Dear Steven and all mpb users, Thanks for your kind response before, I have tried the find-k function, it could work well but still not completely satisfy my concern, since it can give out k(w), however what I would like to get is a relationship between kx/ky and propagation constant beta(q) which in my situation meet the solution form ψ=exp(-iqz)u(x,y) . If I set *kdir *in find-k function to be along kz direction, then the output is still no related with the other two directions. So do you have any idea to help me solve this problem? Thanks a lot for your attention.
Best wishes Yiling Re: [MPB-discuss] propagation constant in MPB Steven G. Johnson Sat, 12 Jul 2008 11:59:04 -0700 On Jul 11, 2008, at 10:41 AM, Yiling Qi wrote: > I am now simulating a 2D (square lattice) photonic crystal. I set k- > points to be Gamma-X-M. instead of the relationship between > frequency and parallel k-vectors, I am more concerned about the > propagation constant(generally named as beta, actually is z > component of wave vector in this situation I think). So how could I > convert frequency into kz? Could it be deduced by the formula shown > as follows: > beta^2=(2pi*f*n)^2-(2pi*kx)^2-(2pi*ky)^2 > ( suppose a=1 and f, kx, ky are all got from MPB) > No, that formula is just for plane waves in a homogeneous medium. In general, there is no analytical formula relating frequency and propagation constant -- solving for this relationship (the dispersion relation) is the whole point of MPB. The propagation constant is just one component of the k vector. So, in MPB you are actually specifying the propagation constant and computing the corresponding frequency; to specify the frequency and compute the propagation constant, see this section of the manual: http://ab-initio.mit.edu/wiki/index.php/MPB_User_Reference#The_inverse_problem :_k_as_a_function_of_frequency Steven
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