On Jul 11, 2011, at 12:06 PM, mf wrote:
Has anybody performed an analysis of the PML efficiency at oblique
incidence ? I am considering a band gap material, and in the gap
region the transmission looks fine (1e-6 to 1e-8 values), but the
reflection oscillates with the frequency. The oscillation are around
the correct value of 1 and their amplitude is about 0.1. My guess is
that there is some effective cavity between the sample and the PML
which give rise to the oscillations. Their amplitude decreases as
with increasing resolution.
(I assume that you have uniform medium, then a sample of periodic
bandgap medium, then uniform medium, with PML in the uniform media.)
An easy way to check whether this has anything to do with the PML is
to increase the distance between the sample and the PML; if the
oscillations are due to PML reflections then this will increase the
frequency of the oscillations.
The decay coefficient within any PML is well-known to have a
cos(theta) factor, where theta is the incidence angle, which makes the
decay become slower as you approach glancing incidence. However, this
is true even at infinite resolution, so if you are seeing an effect
that decreases with increasing resolution then it is something
different. e.g. it may be transition reflections, which you can also
decrease by making the PML thicker instead of increasing the resolution.
Transition reflections also increase as you approach glancing
incidence, because at glancing incidence the phase-velocity mismatch
between incident and reflected waves goes to zero. See e.g. equation
(13) in our paper:
http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-15-11376
The next question is why you would be getting glancing-angle waves.
Glancing-angle waves will occur right after the onset of each
diffracted order. However, for normal-incident light, the first
diffracted order occurs when the wavelength drops below the period,
but since you say you are looking around the band gap then I'm
guessing you are operating at a longer wavelength than this.
Merely oblique waves that are are not approaching glancing incidence,
however, should not normally be a problem. Is there some reason why
you think you may have near-glancing waves?
--SGJ
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