On Mon, 22 May 2006, Chad Husko wrote:
I'm interested in using the first excited state (odd) of a standard
W1 Photonic Crystal Waveguide (PCWG). I'm trying to think of ways
to excite that mode.
Some caveats
- I can't use symmetric excitations (I think) because I'm going to also
include the ground state mode which has opposite (even) symmetry.
You can't use a symmetric excitation regardless, because an even source
will never excite an odd mode.
Why not just use an odd source? e.g. just put a couple of dipoles on
either side of the axis, with amplitudes +1 and -1?
Technically, the first excited mode of a W1 waveguide has even symmetry
(with respect to both mirror planes), whereas the fundamental mode has odd
symmetry. You have to think about how the vector fields transform as a
whole. If you look at a single component, say Hz, you will be
misled...especially for the magnetic field, because it is a pseudovector,
so it is multipled by an extra -1 factor under mirror flips. See the
discussion of vectors and pseudovectors in the section "Exploiting
symmetry in Meep" of the Meep manual/wiki.
General question: What are the sorts of issues associated with using
nonlinearities and complex fields? Is there a reference to read on
this?
Complex fields aren't physical...this is classical electromagnetism, not
quantum mechanics.
The only reason that one can use complex fields is when one has a linear
system, in which case one can always take the real part at the end to get
the physical result. When you have nonlinearities, the physical
interpretation is much more non-obvious.
Note, however, that specifying a complex amplitude does not imply complex
fields. Unless you set force-complex-fields? to true, the the real part
of the source is taken... thus, the complex amplitude is just a phase
shift of the real (sinusoid) source.
Steven
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