Vol. 27, no 23, p. 34323-34342Article in journal (Refereed) Published
Abstract [en]

Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary optimization techniques. The first version is formulated in terms of polarization currents (or equivalent currents) inside the scatterer and generalizes previous results given for a lossless medium. The corresponding bound is referred to here as a variational bound and is valid for an arbitrary geometry with a given material property. The second version is formulated in terms of the T-matrix parameters of an arbitrary linear scatterer circumscribed by a spherical volume and gives a new fundamental upper bound on the total absorption of an inclusion with an arbitrary material property (including general bianisotropic materials). The two bounds are fundamentally different as they are based on different assumptions regarding the structure and the material property. Numerical examples including homogeneous and layered (core-shell) spheres are given to demonstrate that the two bounds provide complimentary information in a given scattering problem.

Place, publisher, year, edition, pages
Optical Society of America, 2019
Keywords
Material properties; Mie theory; Photon counting; Radiative transfer; Refractive index; Scattering
National Category
Other Physics Topics
Research subject
Physics, Waves and Signals
Identifiers
urn:nbn:se:lnu:diva-89962 (URN)10.1364/OE.27.034323 (DOI)000495871300120 ()
Funder
Swedish Foundation for Strategic Research , AM13-0011
Available from: 2019-11-08 Created: 2019-11-08 Last updated: 2019-12-17Bibliographically approved
Nordebo, S., Kristensson, G., Mirmoosa, M. & Tretyakov, S. (2019). Optimal plasmonic multipole resonances of a sphere in lossy media. Physical Review B, 99(5), Article ID 054301.
Open this publication in new window or tab >>Optimal plasmonic multipole resonances of a sphere in lossy media
2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 5, article id 054301Article in journal (Refereed) Published
Abstract [en]

Fundamental upper bounds are given for the plasmonic multipole absorption and scattering of a rotationally invariant dielectric sphere embedded in a lossy surrounding medium. A specialized Mie theory is developed for this purpose and when combined with the corresponding generalized optical theorem, an optimization problem is obtained which is explicitly solved by straightforward analysis. In particular, the absorption cross section is a concave quadratic form in the related Mie (scattering) parameters and the convex scattering cross section can be maximized by using a Lagrange multiplier constraining the absorption to be non-negative. For the homogeneous sphere, the Weierstrass preparation theorem is used to establish the existence and the uniqueness of the plasmonic singularities and explicit asymptotic expressions are given for the dipole and the quadrupole. It is shown that the optimal passive material for multipole absorption and scattering of a small homogeneous dielectric sphere embedded in a dispersive medium is given approximately as the complex conjugate and the real part of the corresponding pole positions, respectively. Numerical examples are given to illustrate the theory, including a comparison with the plasmonic dipole and quadrupole resonances obtained in gold, silver, and aluminum nanospheres based on some specific Brendel-Bormann (BB) dielectric models for these metals. Based on these BB models, it is interesting to note that the metal spheres can be tuned to optimal absorption at a particular size at a particular frequency.

Place, publisher, year, edition, pages
American Physical Society, 2019
National Category
Condensed Matter Physics
Research subject
Physics, Condensed Matter Physics
Identifiers
urn:nbn:se:lnu:diva-80776 (URN)10.1103/PhysRevB.99.054301 (DOI)000457729700001 ()2-s2.0-85061347599 (Scopus ID)
Available from: 2019-02-22 Created: 2019-02-22 Last updated: 2019-08-29Bibliographically approved
Ivanenko, Y., Gustafsson, M., Jonsson, B. L., Luger, A., Nilsson, B., Nordebo, S. & Toft, J. (2019). Passive Approximation and Optimization Using B-Splines. SIAM Journal on Applied Mathematics, 79(1), 436-458
Open this publication in new window or tab >>Passive Approximation and Optimization Using B-Splines
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2019 (English)In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 79, no 1, p. 436-458Article in journal (Refereed) Published
Abstract [en]

A passive approximation problem is formulated where the target function is an arbitrary complex-valued continuous function defined on an approximation domain consisting of a finite union of closed and bounded intervals on the real axis. The norm used is a weighted L-p-norm where 1 <= p <= infinity. The approximating functions are Herglotz functions generated by a measure with Holder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are Holder continuous functions given by the density of the measure and its Hilbert transform, respectively. In practice, it is useful to employ finite B-spline expansions to represent the generating measure. The corresponding approximation problem can then be posed as a finite-dimensional convex optimization problem which is amenable for numerical solution. A constructive proof is given here showing that the convex cone of approximating functions generated by finite uniform B-spline expansions of fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in the convex cone of Herglotz functions which are locally Holder continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, typical physical application examples are included regarding the passive approximation and optimization of a linear system having metamaterial characteristics, as well as passive realization of optimal absorption of a dielectric small sphere over a finite bandwidth.

