On Fri, 17 Nov 2006, Vincent Paeder wrote:
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.
This has nothing to do with MPB vs. Meep, or any other computational package. It is a matter of physics (or mathematics). MPB is giving the correct answer to the physical question you are asking, and any other code will give the same answer to the same question.
If you have a slab that is *infinitely uniform* in the z direction and want to distinguish between different wavevectors in the z direction, the correct thing to do is to use a 2d computational cell and specify the desired out-of-plane wavevector.
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?
A slab of finite thickness is a completely different thing than what you are doing. If this is what you want, you are asking MPB the wrong question, which is why you are getting the wrong answer.
If you want a slab of finite thickness, the correct thing to do in MPB (or any other program) is to use a supercell, where you have a slab of your desired thickness, plus some distance of air (or whatever your substrate is) above/below the slab. The guided modes are then the ones whose wavevectors lie below the light line of the substrate/superstrate.
Because these guided modes are exponentially localized to the slab, whether you have periodic or some other boundary conditions in the vertical direction is exponentially irrelevant as you increase the vertical cell size (*without* increasing the slab thickness).
See also the Phys. Rev. B paper I mentioned in my previous message. See also the hole-slab.ctl example file included with MPB.
Steven _______________________________________________ mpb-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
