Polarization-independent and super broadband flat lens composed of graded index annular photonic crystals

Abstract

Abstract In this paper, we propose two types of all-dielectric polarization-independent graded index annular flat lens with a wide operating frequency range. The lenses are composed of two-dimensional triangular and square lattice photonic crystals with circular silica ( S i O 2 ) rods in the air. We assume in both square and triangular structures, the lenses are obtained by making air holes within each dielectric rod and we consider that the outer radius of the created annular rods is maintained constant while the size of the inner air holes varies along the transverse direction whose the air holes variation follow two types of linear and parabolic function. The graded structures are made in such a way that the modulus of the refractive index is biggest at the centre and decreases towards the edges. The optical properties and the physical background of the polarization-independent focusing mechanism are studied in frequency and spatial domains, using plane wave expansion and finite-difference time-domain methods. Our numerical results show that, through an appropriate set of design, the designed lenses are able to focus the light regardless of polarization for a wide frequency range into approximately same focal length in which difference between the focal distance of TE and TM polarization modes stays below λ 4 . Compared to previously polarization-independent designed photonic crystal based lenses, our proposed structures work under much wider frequency range. Also, in contrast with most of the graded structures, our graded lens are made without altering the lattice constant along the optical axis or transverse to the optical axis. Moreover, the design approach is restricted to the use of silica and non-use of more complicate materials such as liquid crystals, plasma, and the like. Thus, the designed systems can be constructed easier relative to the previously designed lenses.