The paper discusses the methodological questions arising in the study of open electrodynamic structures of resonance quasi optics via time-domain technique. As demonstrated, all of the interesting physical characteristics inherent in these objects (including the objects with various frequency-selective elements) can be obtained through the numerical solution of the relevant model initial bowldaryvalue probhxns. For the first time, a finite difference method equipped with the exact local 'absorbing' conditions on artificial boundaries has been applied for the solution of this kind of open problems. The results of the computational experiments performed have verified the possibility of the efficient selection of oscillations in dispersive open resonators with diffraction gratings, among them the resonators with gratings operating in the quasitotal nonspecular reflection mode.
Abstract-Excitation of the electromagnetic fields by a wide-band current surge, which has a beginning in time, is studied in a cavity bounded by a closed perfectly conducting surface. The cavity is filled with Debye or Lorentz dispersive medium. The fields are presented as the modal expansion in terms of the solenoidal and irrotational cavity modes with the time-dependent modal amplitudes, which should be found. Completeness of this form of solution has been proved earlier.The systems of ordinary differential equations with time derivative for the modal amplitudes are derived and solved explicitly under the initial conditions and in compliance with the causality principle. The solutions are obtained in the form of simple convolution (with respect to time variable) integrals. Numerical examples are exhibited as well.
Excitation of electromagnetic fields in a cavity is studied in the time domain. A signal, which excites the fields, stands in Maxwell's equations as the electric current density given by an integrable function of coordinates and time. The problem is solved within the framework of the evolutionary approach to electromagnetics. The modal field expansions with time-dependent modal amplitudes are derived. Exact solutions for the amplitudes are obtained as the convolution integrals with time as a variable of integration, where the signal function stands as a parameter of the integrands. Two examples of the signal functions having a beginning in time are considered: (a) a surge modeled by the double-exponential function of time and (b) a sinusoid oscillating with an arbitrary frequency.
In the International System of Units (SI), distinct physical dimensions were assigned to the electric (E) and magnetic (H) fields as volt-per-meter and ampere-per-meter, respectively. To save the dimensional balance in the standard Maxwell's equations (MEs) in SI units, a pair of free-space constants, 0 and µ 0 , with their dimensions of farad-per-meter and henry-per-meter were installed heuristically. Eventually, every quantity that participated in each ME in SI units has an individual physical dimension distinct from the other terms therein. This situation hampers the control of the dimensional balance in the processes of analytical manipulations with the MEs during the theoretical studies. Reformatting the freespace constants is performed in this article so that one new constant is obtained with its dimension of volt, and the other one has its dimension of ampere. These gave a handle to scale the electric and magnetic fields appropriately. Ultimately, the new fields are obtained with their common dimension of inverse-meter. Meanwhile, the standard differential procedures 0 ∂ ∂t and µ 0 ∂ ∂t from MEs are obtained in their simple common format of ∂ c ∂t , where c is the speed of light. The MEs in the novel format are exhibited for the fields in the free space, plasma, and dielectrics. The content of this article is destined for the researchers who deal with theoretical studies in electrodynamics, and the level of content is appropriate for and realizable by recent graduates, M.Sc. and Ph.D. students, and professionals.
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