In this chapter we will focus on the design and optimization of Bragg waveguide gratings (for fiber Bragg gratings, see Fiber Bragg Gratings). We will start with 3D finite-difference time-domain (FDTD) simulations of the infinitely long device to access how the performance of the grating is affected by geometric parameters such as the corrugation depth and misalignment. We will then use the eigenmode expansion (EME) solver in MODE to calculate the full transmission spectrum of the device. Finally, we will use the EME solver to study the effect of adding a phase shift to the Bragg grating to create a resonance peak within the stop band. This design can be used as a filter in an integrated optics circuit, as well as a sensor for biological sensing applications.