Design of two-dimensional sampled Bragg grating for a curved waveguide.

Due to the ability of changing light propagation path direction, curved waveguide Bragg grating (CWG) plays an important role in photonic integrated circuits. In this paper, we proposed a cascaded sampled Bragg grating on tilted waveguide (CSBG-TW) structure to equivalently realize CWG. As an example, by designing two-dimensional (2D) sampled gratings, the direction of +1 sub-grating vector in CSBG-TW can be changed. Then if a curved waveguide is divided into several sections of tilted waveguide, we can keep the grating direction being always parallel to the longitudinal direction of each section of tilted waveguide, while the basic grating is uniform. Hence, the required CWG can be equivalently realized, and the light responses such as reflection Bragg wavelength shift and backward mode convert caused by the tilted grating in curved waveguide can be compensated for. The results show that the sampling structures of CSBG-TW is micro-scale and the difference between reflection intensity between the CSBG-TW with four section tilted waveguide and CWG as design target is less than 0.1 dB. Compared with CWG, the CSBG-TW allows convenient holographic exposure and the wavelength can be accurately controlled. Therefore, the CSBG-TW can be used in various photonic integrated devices that require changing propagation paths.