Thanks for your advice. So I'm trying to investigate the effective index by calculating it both theoretically and simulationally.
But, I wondering if the MODE simulation is suitable for the coupled resonator optical waveguide (CROW) based on phase-shifted bragg grating.
As I know, the MODE is analyze the object only in 2D, but the CROW structure is varying for the z-axis due to the phase shifter as I attached images below. 
In this situation, how can I simulate the effective index and mode profile in the MODE simulation