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A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition matrices, the latter of which was used in early definitions of characteristic modes and is uniquely defined for all scattering scenarios. This also makes it possible to extend the known application domain of characteristic mode decomposition to any other frequency-domain solver capable of generating transition matrices, such as finite difference or finite element methods. The formulation of characteristic modes using a transition matrix allows for the decomposition of induced currents and scattered fields from arbitrarily shaped objects, providing high numerical dynamics and increased stability, removing the issue of spurious modes, offering good control of convergence, and significantly simplifying modal tracking. Algebraic properties of the transition matrix are utilized to show that characteristic mode decomposition of lossy objects fails to deliver orthogonal far fields. All aforementioned properties and steps are demonstrated on several numerical examples for both surface- and volume-based method-of-moment formulations.
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Electromagnetic (EM) scattering systems widely exist in EM engineering domain. For a certain objective scattering system, all of its working modes constitute a linear space, i.e. modal space. Characteristic mode theory (CMT) can effectively construct a basis of the space, i.e. characteristic modes (CMs), and the CMs only depend on the inherent physical properties of the objective system, such as the topological structure and the material parameter of the objective system. Thus, CMT is very valuable for analyzing and designing the inherent EM scattering characters of the objective system. This work finds out that integral equation (IE) is not the best framework for carrying CMT. This dissertation proposes a completely new framework for carrying CMT, i.e. work-energy principle (WEP) framework, and at the same time proposes a completely new method for constructing CMs, i.e. orthogonalizing driving power operator (DPO) method. In new WEP framework and based on new orthogonalizing DPO method, this work resolves 5 pairs of important unsolved problems existing in CMT domain.
1-Dimensional (1D) photonics crystals with and without defects have been numerically studied using efficient Transfer Matrix Method (TMM). Detailed numerical recipe of the TMM has been laid out. Dispersion relation is verified for the periodic Photonics Band Gap (PBG) structure. When there are defects, the transmission spectrum can be decomposed into one or more quasi modes with excellent agreement. The Density of States (DOS) is obtained from the phase derivative of the transmission spectrum. Greens function is also obtained showing much sharper mode characteristics when the excitation source is localized at the peaks of the quasi modes.
This paper has been withdrawn by the authors because the paper is largely revised and improved, and to appear in Mechanics Research Communications.
In terms of the quantitative causal principle, this paper obtains a general variational principle, gives unified expressions of the general, Hamilton, Voss, H{o}lder, Maupertuis-Lagrange variational principles of integral style, the invariant quantities of the general, Voss, H{o}lder, Maupertuis-Lagrange variational principles are given, finally the Noether conservation charges of the general, Voss, H{o}lder, Maupertuis-Lagrange variational principles are deduced, and the intrinsic relations among the invariant quantities and the Noether conservation charges of the all integral variational principles are achieved.
A simulation of electric current pulses formed by a packet of gamma-quanta moving through an absorptive medium is presented. The electromagnetic fields of the current pulse moving along the straight line with super light velocity are obtained
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