Analysis of Electromagnetic Fields and Waves

Pregla, R.

doi:10.1002/9780470058503

Cited by 53 publications

(84 citation statements)

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“…These are algorithms with impedances/admittances (see e.g. Rogge and Pregla, 1993;Pregla, 2008) or with scattering parameters (e.g. Helfert and Pregla, 2002).…”

Section: S F Helfert: Left Eigenvectors 21mentioning

confidence: 99%

“…[More details can be found e.g. in Pregla, 2008]. Now, the fields are combined in vectors, and the operators Q, R becomes operator matrices that contain the approximations of the derivatives with finite differences and the material parameters.…”

Section: S F Helfert: Left Eigenvectors 21mentioning

confidence: 99%

“…Since the MoL is well documented in the literature we just mention some book chapters (Pregla and Pascher, 1989) (Pregla, 1995) and the book (Pregla, 2008), here. For threedimensional structures a two-dimensional discretization is required and the occurring matrices become very large.…”

Section: Introductionmentioning

confidence: 99%

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Efficient determination of the left-eigenvectors for the Method of Lines

Helfert

2015

Adv. Radio Sci.

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Abstract. The efficient determination of left eigenvectors in the method of lines (MoL) is described in this paper. The electromagnetic fields are expanded into eigenmodes and the eigenmodes are determined from an explicit matrix eigenvector problem. To study complicated structures with a moderate numerical effort, the analysis is done with a reduced set of these eigenmodes. The enforcements of the continuity of the transverse electric and magnetic fields at interfaces leads to expressions with rectangular matrices. Now left eigenvectors can be considered as inverse of these rectangular matrices. Until now, the left eigenvectors were determined from a second explicit eigenvalue problem. Here, it is shown how they can be determined with simple matrix products from previously determined right eigenvectors. This is done by utilizing the relation between the transverse electric and magnetic fields. The derived formulas hold for structures with Dirichlet, Neumann or periodic boundary conditions and the materials may be lossy. Open structures are modeled with perfectly matched layers (PML). To verify the expressions, various devices that contain such PMLs and lossy metals were studied. In all cases, error measures show that the algorithm derived in this paper works very well.

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“…These are algorithms with impedances/admittances (see e.g. Rogge and Pregla, 1993;Pregla, 2008) or with scattering parameters (e.g. Helfert and Pregla, 2002).…”

Section: S F Helfert: Left Eigenvectors 21mentioning

confidence: 99%

Section: S F Helfert: Left Eigenvectors 21mentioning

confidence: 99%

See 1 more Smart Citation

Efficient determination of the left-eigenvectors for the Method of Lines

Helfert

2015

Adv. Radio Sci.

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“…Details can be found e.g. in the book articles Pregla and Pascher, 1989;Pregla, 1995 or the book Pregla, 2008.…”

Section: Introductionmentioning

confidence: 99%

The Method of Lines in the time domain

Helfert

2013

Adv. Radio Sci.

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Abstract. The Method of Lines (MoL) is a semi-analytical numerical algorithm that has been used in the past to solve Maxwell's equations for waveguide problems. It is mainly used in the frequency domain. In this paper it is shown how the MoL can be used to solve initial value problems in the time domain. The required expressions are derived for onedimensional structures, where the materials may be dispersive. The algorithm is verified with numerical results for homogeneous structures, and for the concatenation of standard dielectric and left handed materials.

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“…Clearly, Δ Fn Δ Bn X n = (X n+1 -2X n + X n-1 )/a 2 . We may refer to this quantity as Δ n 2 X n , where Δ n 2 is a second-order This approach is clearly directly analogous to the well-established transmission-line matrix method [41,42], and related to the method of lines [43], which only uses discretization in one direction. Elimination of the currents I Xn and I Zn then yields the wave equation:…”

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confidence: 99%

Loss and thermal noise in plasmonic waveguides

Syms

Solymár

2014

Journal of Applied Physics

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Rytov's theory of thermally generated radiation is used to find the noise in twodimensional passive guides based on an arbitrary distribution of lossy isotropic dielectric.To simplify calculations, the Maxwell curl equations are approximated using difference equations that also permit a transmission-line analogy and material losses are assumed to be low enough for modal losses to be estimated using perturbation theory. It is shown that an effective medium representation of each mode is valid for both loss and noise, and hence that a one-dimensional model can be used to estimate the best achievable noise factor when a given mode is used in a communications link. This model only requires knowledge of the real and imaginary parts of the modal dielectric constant. The former can be found by solving the lossless eigenvalue problem, while the latter can be estimated using perturbation theory. Because of their high loss, the theory is most relevant to plasmonic waveguides, and its application is demonstrated using single interface, slab and slot guide examples. The best noise performance is offered by the long-range plasmon supported by the slab guide. KEYWORDS:Dielectric waveguide, Plasmonic waveguide, Amplification using a dye has also been proposed to compensate for losses [20,21].Communication systems also suffer from noise. In fibre optics, propagation loss is so low that the focus is on amplified spontaneous emission in amplifiers [22][23][24] Rytov's methods are hard to apply to general geometries. Spurred by the development of metamaterials, for which an equivalent circuit model is realistic, we have developed a transmission line approach to one-dimensional (1D) thermal noise, which involves replacement of differentials with discrete equivalents [35]. The problem of integrating the effect of noise sources is then replaced with summation. Analytic proofs -that noise is linked to effective medium properties -may then be arrived at easily. Emission and related metrics such as the noise factor may be computed directly, and additional effects such as noise carried by internal lattice waves may also be incorporated [36].Here, we adapt the method to more general 2D guides. Once again, we use difference equations that allow a transmission-line analogy. To simplify calculations, losses are assumed to be low, so perturbation theory can be used. Because most dielectric guides have low loss and TEM-like modes, there are few literature discussions of loss or polarization effects. An exception is the difference between TE and TM mode gain in semiconductor lasers [37,38]. However, losses are much higher in plasmonics, and polarization is crucial. Here both polarizations are considered together. The aim is to prove that modal noise is directly linked to modal effective medium properties, and hence that noise can be computed directly in a 1D calculation. If this can be done, thermal noise may easily be incorporated into transmission line models of plasmonics [39], or network models of amplification [40]. The wave equat...

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Analysis of Electromagnetic Fields and Waves

Cited by 53 publications

References 0 publications

Efficient determination of the left-eigenvectors for the Method of Lines

Efficient determination of the left-eigenvectors for the Method of Lines

The Method of Lines in the time domain

Loss and thermal noise in plasmonic waveguides

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