Holographic fabrication of functionally graded photonic lattices through spatially specified phase patterns

In this paper, we present a method for the mathematically formulated phase engineering of interfering laser beams through a spatial light modulator for a holographic fabrication of graded photonic lattices. The desired phases can be programmed at specific locations by assigning gray levels in cellular structures. The method is demonstrated by embedding single-lattice structures or missing lattices in dual-lattice periodic photonic structures. The demonstrated method can be potentially combined with the coordinate transformation technique in transformation optics for the fabrication of graded photonic devices.