Re: Relationship between primitive cell andreciprocal lattice vectors

Steven,

Thanks for the response and the midterm/solution link. That problem and
the answer captured the subtlety very nicely. I think I have read most of
the "band folding" posts in the archive, but had an overly strict definition
of super-cell.

Bruce



"Steven G. Johnson" <[email protected]> wrote in message 
news:[email protected]...
>
> No it doesn't.  If the dielectric function is a multilayer film and
> hence is univariate, the problem can always be reduced to a 1d one
> because the other dimensions are separable.  In MPB, you would still
> specify a 1d unit-cell with two no-size dimensions, and off-axis
> propagation is specified simply by giving a k vector that has a
> component along one or both of the no-size directions.
>
> In fact, you *really* don't want to give a non-zero cell size along
> the invariant directions, because doing so will result in artificially
> folded bands.  (This is a common point of confusion.  I actually posed
> this as a question on the mid-term exam for my nanophotonics course
> last year.  See question 2 in: 
> http://www-math.mit.edu/~stevenj/18.369/spring07/midterm.pdf
>  and the solution in 
> http://www-math.mit.edu/~stevenj/18.369/spring07/midterm-sol.pdf)
>
> Your unit cell should be dictated by the periodicity of the structure,
> not by the propagation direction.
>
> Regards,
> Steven G. Johnson