you can find propagation constant vs frequency and use its properties like boundaries (phase shift) and background for your structure, also there is a very useful pdf about propagation constant for other structure that I've attached.
Dr. Samaneh is right. For getting out dispersion characteristic, set the boundary as periodic boundary from the boundary conditions and the set the value of theta whatever you need, then go to parametric sweep or settings, analyze dispersion curve. click apply and you will get the result.
If you just select eigenmode solver and click on start you will see the attached problem(no dispersion in 1D results) so select again eigenmode solver and then click on par.sweep and click on start in this window, by this way you can find dispersion in 1D result
CST Eigen Mode captures only the real modes. Multi modal Bloch Analysis using Bloch Floquet Mode Theorem with CST FDS can be helpful to see the exhaustive modes. How to check which mode is evanescent?