I also think I am doing something wrong. Would you be so kind to point me
where the mistake is?
I am modeling a planar waveguide which has a finite thickness in the
z-direction and is infinite in the xy-plane. To model this I use a
one-dimensional computational cell along the z-direction and look for the
propagation in the x-direction.
Now for the polarization/symmetry part:
TE polarization has the electric field confined to the xy-plane.
The electric field is given by
Ey(x,z,t) = Em(z) * exp[i(w*t-k*x)]
Hx and Hz are simple functions of Ey. Also, Ex = Hy = Ez = 0.
TM polarization has the magnetic field confined to the xy-plane.
The magnetic field is given by
Hy(x,z,t) = Hm(z) * exp[i(w*t-k*x)]
Ex and Ez are simple functions of Hy. Also, Hx = Ey = Hz = 0.
Em(z) and Hm(z) are the mode profile functions and are even for m =
0,2,4,... and odd for m = 1,3,5,...
When I now run the .ctl file given below with (run-te), (run-tm); MPB
outputs zevenfreqs and zoddfreqs. When I look at the fields at k = (1,0,0)
I find the following:
1st zeven - 1st TE mode
2nd zeven - 2nd TM mode
3rd zeven - 3rd TE mode
1st zodd - 1st TM mode
2nd zodd - 2nd TE mode
3rd zodd - 3st TM mode
Clearly my TE/TM convention is different from the one MPB uses. What is
this other convention?
Your help is highly appreciated,
Thanks in advance,
Fitzgerald
;==========================================================================
; define geometry
(set! geometry-lattice (make lattice (size no-size no-size 10)))
(set! geometry (list
(make block
(material (make dielectric (epsilon 12.1)))
(center 0 0 0)
(size infinity infinity 1)
)
))
; define sample space
(set! k-points (interpolate 49 (list (vector3 0 0 0) (vector3 1 0 0))))
; define simulation resolution and bands
(set! resolution 256)
(set! num-bands 3)
(run-te (output-at-kpoint (vector3 1 0 0) output-efield output-hfield))
(run-tm (output-at-kpoint (vector3 1 0 0) output-efield output-hfield))
;==========================================================================
On Fri, 17 Sep 2010 01:45:18 -0400, "Steven G. Johnson"
<[email protected]> wrote:
> On Sep 16, 2010, at 5:44 AM, <[email protected]> <[email protected]> wrote:
>> I am trying to calculate the dispersion diagram for a photonic slab
>> waveguide. For this I use a 1-dimensional computational cell in the
>> z-direction. The waveguide itself is in the xy-plane and has a
>> thickness of
>> 1. In the attachments you find the Scheme file I used and a simple
>> bash
>> script with the commands I used to execute it.
>>
>> What I expected:
>> (run-zeven) yields bands TE0, TE1, TE2, ...
>> (run-zodd) yields bands TM0, TM1, TM2, ...
>>
>> What I found:
>> (run-zeven) yields bands TE0, TM1, ...
>> (run-zodd) yields bands TM0, TE1, ...
>>
>> What am I doing wrong?
>
> Probably you are just confused because there is more than one
> convention for "TE" and "TM" in the literature. The TE you are
> probably thinking of corresponds to run-yodd and the TM you are
> probably thinking of corresponds to run-yeven.
>
> The key thing is to figure out what is transverse to what in your TE/
> TM convention, and what symmetry that corresponds to. (See chapter 3
> of our photonic-crystals book, ab-initio.mit.edu/book, to understand
> how polarization corresponds to symmetry.)
>
> --SGJ
>
>
> _______________________________________________
> mpb-discuss mailing list
> [email protected]
> http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
_______________________________________________
mpb-discuss mailing list
[email protected]
http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
