Re: invisibility cloak
Hi!
I see that several of you guys have similar problems: point source in TM and matrix values of epsilon and mu in 2D Comsol simulations.
Firstly, in order for a problem to be 2D it has to satisfy certain conditions.
1. you can't have a point source in a 2D problem. If you have a point source - it's 3D. If, however, you meant line source for TM, I think perhaps in Comsol you can't define magnetic line currents (while you can define electric currents). However, why do you have to do TM? Just do the TE simulation and exchange everything: H<->E, mu<->-epsilon, magnetic line currents<-> electric line currents.
This is perfectly good for perfect or hyperlenses (whatever you are doing). I know, because I tried it some time ago and it worked perfectly well. Just do the TE simulation and then say you did TM - it is really the same if you make the above substitutions.
2. epsilon and mu: write down the Maxwell equations with anisotropic eps and mu. Use the general (second rank tensor) for for eps and mu. See what conditions these tensors (matrices) have to satisfy so that the TE and TM modes can be decoupled. The block diagonal form in a given basis is a sufficient condition.
Then, write down the decoupled equations for the TE and TM fields. Then, you'll see what values (matrix elements) of eps and mu are relevant to the present case.
If you are lazy, just use the simple recipe:
TE case: eps_z, mu_xx, mu_xy, mu_yx and mu_yy matter. For TM its the opposite: mu_z, eps_xx, eps_xy, eps_yx and eps_yy. The other values are redundant so you don't need to specify them.
Regards