Properties of split-ring metamaterials are governed by inter-element interactions. These interactions lead to slow
eigenmodes of coupling, which, due to their short wavelengths, are ideal candidates for the design of near-field
manipulating devices. In this paper we explore the electric and magnetic coupling mechanisms in nano-U and nano-SRR
dimers comprising of two identical nano-resonators arranged axially and twisted relative to each other by an arbitrary
angle. We study theoretically the couplings in a periodic chain of nano-dimers for the frequencies from 100 to 300 THz.
In our analytical model, the electric and magnetic couplings can be expressed through the self and mutual terms for the
magnetic and electric field energy. In addition, we incorporate the effect of kinetic inductance due to the inertia of the
electrons (noticeable as element dimensions approach 100nm or smaller). The resulting dependence of the electric,
magnetic and the total coupling constants on the twist angle within the dimer obtained analytically is shown to agree
with numerical simulations (CST Microwave Studio). Our approach should enable an effective design of metamaterial
structures with desired properties and would be a useful tool in developing THz range manipulating devices based on
propagation of slow waves by virtue of coupling.
The dispersion equation of a magneto-inductive wave along a line of magnetically coupled resonant elements is investigated under conditions when retardation must be taken into account. It is shown that both the radiation resistance and the imaginary part of the mutual inductance appear in the modified dispersion equation which allows interaction up to the <i>p</i><sup>th</sup> neighbour. The problems arising in the solution of the full dispersion equation are discussed and it is concluded that the general solution leading to a large number of high-attenuation branches may not lead to a solution that is easily interpretable physically. It is suggested that the dispersion equation is to be derived from the variation of the current along an array of a finite number of elements excited by a voltage applied to the first element. The solution is obtained for a planar array of capacitively loaded loops in a closed form by inverting the complex mutual inductance matrix. It is shown that retardation and higher order interactions have greater effect upon the attenuation of the arising backward wave than upon the phase change per element. The appearance of a forward wave with a phase velocity close to that of light is also shown.
We describe subwavelength properties of magnetic metamaterials designed to manipulate and control the near field by employing magnetoinductive (MI) waves. MI waves owe their existence to the magnetic coupling between metamaterial elements. Magnetic field distributions and Poynting vector streamlines are used to visualise the diamagnetic and paramagnetic properties of metamaterials and to analyse working principles of MI waveguides and MI waveguide components.
One-dimensional lines of metamaterial elements supporting magneto-inductive waves are investigated for the case when elements' properties vary in a doubly periodic manner. It is shown that the dispersion of the magneto-inductive waves in this case demonstrates (analogously to acoustic waves in solids) an "optical" and an "acoustic" branch. The properties of the dispersion relation are investigated with attention paid to the width of pass- and stop-bands and the possibility of tailoring the dispersion properties within this approach is discussed.
On the base of the analytical solution of the couple differential equations system in the photorefractive piezocrystal with transmission holographic grating the optimization of the diffraction efficiency is conducted by choice of the crystal orientation and linear polarization of the reading light. It has been theoretically established, that for bi<SUB>12</SUB>SiO<SUB>20</SUB> piezocrystal with thickness 10 mm at different values of external electric field E<SUB>0</SUB> the maximum diffraction efficiency (eta) <SUP>M</SUP> is reached for the following magnitudes of the (theta) and (Psi) respectively: without electric field (theta) =42 degree(s), (Psi) =35 degree(s), with electric field 5 kV/cm (theta) =51 degree(s), (Psi) =19 degree(s). Without taking into account the piezoelectric effect these orientation and polarization angles have the following values: without electric field (theta) =0 degree(s), (Psi) =107 degree(s), with electric field 5 kVcm (theta) =43 degree(s), (Psi) =31 degree(s). It is shown, that taking into account the piezoelectric effect increases the maximum diffraction efficiency (eta) <SUP>M</SUP> in 2.13 times at E<SUB>0</SUB>; in 2.47 times at E<SUB>0</SUB>=5 kV/cm; in 1.75 times at E<SUB>0</SUB>=1- kV/cm; in 1.43 times at E<SUB>0</SUB>=15 kV/cm.
The analytical dependencies of crystal thickness, for which the diffraction efficiency optimized on the polarization angle reaches the maximum values, on the orientation angle are derived. It is shown that optimum thickness of the crystal is inversely proportional to its specific rotation and plots of dependence of crystal optimum thickness on the orientation angle are set of an equidistant curves with period 180 degree(s) corresponding different local maxima. A distance between these curves is defined by the specific rotation of the crystal (alpha) . The optimum thickness for the first local maximum can not be less than (pi) /(2(alpha) ). The magnitudes of crystal thickness, optimal for the diffraction efficiency of the hologram and gain coincide for some intervals of the orientation angle (theta) between the gating vector and direction . Analytical expression, permitting to determine the azimuths of polarization of a reading light, at which the diffraction efficiency will be optimized simultaneously on the polarization angle and the crystal thickness, is found.
In this talk I shall show you how the electro-optic effect is modified by elasticity and also give a few applications from the field of volume-holography in photo-refractive crystals. I shall also comment on a striking similarity between the electro-optic effect owing to elasticity and the magnetostatic field owing to a distribution of electric currents.
Within the framework of dynamic holography we present a theoretical model based on geometric optics ideas which is capable to describe two wave mixing and four wave mixing processes with waves of arbitrary shape in photorefractive crystals. The model takes into account the nonplanarity of the waves and optical activity of the crystal materials. In the slowly varying amplitude approximation coupled partial differential equations describing the evolution of the wave amplitude are derived. These equations are solved numerically by introducing the lightpaths as characteristics. We study the influence of the beam properties like amplitude profiles and polarization as well as the geometrical arrangements and crystal properties on the two wave mixing efficiency.