Numerical simulation of planar Bragg waveguide bends

An analytical form was found and transparency boundary conditions were numerically approximated for the parabolic wave equation in curvilinear coordinates. It was shown that the solutions obtained by the parabolic equation method are in agreement with the solutions to the spectral problem defining the Bragg waveguide modes. The field amplitude and bending loss were numerically simulated depending on the curvature radius and parameters of the Bragg waveguide.