Numerically Stable and Reliable Computation of Electromagnetic Modes in Multilayered Waveguides Using the Cauchy Integration Method With Automatic Differentiation

2018 ◽  
Vol 66 (9) ◽  
pp. 3981-3992 ◽  
Author(s):  
Krzysztof A. Michalski ◽  
Mazin M. Mustafa
Author(s):  
K. A. Michalski ◽  
M. M. Mustafa

A reliable method is presented for the computation of the propagation constants and the corresponding hybrid modal fields in multilayered planar dielectric stacks comprising multiple anisotropic conducting sheets. The appropriate dispersion functions (DFs) are formulated and evaluated using a numerically stable scattering matrix methodology. The roots of the DFs are computed by the Cauchy integration method with automatic differentiation of the DF.


The analysis of integration of the legal systems of states in the American region is held. In the Southern subregion, a combination of integration and disintegration in cooperation of states led to the creation of two integration entities – MERCOSUR and the Andean Community (AC), in the Northern subregion – NAFTA. The author concludes that the convergence on the American continent, especially using the integration method, helped to implement a special scenario in the southern part of this continent – the meta-integration scenario, with the creation of the Union of South American Nations, uniting the Andean Community and MERCOSUR – something resembling a European one, but at the same time different from it. UNASUR is an effective mechanism for bringing together and integrating the states of the South American continent. Within this Union with notable leadership of Brazil and Argentina the first steps in the direction of the foreign policy integration of the member states are traced. In terms of economic integration, the Union uses the achievements of the AC and MERCOSUR, unifying the legal regulators in the economic sphere and bringing rapprochement to the legal systems of the member states.


2010 ◽  
Vol 30 (9) ◽  
pp. 2370-2373 ◽  
Author(s):  
Jiong LANG ◽  
Yan-bing LIU ◽  
Shi-yong XIONG

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