On Oct 30, 2008, at 5:35 AM, Yiling Qi wrote: > Dear Steven, > My simulated structure is a 2D periodic photonic lattice (the > contrast of refractive index is very small, the order is only > around exp(-4). Then kx and ky are meaningful for the bandstructure, > but apparently there will be no bandgap with respect to frequency(w) > along kx/ky. But it is supposed to have bandgaps of propagation > constant(beta) to kx/ky. The solution form can be deduced to be > &(wavefunction)=exp(-iqz)u(x,y), and following the Bloch's theorem, > the eigenfunction u(x,y) can be written as u(x,y)=Uk(x,y)*exp(iK*r), > where Uk(x,y) is periodic have the period of the lattice. From this > solution form, it seems exp(-iqz) replaces exp(iwt) in the ordinary > plane wave form. So do you think MPB can still solve it?
MPB can certainly solve any problem of that form. However, you still need a frequency in order to define your mode; given K (the in-plane wavevector with components kx and ky) and q (the z wavevector, although have switched the sign convention so that q = -kz) there are infinitely many eigenmodes with different frequencies. Without a frequency your problem seems to be ill-posed. MPB solves the problem where, given (kx,ky,kz) you find the frequencies. Alternatively, with find-k you can give (kx,ky) and the frequency and then solve for kz (q). Steven _______________________________________________ mpb-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
