How to determine the effective thickness of metamaterial

I think you need to provide more information.

What kind of metamaterial? Thickness in which dimension?

This method doesn't require an effective metamaterial thickness calculation for the calculation of the effective parameters. Also, code is provided online for the algorithm (see references in paper).

A Unique Extraction of Metamaterial Parameters
Based on Kramers?Kronig Relationship
Zsolt Szabó, Gi-Ho Park, Ravi Hedge, and Er-Ping Li, Fellow, IEEE

http://download.polytechnic.edu.na/p...tparam/EMPEx.m