Re: how to find wavelength in matlab

Rune Allnor wrote:
On 14 May, 23:12, "R.H. Allen" <kka...@xxxxxxxxxxx> wrote:
Rune Allnor wrote:
On 14 May, 06:59, rober...@xxxxxxxxxxxxxxxxxx (Walter Roberson) wrote:
(Say -- that "invisiblity" stuff that uses negative index of refractions:
does that imply that light travels faster than c, since traditional
definitions of speed in a media are framed in terms of the index of
refraction ?)
I have no idea what a "negative refraction index" means in terms
of EM propagation, but I once ran into an imaginary reflection angle.
I used to work with data that propagated as normal modes. Some of
these modes -- the ones I was interested in -- were caused by some
particular interaction between a curved wavefront and the plane
sea bed. The curious thing was that these modes satisfied the
dispersion equation,
w^2/v^2 = k_r^2 + k_z^2
but they travelled very slowly. In fact, k_r^2 > w^2/v^2,
meaning that k_z^2 < 0 and the vertical wavenumber (or,
almost equivalently, the wavelength) becomes imaginary.
So to understand what was going on, I had to find out
how to deal with questions like
"What does an imaginary wavelength look like?"
"That's easy!" my boss said, "an imaginary wavelength
appears when a real wave is reflected with an imaginary
angle."
An "imaginary angle" is, to my mind, not a lot better
than an "imaginary wavelength," so I decided to just
stick with the textbook explanation, using terms like
"evanescent wave" and "imaginary wavenumber."
This is a little off-topic, but I would be interested to know more about
how you dealt with this imaginary angle. I once worked on a problem that
involved optical scattering in solid media. As I recall, the issue arose
when I followed a ray through an absorbing solid medium with
non-parallel planar interfaces. Because the medium was absorbing, the
angle had to be complex once the ray entered the medium in order to
satisfy Snell's law. As long as the interfaces were parallel, this was
no big deal -- the ray would reach the second interface and Snell's law
would ensure that the angle was real as the ray exited the medium.
However, when the interfaces were not parallel Snell's law left me with
a complex angle as the ray exited, and that made no sense to me.

I had similar issues when I tried to address scattering within the solid
-- if a ray with a complex angle is scattered, do I randomize the real
part of the angle? The imaginary part? Both? I was never able to find a
satisfactory answer to any of these questions and eventually dropped the
project.

I ended up with shutting the whole concept of an "angle" out of the
discussion. The experimental set-up was a linear array of sensors
which were mounted on the sea floor, and a pulse signal source
which was set off on an axis colinear with the array axis.

In a cylindrical (r,z) geometry, the source was set off at (0,zs)
and the array was mounted along a radial (za,r1)...(za,rN).

If the quasi-explosive source was set off near the sea floor,
the acoustic pulse front which hit the sea floor was still curved
and excited the Scholte wave, which was what I was interested
in. The Scholte wave then popagated along the radial -- and
along the array -- in the horizontal plane and from a known
direction. But it propagated very slowly.

I could only observe the wave along the horizontal plane,
so I ended up treating the horizontal component of the
propagation vector, k_r, as a wave as usual. The vertical
part k_z I only needed for the maths, so I settled for the
indirect expression k_z^2 = w^2/v^2 - k_r^2, and never
really attempted to wrap my mind around any "physical"
interpretations. As long as the maths worked and the
data anlysis made sense, I saw no reason to get
bogged down with philosophy.

I see. I don't think it would really have helped with my problem, but thanks for elaborating nonetheless.
.

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