Investigation of the coupling efficiency between graded index photonic crystal-based flat lenses and various types of waveguides

The importance of transmission, guiding and delivery of electromagnetic waves to the targeted part of a photonic circuit, leads to design couplers with high coupling efficiency. In the present work, we apply two types of photonic crystal-based flat lenses for designing the couplers. The lenses are made of annular 2 rods with a triangular structure embedded in air. To design the lenses, the outer radius of the annular cylinders is kept constant while the inner radius follows two linear and parabolic functions. At the next step, the lenses are placed along a slot waveguide, conventional photonic crystal waveguide and funnel-form photonic crystal waveguide, separately, for creating coupled structures. The incident light is focussed by the graded index flat lenses and transmits through the waveguides. In the following, we study the coupling efficiency of all mentioned structures, using finite-difference time-domain and plane wave expansion methods. The results reveal that the coupled funnel-form waveguide with the linear lens gives the highest coupling efficiency, which is 7.49 and shows great improvement compared to the previous works.