On Mon, 16 Jul 2007, Andrea Locatelli wrote: > I'm trying to simulate an asymmetric PC slab. I'm using the > display-zparities function in order to distinguish quasi-even and > quasi-odd modes, but I also need to discriminate between TE and TM > modes, because my slab waveguide doesn't support TM modes... To this > goal, I'm using the output-dpwr function, I'm extracting the > d-energy-components line through grepping, then if the in-plane > component is larger than the out-of-plane one I consider that as a TE > mode, and viceversa for the TM modes.
What you want to know is what modes your slab waveguide mode is allowed to couple to. This is not determined by the fraction of the field in particular directions, since there are no purely polarized modes in a PC slab. The real thing that determines what modes can couple is symmetry. (In PC slabs, I prefer to talk about "TE-like" and "TM-like" modes, emphasizing that this is just a qualitative description; the only rigorous mode classification is by symmetry.) Three things matter here. First, your input light....I'm assuming that is from a slab waveguide (i.e. no periodic holes, just a uniform slab on a substrate). Second, your crystal modes. Third, the interface of the crystal. I'm supposing you have a slab parallel to the xy plane, so that z is perpendicular to the slab and your substrate. Let me also suppose that you have light incident in the y direction. When you say "TE" and "TM" modes of your slab waveguide, this is really a consequence of the fact that y=0 is a mirror symmetry plane. Modes that are odd with respect to this mirror symmetry plane are usually called "TE" in the classic waveguide literature (with electric field purely in the y direction), while modes that are even are called "TM" (with magnetic field purely in the y direction). In the photonic crystal, you have no purely polarized modes, but you may still have a y=0 mirror symmetry plane. First, I'm assuming that your crystal interface is still mirror symmetric. Second, I'm assuming that the input light is normal incident on the crystal, so that the surface-parallel wavevector component k=0 does not break the symmetry. In this case, you can only couple to modes in your PC slab that (1) have the same (zero) surface-parallel wavevector component and (2) have the same symmetry with respect to the y=0 mirror plane. (You might be tempted to check the symmetry with respect to y=0 by using display-yparities, but this won't work if you are using a triangular lattice...display-yparities only works if one of the lattice vectors is in the y direction and the other two lattice vectors is perpendicular.) If the y=0 symmetry is broken for any reason, either because the crystal interface does not have a mirror plane or because the light is not normally incident, then all bets are off. There is no longer any rigorous selection rule that will prevent you from coupling to certain modes. Of course, you still couple to some modes more strongly than others, but computing this coupling coefficient exactly is not possible with MPB (there are some approximations you can use, but an exact calculation requires that you take evanescent modes into account). Regards, Steven G. Johnson _______________________________________________ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
