I believe this might be more theoretical than simulation.
If this device can be simulated, it is better to get simulation result, instead of approcimation.
If case it cannot be simulated due to device size, and you want to build up a new model with its effective index, care should be taken: You will need to validate the effectiveness of this method from a simple case. Usually the effective material parameters are extracted through S parameters, or reflection/transmission, and most likely the result is polarization dependent.
You may refer to this example, which is isotropic: Metamaterial parameter extraction - Smith