Adjustable band gaps structures and semi-Dirac points in two-dimensional linear function photonic crystals

We have proposed a new two-dimensional function photonic crystals, which the dielectric constants of medium columns are the function of space coordinates r→. The photorefractive nonlinear optical effect or electro-optic effect can turn the dielectric constants of medium column into the function of space coordinates. In this paper, we studied the dielectric constants of medium columns are the linear function of space coordinates, i.e., ε(r→)=k r+b, and calculated the band gaps structures of TE and TM waves. We have found there are absolute band gaps and semi-Dirac points in the two-dimensional function photonic crystals. When the parameters k, b and the medium column radius ra change, the band gaps number, location and width, the absolute band gaps and semi-Dirac points should be changed, which can realize the adjustability of band gaps structures. The two-dimensional function photonic crystals should provide a new method for designing optical device.