Spatial differentiation of Bloch surface wave beams using an on-chip phase-shifted Bragg grating

Bloch surface waves (BSWs) supported by the interfaces between a photonic crystal and a homogeneous medium are considered as a prospective information carrier in integrated photonic circuits. In the present work, we study the application of on-chip phase-shifted Bragg gratings for spatial differentiation of BSW beams. The presented simulation results demonstrate a high accuracy of the performed differentiation. It is shown that upon differentiation of a Gaussian BSW beam, a two-dimensional analogue of the Hermite-Gaussian mode is generated in reflection. The obtained results may find application in the design of new planar devices for analog optical information processing.