How Do S-Parameters Reveal Resonant Frequencies in Metamaterial SRR Microstrip Antennas?

hello everyone! The last 5 months I study about antennas, I am new in this field and I want your help. 

I have designed a multiband antenna(microstrip rectangular) based on metamaterials(SRR). My resonant frequency is 2.5GHz, but my antenna is also multiband at frequencies 2.41, 4.27, 5.47, 6.51, 9. I have not discrete ports, I have a waveguide port(so I have only S11). Can you please explain me from where do derive these frequencies in S-parameters? Why is there a frequency at 4.27 and not at 6 or 8 or anywhere else? I understand that I have a frequency at 2.5GHz because of the dimensions and because I wanted this frequency, but the rest frequencies I get are random? It cant be random!!It is something that I dont understand. My main question is in which theory do the S-parameters based on, so I can realise why I have these results(frequencies).

Thanks in advance

Just google S-parameter. There might be references that would help you in these queries. I'm not an expert on this so, i'll leave this "here("")":https://www.microwaves101.com/encyclopedias/438-s-parameters-microwave-encyclopedia-microwaves101-com.

I already took a look at these weeks ago.

I am not sure I understand your question, you seem to imply that the S parameters are in some way perturbing your results. S parameters are just a measured or derived mathematical representation of a physical system, and come out of the design. They will tell you that the design may or may not have met a set of target parameters. Most likely problem is in your design /simulation or measurement method.
You probably need to use google scholar to search for papers on the topic of metamaterial UHF antenna and see what you can find,
cheers,
Richard

WOw radio communications its interesting! but unfortunatly to talk about em u have to own a minimu a profesional diploma in that branch!