Re: reflection from dielectric slab

"What I have done so far looks almost the same as the published data, i.e. a
sinusoid gradually decreasing in amplitude as slab thickness increases,
except the published data doesn't go above 1, whereas my results reach a
maximum of 1.0825 + 0.0714i at 0.14 landa."

Jim,

    Not following everything that you're talking about -- this seems like a
problem of just plotting the normalized values asoppoed to the calculated
values.

    Cheers

"jim jones" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
>
> "Phil Hobbs" <[EMAIL PROTECTED]> wrote in message
> news:[EMAIL PROTECTED]
> > jim jones wrote:
> > > Dear all,
> > >
> > > I am trying to calculate the reflection coefficient for a normally
> incident
> > > ray impinging on a slab of dielectric material.
> > >
> > > Thee reflection coefficient comprises of two components, a reflection
> from
> > > the front face (r12) and a reflection from the back face
(t12*r23*t21).
> r12,
> > > t12 etc are calculated using the fresnel equations: r12 =
> (n2-n1)/(n1+n2)
> > > t12 = 2n1 / (n1+n2), where n denotes the refractive index in each
> material.
> > > There is also a phase change to consider, this is e^(-j*2*k*d) where k
> is
> > > the wavenumber in the slab and d is the thickness of the slab.
> > >
> > > So far so good, when i put it all together i get the following
equation:
> > >
> > > RCoef = r12 - (t12*r23*t21*exp(-j2kd))
> > >
> > > Everything makes sense and looks ok untill I put real data into the
> > > equation. If I put n1 =1, n2=1.5 and n3=1 and vary the thickness from
0
> to
> > > 1wavelength, I get a result as one would expect where two minima occur
> at
> > > 0.25landa and 0.75landa.But, if I put n1 =1, n2 = square
root(2.5-0.16i)
> > > (which is the relative permativity of plywood) and n3  = iron (which
> makes
> > > r23 = 1) in and vary the width of the plywood slab I get a reflection
> > > coefficient greater than 1 at certain thickness'!! This is obviously
> > > incorrect but can anyone see where I have gone wrong??
> > >
> > > Many Thanks,
> > >
> > > Jim.
> > >
> > >
> > You picked the wrong Fourier transform sign convention.  Change the sign
> > of the imaginary part so that it produces loss instead of gain.
> >
> > Cheers,
> >
> > Phil Hobbs
> >
>
> Thanks for the reply Phil,
>
>
>
> I have split the phase component up into its real and imaginary parts and
> plotted each. As far as I can tell the results look ok, the real part
> produces a sinusoid from +1 to -1 and the imaginary part produces a steady
> decrease from 1 to about 0.5 over 1 landa. Also, if I do change the sign
of
> the complex part I get a very rapid increase which definitely looks wrong.
>
>
>
> As suggested in the previous post I got a book on the subject, Optics, 2nd
> Ed. Hecht, the treatment of this problem has been covered in a very
similar
> way, however, I have noticed some mention of an absorption term, I wonder
if
> that applies to my problem?
>
>
>
> Finally, the reason I am using the refractive index values mentioned in my
> original post is because I have some published data to compare my results
> with. What I have done so far looks almost the same as the published data,
> i.e. a sinusoid gradually decreasing in amplitude as slab thickness
> increases, except the published data doesn't go above 1, whereas my
results
> reach a maximum of 1.0825 + 0.0714i at 0.14 landa.
>
>
>
> Any other ideas?
>
>
>
> Cheers for the help so far,
>
>
>
> Jim.
>
>