Please observe the answers in this link:

https://www.researchgate.net/post/How_to_figure_out_number_of_modes_in_HFSS 

Dear Robert, Please follow the link as given by Anvesh. Mode identification will be easy if you follow this path. To identify mode nomenclature (i.e. TM10/TM21 etc), I'm afraid to inform you that there is no work. Using mode nomenclature of Equilatral triangular waveguide, Joseph Helszajn published some works on hexagonal. Paper are available at IEEE. Please search using 'Helszajn'. But the mode nomenclature will be quasi as the exact analytical solution is not available. I would suggest you to learn mode nomenclature for equilateral and rectangular microstrip antenna (TM case only).  Simulate one hexagonal patch. Compare its field patterns with triangular/rectangular one. Similarity will be found with triangular one, as per my knowledge goes. Please inform us, We will go accordingly...

Mode nomenclature is available for rectangular, circular, elliptical, annular ring and equilateral, 30-60-90, 45-45-90 triangular shaped objects. Hexagonal case is not available. Even the mode nomenclature for rectangular ring shaped object is also not available.

 Thank you for the above comment .

I will simulate and try to compare the result with that of rectangle patch.

We are waiting for your kind update(s)

I have calculated and compare my proposed designed with that of Rectangle patch using formula. I have attached the document for comparison with corresponding mode of operation.

Please comment regarding any query.

Dear Robert, please show the photograph of your hexagonal ring antenna...

If you compare the results of rectangular ring shaped antenna with rectangular microstrip antenna, you may not get correct result. here, you are dealing with hexagon...Proper mode nomenclature is required. Observe internal field variations and resonant frequency both before identifying the mode as TM_mn mode

Designed hexagon shaped fractal antenna.

As you have used 4 hexagonal ring, it is not a good way to identify the modes. Normal mode nomenclature for hexagonal patch (or waveguide or resonator) is not available as per my knowledge goes. Therefore, mode identification of hexagonal ring shaped antenna may not correct. My comments may disappoint you. If you really want to identify modes, then work for single hexagonal antenna. In case hexagonal ring shaped antenna, try to use first mode, 2nd mode etc...

Thank you Sir for your comment.

For my future design I try to use normal patch geometry for Multi band antenna designing.

We are also working on hexagonal microstrip antenna. We are facing several problems to identify its modes....If you get any results, please inform us after your publication.....not before that

Yes sir if I identify and get any result, I sure will share the result and procedure.

Thank you for all Your comment 

Thanks, We are waiting for new mode nomenclature from you. All the best Robert.

To me this looks like a log-periodic antenna, not a fractal antenna.  You may find that the literature about log-periodic antennas (there is a lot of it, and they are used a lot) is more useful to you in understanding and predicting the performance of this antenna than anything about fractal antennas.

Yes sir the design is based on log periodic concept but it follow a self similar geometry, that why its fractal based antenna. 

Sir

Can we do mode analysis for structures with defected ground or parasitic elements?

yes, we can do mode analysis of any electromagnetic object. But, the question is: how to iddentify a particular mode as TE10 or TM23 etc. Regular and some specific objects have proper mode nomenclature which includes rectangular, circular, equilateral triangular, elliptical, annular ring and 45-45-90 triangular object.

More precidesly, rectangular ring shaped microstrip structure does not have proper mode nomenclature.

Please read my other comments also.

Thank you sir for response. I read all discussion. But does mode analysis applicable for finite ground and infinite ground structure both.?

yes... mode will be given for electromagnetic object...if finite gnd plane is there, the effect will be reflected. Little distortion may appear. But, we can identify mode.

Using CMA technique you can identify all mode of an antenna