 #1
 9
 0
Main Question or Discussion Point
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 vortexlike 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!
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 vortexlike 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!
Attachments

832 bytes Views: 238