On Thu, 2006-11-09 at 11:15 -0500, Steven G. Johnson wrote: > Your assumptions are incorrect. The 3d case *should* have additional > bands compared to the 2d case. > > In two dimensions, you are only looking at light propagating in the plane > (for kz = 0). > > When you include a finite cell size S in the z direction, then you are > including out-of-plane wavevectors kz + 2*pi*n/S for all integers n, by > the periodic boundary conditions. These out-of-plane wavevectors are what > are giving you your additional states, which depend on S. This is not a > numerical effect, it is a physical consequence of the question you are > asking MPB to solve. > > You can think of this as the "folding" into the finite Brillouin zone of > the vertical periodicity S (recall that MPB uses periodic boundary > conditions). (In the 2d case where S=0 the Brillouin zone in the vertical > direction is infinite and there is no folding.) > > Or, if you like, you can think of this in terms of higher-order > "standing-wave" modes in the vertical direction. That is, the vertical > mode profile need not be constant, it can be cos or sin of 2*pi*n/S for > any n. > > See e.g. my paper in Phys. Rev B vol. 60, p. 5751 (1999) for further > discussion of the consequences of slab thickness. Or some of my > tutorial presentations at ab-initio.mit.edu/photons/tutorial > > Cordially, > Steven G. Johnson > > _______________________________________________ > mpb-discuss mailing list > mpb-discuss@ab-initio.mit.edu > http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
Thanks for your most helpful answer. I've tried the case of a slab of silicon cylinders in n=1.5 medium (the previously attached ctl file), and I also end up with folded bands. So I guess MPB isn't most appropriate for treating slabs, or is there a way to discriminate the bands arising from the imposed periodicity? If not I think I'll allow myself to have a bit of fun with MEEP. I'm mostly interested in superprism effects and the like, so I don't care much about the bandgap. However the band profiles do matter. On the band diagrams in your paper, it looks like there's more impact in the higher frequency bands. Are they also a consequence of the periodicity assumptions of the PWEM or are they really due to the slab finite thickness? _______________________________________________ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