Keywords
approximation, Herglotz functions, B-splines, passive systems, convex optimization, sum rules
National Category
Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-81228 (URN)10.1137/17M1161026 (DOI)000460127100021 ()2-s2.0-85063407473 (Scopus ID)
Available from: 2019-03-22 Created: 2019-03-22 Last updated: 2020-03-24Bibliographically approved
Ivanenko, Y. & Nordebo, S. (2019). Passive Approximation with High-Order B-Splines. In: Karl‐Olof Lindahl, Torsten Lindström, Luigi G. Rodino, Joachim Toft, Patrik Wahlberg (Ed.), Analysis, Probability, Applications, and Computation: . Paper presented at 11th ISAAC Congress, Växjö (Sweden) 2017 (pp. 83-94). Birkhäuser Verlag
Open this publication in new window or tab >>Passive Approximation with High-Order B-Splines
2019 (English)In: Analysis, Probability, Applications, and Computation / [ed] Karl‐Olof Lindahl, Torsten Lindström, Luigi G. Rodino, Joachim Toft, Patrik Wahlberg, Birkhäuser Verlag, 2019, p. 83-94Conference paper, Published paper (Refereed)
Abstract [en]

Convex optimization has emerged as a well-suited tool for passive approximation. Here, it is desired to approximate some pre-defined non-trivial system response over a given finite frequency band by using a passive system. This paper summarizes some explicit results concerning the Hilbert transform of general B-splines of arbitrary order and arbitrary partitions that can be useful with the convex optimization formulation. A numerical example in power engineering is included concerning the identification of some model parameters based on measurements on high-voltage insulation materials.

Place, publisher, year, edition, pages
Birkhäuser Verlag, 2019
Series
Trends in Mathematics, ISSN 2297-0215, E-ISSN 2297-024X
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82770 (URN)10.1007/978-3-030-04459-6_8 (DOI)2-s2.0-85065446429 (Scopus ID)978-3-030-04458-9 (ISBN)978-3-030-04459-6 (ISBN)
Conference
11th ISAAC Congress, Växjö (Sweden) 2017
Available from: 2019-05-27 Created: 2019-05-27 Last updated: 2019-11-21Bibliographically approved
Nordebo, S., Dalarsson, M., Khodadad, D., Müller, B., Waldermann, A. D., Becher, T., . . . Bayford, R. (2018). A parametric model for the changes in the complex valued conductivity of a lung during tidal breathing. Journal of Physics D: Applied Physics, 51(20), Article ID 205401.
Open this publication in new window or tab >>A parametric model for the changes in the complex valued conductivity of a lung during tidal breathing
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2018 (English)In: Journal of Physics D: Applied Physics, ISSN 0022-3727, E-ISSN 1361-6463, Vol. 51, no 20, article id 205401Article in journal (Refereed) Published
Abstract [en]

Classical homogenization theory based on the Hashin–Shtrikman coated ellipsoids is used to model the changes in the complex valued conductivity (or admittivity) of a lung during tidal breathing. Here, the lung is modeled as a two-phase composite material where the alveolar air-filling corresponds to the inclusion phase. The theory predicts a linear relationship between the real and the imaginary parts of the change in the complex valued conductivity of a lung during tidal breathing, and where the loss cotangent of the change is approximately the same as of the effective background conductivity and hence easy to estimate. The theory is illustrated with numerical examples based on realistic parameter values and frequency ranges used with electrical impedance tomography (EIT). The theory may be potentially useful for imaging and clinical evaluations in connection with lung EIT for respiratory management and control.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2018
National Category
Medical Image Processing
Research subject
Natural Science, Medicine
Identifiers
urn:nbn:se:lnu:diva-74401 (URN)10.1088/1361-6463/aabc04 (DOI)
Available from: 2018-05-18 Created: 2018-05-18 Last updated: 2019-07-09Bibliographically approved
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ORCID iD: ORCID iD iconorcid.org/0000-0002-7018-6248

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