Hi guys, I have a question when solving 3D Helmholtz equation derived from Maxwell equations. Normally I will get a plane wave solution. But when I used the method of separation variables for the three components Ex Ey and Ez, I found that the vector k in these three can be different as long as their lengths are the same. So Ex has a phase of vector(kx)*vector(r), Ey has a phase of vector(ky)*vector(r) and Ez has a phase of vector(kz)*vector(r), where |kx|= |ky|=|kz|=Constant. Besides this solution meets all the conditions in Maxwell equations(as least I have calculated). Attached is two matlab codes describing the normal plane wave solution and this vortex-like solution in 2D situation. I haven't found any material describing this wired solution in EM theory. All of them give out plane wave solutions. Is there anything wrong with this solution? THANKS ALL!