Maybe to add to the discussion: The behavior in the 2-dimensional case is
as expected. There the (run-te) modes have Hx=Hy=0 and the (run-tm) modes
have Ex=Ey=0 (as expected!).
Could it be that mpb is using the other convention in 1-dimensional
calculations?
For the record the version I use is:
MIT Photonic Bands 1.4.2, Copyright (C) 1999-2001 by MIT.
Using libctl 3.1 and Guile 1.8.7.
Running on Ubuntu 10.04.1 LTS
Regards,
Fitzgerald
On Fri, 17 Sep 2010 13:19:14 +0200, <[email protected]> wrote:
> 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
>
>
> _______________________________________________
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> [email protected]
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