Graded index photonic crystals.

We explore two-dimensional triangular lattice photonic crystals composed of air holes in a dielectric background which are subject to a graded-index distribution along the direction transverse to the propagation. The proper choice of the parameters such as the input beam width, gradient coefficient, and the operating frequency allow the realizations of the focusing (lens) and guiding (waveguide) effects upon which more complex optical devices such as couplers can be designed. Numerical results obtained by the finite-difference time-domain and planewave expansion methods validate the application of Gaussian optics within a range of parameters where close agreement between them are observed.