On Apr 21, 2008, at 12:37 AM, Bruce Burckel wrote: > > As a prelude to studying a larger problem, I have been knocking > around a toy > problem with MPB and have confirmed some cloudy areas in my > understanding of > the program. I would like to study the behavior of a "nominally" 1-D > bragg > stack with variable angle with respect to the x-axis in the unit > cell. I say > nominally 1-D because with either 0 degrees of tilt (horizontal > slabs) or 90 > degrees of tilt (vertical slabs) the problem is truly 1-D, but with > angles > between these two, the problem becomes 2-D in the sense that the > unit cell > requires finite dimensions in both x and y. To keep things consistent > regardless of the tilt angle, I would like to study the problem as a > 2-D > problem for all angles.
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 _______________________________________________ mpb-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
