A new concept for a flat lens design using dielectric cylinders

A new design method called the array scattering method for a flat lens made of dielectric cylinders is presented. The method reconstructs the far-field radiation pattern of a 2-D arbitrary geometrical shape dielectric scatterer. Since the method has no restrictions on the near field, it allows us to alter the polarization currents distribution in order to obtain a better far-field performance for a periodic structure with a given unit cell size. The method also allows us to perform a simple parametric study on the limits of the unit cell size, taking into account the scatterer geometrical dimensions. This parameter (unit cell size) does not appear in the formulation if we use a method that assumes an infinite array of cylinders. The realization is done using the multiple scattering method, which is one of the most accurate methods to deal with arrays scattering. Nevertheless, the method is almost entirely analytic, not iterative and does not require multiple simulations in order to obtain the required objective.