On-chip phase-shifted Bragg gratings and their application for spatiotemporal transformation of Bloch surface waves

In this work, we study numerically and theoretically phase-shifted Bragg gratings (PSBG) for Bloch surface waves (BSW) propagating along the interfaces between a 1D photonic crystal and a homogeneous medium. The studied on-chip structure consists of a set of dielectric ridges located on the photonic crystal surface constituting two symmetrical onchip Bragg gratings separated by a defect layer. Rigorous simulation results demonstrate that the surface wave diffraction on the proposed on-chip PSBG is close to the diffraction of plane electromagnetic waves on conventional PSBG. For the considered examples, the correlation coefficient between the spectra of conventional PSBG and on-chip PSBG exceeds 0.99 near the resonance corresponding to the excitation of the eigenmodes localized in the defect layer. Conventional PSBG are widely used for spectral filtering as well as for temporal and spatial transformations of optical pulses and beams including differentiation and integration of pulse envelope or beam profile. In the present work, we discuss the capability of on-chip PSBG to implement the operations of temporal and spatial differentiation of BSW pulses and beams. The presented examples demonstrate the possibility of using the proposed structure for high-quality differentiation. The obtained results can be applied for the design of the prospective integrated systems for on-chip alloptical analog computing.