Continuum modelling of a circular planar array of coupled microwave oscillators
in this paper the phase distribution in an array of coupled oscillators arranged on a circular surface is discussed. Coupling is considered to be weak and each oscillator is coupled to its four nearest neighbours. In a continuum limit where the number of oscillators goes to infinity a theoretical formulation in polar coordinates is proposed to describe the dynamic behaviour of phases of the array elements. A Green's function for phase distribution of the array is proposed in terms of its normalized eigenfunctions. Beam steering can be done via detuning the edge oscillators.
On the dynamics of two-dimensional array beam scanning via perimeter detuning of coupled oscillator arrays
Arrays of voltage-controlled oscillators coupled to nearest neighbors have been proposed as a means of controlling the aperture phase of one-dimensional (1-D) and two-dimensional (2-D) array antennas. It has been demonstrated, both theoretically and experimentally, that one may achieve linear distributions of phase across a linear array aperture by tuning the end oscillators of the array away from the ensemble frequency of a mutually injection-locked array of oscillators. These linear distributions result in steering of the radiated beam. It is demonstrated theoretically that one may achieve similar beamsteering in two dimensions by appropriately tuning the perimeter oscillators of a 2-D array. The analysis is based on a continuum representation of the phase in which a continuous function satisfying a partial differential equation of diffusion type passes through the phase of each oscillator as its independent variables pass through integer values indexing the oscillators. Solutions of the partial differential equation for the phase function exhibit the dynamic behavior of the array during the beamsteering transient.
Investigations of dielectric gratings using electrodynamic models based on volume integral equations
Eigenmodes of planar and cylindrical dielectric gratings (DGs) and electromagnetic wave scattering from multiplayer DGs are investigated. The DG characteristics are calculated using numerical-analytical solution of integral equations (IEs).