Photonic crystal slab Laplace operator for image differentiation

Spatial differentiation is important in image-processing applications such as image sharpening and edge-based segmentation. In these applications, of particular importance is the Laplacian, the simplest isotropic derivative operator in two dimensions. Spatial differentiation can be implemented electronically. However, in applications requiring real-time and high-throughput image differentiation, conventional digital computations become challenging. Optical analog computing may overcome this challenge by offering high-throughput low-energy-consumption operations using compact devices. However, previous works on spatial differentiation with nanophotonic structures are restricted to either one-dimensional differentiation or reflection mode, whereas operating in the transmission mode is important because it is directly compatible with standard image processing/recognition systems. Here, we show that the Laplacian can be implemented in the transmission mode by a photonic crystal slab device. We theoretically derive the criteria for realizing the Laplacian using the guided resonances in a photonic crystal slab. Guided by these criteria, we show that the Laplacian can be implemented using a carefully designed photonic crystal slab with a non-trivial isotropic band structure near the Gamma point. Our work points to new opportunities in optical analog computing as provided by nanophotonic structures. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement