Polarization-independent and tunable flat lenses based on graded index two-dimensional photonic crystals

In this paper, we perform numerical analyses on polarization-independent and tunable graded index lenses based on two-dimensional graded photonic crystals and utilizing liquid crystals. A simple triangular lattice is used for the graded lens, in which the refractive index profile in the transverse direction varies in such a way that the modulus of the refractive index is biggest at the centre and decreases towards the edges. Three variation functions of linear, parabolic and hyperbolic are implemented for creating graded structures and investigating focusing characteristics of the designed lenses, using plane wave expansion and finite-difference time-domain methods. Finally, we study the variation of the lenses properties by changing the optical axis orientation of liquid crystals. Our numerical results show that, through an appropriate set of design geometrical parameters, polarization-independent and tunable lenses can be achieved.