Hi Samantha,
I apologize for the late response. May I ask if you're solving the modes with PML or metal boundaries? I ran the simulation based on the parameters of the first configuration and I obtain 1 TE and 1 TM mode. Sometimes you might get additional modes as a result of the artifacts of the boundary conditions. These modes are not physical solutions. If you're using Metal boundaries, I would suggest you to change to PML and check if you still observe the additional mode.
Regards,
Amrita