Hello, I have bellow the results of waveguide simulation from photo 1 i can see that its has 2 half wavelength along the width and zero on the other side.
On photo 2 we have from top view some circles.

but how can i see those circles in the formulas in the formulas of TE TM modes shown in the end?
Also how to know from the field plots bellowif its TM or TE mode?
In photo 3 taken from a manual Each field compent is designated by different color but in simulation there is no defiirent colors there is only one type of coloring.
How can i see the X and Y direction of the electric field in the simulation?
Thanks.

 

Describing and understanding rectangular waveguide modes has to be one of the most documented and illustrated topics on the web. Google 'rectangular waveguide modes' as click on images - you will find colour images, B/W images, field lines, current maps, etc.... Click on any that you find helpful.

I'd recommend finding a coherent description / derivation in a book or lecture notes that fits your learning style and work through it. There are heaps of them out there as well.