How to determine cutoff wavelength for a microstrip transmission line?

I have fabricated a microstrip transmission antenna and I have intended to find its εr and μr.

I outsourced it for the same where they fed it to a VNA and provided me with S11 and S12.

I have to find expressions to find εr and μr using the same, which I did find.

There is a term called cut off wavelength which I need to substitute in the expressions.

Any method to find it?

Microstrip TL frequency limit is given by the lowest order transverse resonance, which occurs when width of the line (plus fringing field component) approaches a half-wavelength in the dielectric. So for broad bandwidth, have to avoid using wide lines.

To be exact, the term "cutoff wavelength " relates to hollow waveguides, and it is the longest wavelength the waveguide can pass. In microstrip, in reverse, the limiting shortest wavelength is that at which other than TEM mode is propagated, either as above explained, or, radiated by non-TEM modes. This kind of radiation loss is often also affected by inhomogeneities of the microstrip line, like bends, tuning stubs, components and the like.

---------- Post added at 20:42 ---------- Previous post was at 20:40 ----------

By the way, terms of permittivity and permeability do not relate to any antenna but to a dielectric or magnetic material used in it and exposed to electromagnetic waves. So your device is not an antenna but a test jig allowing to measure material properties.