On Fri, 22 Jun 2007, F.S.F. Brossard wrote: > Below is a simple program performing 3D calculations of an air-bridge H1 > cavity (one missing hole). When using supercell-size 2 sz=2, one finds > the main mode at band 26 (see attachment). Using sz=3 the mode is now > located at band 35, increasing sz further shifts the main mode to higher > order bands. Considering that band folding is not affected by the > supercell size in the out-of-plane direction (non periodic) how can the > appearance of additional bands be explained? and if possible, can the > position of the main mode be predicted as a function of sz? I have tried > increasing the resolution, using different k-point...without solving > that issue. Any suggestions?
In this kind of structure you don't have a complete gap because of the light cone (the modes propagating in the air infinitely far away). In an infinite computational cell, there are a continuum of eigenmodes in the light cone. For a finite cell, there are finitely many modes, but there are more and more as you increase the supercell size in the z direction. This is what you are observing. Note also that the cavity mode in this case is a resonant mode. This means, in an infinite computational cell, that it would actually not be a single eigenvalue but rather a continuum of eigenvalues where the amplitude in the cavity is large. If you make the computational cell large enough, therefore, you should get multiple "modes" that have the same local field pattern in the cavity but different field patterns far away; from the frequency bandwidth of these modes (when you include kz variation) you can in principle estimate the Q. However, in practice, it is probably easier to calculate the resonant modes of a leaky cavity like this using Meep (our FDTD code) or some similar program -- that's what I almost always do. Because Meep supports absorbing (PML) boundaries, that turns the resonant peak into a single mode with a complex eigenvalue (and Meep has built-in functions to get the Q etc.). (Technically, the relationship of the "complex-frequency" leaky mode to the actual continuum of modes in the infinite system is quite tricky, as it is essentially a saddle-point approximation for the local field pattern rather than an eigenmode per se. But for the most part you don't have to worry about this subtlety.) Regards, Steven G. Johnson _______________________________________________ mpb-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
