Re: 3D doubts (partly cleared up)

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