Study of Coupling Length of Concentrically Curved Waveguides

In this paper, we propose a method based on Helmholtz equation to determine the coupling length of the light propagating in concentrically curved waveguides by the conformal transformation. After the transformation, the concentrically curved waveguides are regarded as straight directional couplers, and the coupling length can be obtained rapidly by using this method. We also calculate the coupling length by the finite-difference time-domain (FDTD) method to compare with the result obtained by our method. The results show a good agreement between the coupling length obtained by the conformal transformation and the FDTD method.