Tunable coupling coefficient in the lens-waveguide coupled photonic crystal structures

The efficient lens-to-waveguide light coupling has been an important issue in integrated photonic crystal circuits during the last years. In the present work, we theoretically study a hybrid structure consisting of photonic crystal lenses and waveguides. The lenses are made of circular Zirconia rods with the triangular structure in the air host in which the radii of the rods decrease from the center toward the edges along the transverse direction. We assumed that the rods are hollow and are infiltrated with nematic liquid crystals. The designed lenses are considered alongside square and triangular lattice waveguides made of Zirconia rods, for creating the coupled lens-waveguide structures. Then, the coupling efficiency of all mentioned structures is investigated, using finite-difference time-domain and plane-wave expansion methods. Finally, we study the variation of the coupling efficiency by changing the optical axis orientation of liquid crystals. Our numerical results show that through an appropriate set of optimum geometrical parameters, the coupling efficiency of 8.55 dB was obtained in our simulations, which can be tuned and controlled easily by an applied external static electric field. (author)