Refraction and diffraction of waves in natural crystals and artificial crystals formed by anisotropically scattering centers are considered. A detailed study of the electromagnetic wave refraction in a two-dimensional photonic crystal formed by parallel threads is given by way of example. The expression is derived for the effective amplitude of wave scattering by a thread (in a crystal) for the case when scattering by a single thread in a vacuum is anisotropic. It is established that for a wave with orthogonal polarization, unlike a wave with parallel polarization, the index of refraction in crystals built from metallic threads can be greater than unity, and Vavilov-Chrernkov radiation becomes possible in them. The set of equations describing the dynamical diffraction of waves in crystals is derived for the case when scattering by a single center in a vacuum is anisotropic.Because a most general approach is applied to the description of the scattering process, the results thus obtained are valid for a wide range of cases without being restricted to either electromagnetic waves or crystals built from threads.

Photonic crystals, formed by the periodically strained parallel metallic threads, can be used (and already are in use) in the most various applications, first of all for microwave antenna applications [1]. Moreover, such structures are applied as resonators in volume free electron lasers (VFEL) [2].According to the analysis [3] such a photonic crystal is an analogue of an optically anisotropic crystal, because the refractive index for an electromagnetic wave with E parallel to the threads is not equal to that for the wave with E orthogonal to the threads. Since the wave with the polarization parallel to the threads is mainly responsible for generation in VFEL, all the previous studies were focused on analysis of its behavior [3]. In the present paper the refraction of the wave polarized orthogonally to the threads is investigated in details.According to [3] the index of refraction can be expressed via amplitude of zero-angle scattering by an elementary scatterer (the metallic thread in the case under consideration): 2Jrp n 1-,1I = 1 + 7 11-,11 (0),where p is the density of scatterers, k is the wave vector of the incident wave, 11-,11 (0) is the amplitude of electromagnetic wave scattering by the metallic thread at zero angle; n 1-,1I comply with 1 n 1-,1I -11« 1.Let us precede consideration of the refraction of waves with the orthogonal polarization in the photonic crystal with analysis of wave scattering by a single thread. Suppose the thread to be cylindrical with the radius R much shorter than the thread length L .Then analytical calculations can be done for the thread with the infinite length.For simplicity, let us consider the case when the wave vector k is perpendicular to the cylinder axis. Then, the field of the scattered wave with orthogonal polarization can be written as follows [4 ]: where 00 H = e " i" e 1-H (kr)e-i mp e z L.,. n n ' n =-oo -I n( kzR) J�( kR) + � J�( kzR) Jn(kR) 1-vS e n = 1 ' I n (kzR)H� (kR) --Fe J ; (k Z R)H n (kR)(2) I n is the Bessel function of the order n, H n is the Hankel function of the 1st kind of the order n, kz = k -Fe , S is the permittivity of the thread material (for pure metal s = 1 + 4JrO'i / OJ, where OJ is the frequency of the electromagnetic field, 0' is the conductivity; permeability J1 is assumed to be equal to 1), er, e .." e z are the unit vectors of cylindrical coordinate system ("z" is the cylinder axis), the amplitude of the incident wave is assumed to be equal to 1. Considering the limits for the Bessel and Hankel functions of small arguments, we can find that for a perfectly conducting cylinder at kR« 1 the relations e� "'" -e;l and e� »e ; are correct for any Inl > 1. In case of nonideal conductor, the approximate equality e� "'" -e;l is violated, but the coefficients e� and e;l are comparable in magnitude. Thus, when kR« 1 the only terms with n = 0 and n = ±1 in series (2) are sufficient.Note that in the long-wavelength limit for the wave with parallel polarization for any Inl > 0 e� » e� [3].Returning to our problem, let us remind that the second equat...

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We study the behavior of the generation efficiency and radiation spectrum of a three-cavity axial vircator as a function of the injected electron-beam radius, impedance, and energy homogeneity. We show that for each geometry of a three-cavity resonator, there exist optimal (maximizing the generation efficiency) values of these parameters and determine the range over which they may vary without losing the efficiency of generation.

The design concept of effective microwave absorbers and compact matched loads based on 3D-printable lossy nanocarbon-based composites with filler content above the percolation threshold is proposed. The DC-conductive (σ DC =0.39 S/m) 3D-printable filament based on poly(lactic) acid (PLA) filled with 12wt.% of multiwalled carbon nanotubes (MWCNTs) was used. The electromagnetic properties of 3D-printed pyramidal regular structures were experimentally investigated and numerically simulated in 12-18 GHz (Ku-band) and 26-37 GHz (Ka-band) frequency ranges. Within the proposed model the structures under study were considered as graded refractive index material. The optimal geometrical parameters of designed microwave components were successfully evaluated using numerical modeling. Tested components demonstrate remarkable shielding efficiency (> 20 dB) within whole Ku-and Ka-bands and are suitable for practical application related to effective absorption of microwave radiation. The production of 3D-printable materials with controlled and predicted losses offers the possibility for miniaturization of 3D printed microwave components, such as absorbers and loads. The developed technique, estimating the geometrical parameters of the components vs dielectric properties of the conductive filament, could be used as a versatile platform for predesign of compact microwave devices taking into account constituent dielectric parameters of available printable materials and filaments.