Computing zeros of analytic functions in the complex plane without using derivatives

Gillan, Charles J.; Schuchinsky, Alexander; Spence, Ivor

doi:10.1016/j.cpc.2006.04.007

Cited by 24 publications

(22 citation statements)

References 17 publications

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“…As mentioned in Section 2, this was achieved by formulating the problem for the bounded structure containing the parallel-plate waveguide enclosure. While this model preserves all the spectral features of the eigenwaves guided by the layered structure, the DE (5) is amenable to the solution and verification by using the rigorous numerical-analytical method described in [11].…”

Section: Numerical Solution Of the Dispersion Equationmentioning

confidence: 99%

Nonreciprocal magnetoplasmons in imperfect layered structures

Schuchinsky

Yan

2008

Metamaterials III

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Nonreciprocal properties of magnetoplasmons in the imperfect magnetised semiconductor films sandwiched between the dielectric layers have been explored. It is demonstrated that losses qualitatively alter the eigenwave spectrum and the properties of magnetoplasmons. The effect of the structure parameters is analysed, and it is shown that strongly nonreciprocal attenuation of the eigenmodes in asymmetric structures may result in the unidirectional propagation of magnetoplasmonic modes. The competing effects of the reciprocal and nonreciprocal field displacement, and the impact of the field and power flux distributions on the mechanisms of nonreciprocal and unidirectional magnetoplasmon propagation in the imperfect semiconductor films are discussed.

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Section: Numerical Solution Of the Dispersion Equationmentioning

confidence: 99%

Nonreciprocal magnetoplasmons in imperfect layered structures

Schuchinsky

Yan

2008

Metamaterials III

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“…For these contours a discretized form of Cauchy's Argument Principle (CAP) is applied, in order to verify the existence of roots or poles in the candidate regions. The Discretized Cauchy's Argument Principle (DCAP) does not require the derivative of the function and integration over the contour, as it is presented in [25], [26] and [27]. In the proposed approach a minimal number of the function samples is utilized for DCAP (sometimes only four) and the contour shape is determined by the mesh geometry.…”

Section: Introductionmentioning

confidence: 99%

Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis for Propagation and Radiation Problems

Kowalczyk

2018

IEEE Trans. Antennas Propagat.

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A flexible and effective algorithm for complex roots and poles finding is presented. A wide class of analytic functions can be analyzed, and any arbitrarily shaped search region can be considered. The method is very simple and intuitive. It is based on sampling a function at the nodes of a regular mesh, and on the analysis of the function phase. As a result, a set of candidate regions is created and then the roots/poles are verified using a discretized Cauchy's argument principle. The accuracy of the results can be improved by the application of a self-adaptive mesh. The effectiveness of the presented technique is supported by numerical tests involving different types of structures, where electromagnetic waves are guided and radiated. The results are verified, and the computational efficiency of the method is examined.Index Terms-Complex roots finding algorithm, complex modes, propagation, radiation corresponds to mesh resolution ∆r = 0.15 and, obviously, any higher resolution leads to the same results -twelve single roots: z (1) = −0.096642302459942 − 0.062923397455697i, z (2) = −0.096642302459942 + 0.062923397455697i, z (3) = 0.096642302459942 − 0.062923397455697i, z (4) = 0.096642302459942 + 0.062923397455696i, z (5) = −0.444429043110023 + 0.000000000000000i, z (6) = 0.444429043110023 − 0.000000000000000i, z (7) = −0.703772250217811 + 0.000000000000000i, z (8) = 0.703772250217811 − 0.000000000000000i, z (9) = −0.775021522202022 + 0.000000000000000i, z (10) = 0.775021522202023 − 0.000000000000000i, z (11) = −0.856115203911565 + 0.000000000000000i, z (12) = 0.856115203911564 − 0.000000000000000i and two second order poles: z (13) = 0.000000000000000 + 0.100000000000000i, z (14) = 0.000000000000000 − 0.100000000000000i. The parameters and results of the analysis for various accuracy δ are collected in Table I and in Figure 3.Similar discrete algorithm [22] requires 721 samples (corresponds to ∆r = 0.06) for the initial mesh and this number

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“…Nevertheless for certain classes of analytical functions, their roots can be reliably calculated with the aid of the principle of argument combined with the gradient methods [26], [27]. Since the DE (2) for the bounded layered structure can be cast in the form of an analytical function, the latter approach has been adopted here for the analysis of eigenwaves in layered structure of Fig.…”

Section: Full-wave Analysis Of Eigenmodes In Lossy Semiconductor-dielmentioning

confidence: 99%

Surface plasmons in layered structures with semiconductor and metallic films

Schuchinsky

Yan

2009

Eur. Phys. J. Appl. Phys.

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The complete spectrum of eigenwaves including surface plasmon polaritons (SPP), dynamic (bulk) and complex waves in the layered structures containing semiconductor and metallic films has been explored. The effects of loss, geometry and the parameters of dielectric layers on the eigenmode spectrum and, particularly, on the SPP modes have been analysed using both the asymptotic and rigorous numerical solutions of the full-wave dispersion equation. The field and Poynting vector distributions have been examined to identify the modes and elucidate their properties. It has been shown that losses and dispersion of permittivity qualitatively alter the spectral content and the eigenwave properties. The SPP counter-directional power fluxes in the film and surrounding dielectrics have been attributed to vortices of power flow, which are responsible for the distinctive features of SPP modes. It has been demonstrated for the first time that the maximal attainable slow-wave factor of the SPP modes guided by thin Au films at optical frequencies is capped not by losses but the frequency dispersion of the actual Au permittivity.

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Computing zeros of analytic functions in the complex plane without using derivatives

Cited by 24 publications

References 17 publications

Nonreciprocal magnetoplasmons in imperfect layered structures

Nonreciprocal magnetoplasmons in imperfect layered structures

Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis for Propagation and Radiation Problems

Surface plasmons in layered structures with semiconductor and metallic films

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