Re: Difference beetween methods (Rafael Gonzalez) and Re: Difference beetween methods (Manish Kumar)

Hello,

my comments are to both of you.
When using 2D calculations a lot of people apply an effective index 
method, to use a 2D calculation to model a final 3D structure. In this 
case the index that is being use for the high index material is not the 
refractive index itself, but depends on the slab thickness.
In most cases this does not affect the shape of the dispersion diagram 
very much, but can significantly alter the actual values (i.e. 
frequencies) of bands and band gaps.
Are you both sure that the papers you are trying to reproduce are not 
applying this method. If it is unclear from the paper I would contact 
the authors directly to find out if they where using this method or not.

I hope this helps

Sebastian Schulz



On 11/08/2012 12:00, [email protected] wrote:
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>     1. Difference beetween methods (Rafael Gonzalez)
>     2. Re: Difference beetween methods (Manish Kumar)
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> ----------------------------------------------------------------------
>
> Message: 1
> Date: Fri, 10 Aug 2012 15:18:52 -0500
> From: Rafael Gonzalez <[email protected]>
> To: mpb-discuss <[email protected]>
> Subject: [MPB-discuss] Difference beetween methods
> Message-ID:
> 	<CAJLkPfT-iq_HK-0T=DyGRxXP1PskkkjXu8YCCLCFqCXEaE81ow@mail.gmail.com>
> Content-Type: text/plain; charset=UTF-8
>
> Hello
>
> I'm trying to reproduce a paper on bandgaps for 2D lattices. These
> authors report using a FEM method. I understand this approach is
> different from the one that MPB uses. And so are the results. I get
> very similar in shape dispersion diagrams but the bandgaps reported by
> them are completely different. I thought it could be provoked for ther
> lack of resolution of the simulation I ran, but the same results were
> obtained. I also changed the cell size for the averaging and the block
> size of the eigen solver but none of these parameters seemed to be the
> reason of the discrepancy. I also thought it could be the difference
> of the approaches to solve the eigenvalue problem, but I guess that a
> given geometry must have a unique dispersion diagram. Numeric errors
> are to be expected but I guess either one of us is doing something
> wrong. Anyone has any clue?
>
> Best regards
>
>
>
> ------------------------------
>
> Message: 2
> Date: Sat, 11 Aug 2012 10:57:17 +0900
> From: Manish Kumar <[email protected]>
> To: Rafael Gonzalez <[email protected]>,	mpb-discuss
> 	<[email protected]>
> Subject: Re: [MPB-discuss] Difference beetween methods
> Message-ID:
> 	<CAOstkv7K01A0uKq5Rrr80ci-TOs4XZ4oJzVzTZFfKBQ+p4CcJw@mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
>
> Hello MPB users,
>
> To add on to Rafael's query I had problems in matching results of a paper
> which does calculations using plane wave expansion method itself. I had
> posted my query and is in archive unanswered till now :(
> http://www.mail-archive.com/[email protected]/msg00854.html
>
> I am copying my same query here as well:
>
> I tried to reproduce the band-diagram results of a famous paper from *M*. *
> Notomi* :  *Phys*. *Rev*. *B* 62, 10696 (*2000*)
> In this paper figure 7(b) shows a band-diagram of hexagonal pillars of GaAs
> (n = 3.6) rods of radius 0.35a in air (n = 1).
> It was very easy to modify the mpb example tri-rods.ctl to do the same
> diagram. I tried but could not match the band diagram as given in the paper
> !
> Appearance wise both results look very similar on first hand but closer
> inspection shows the difference.
> In the paper e.g. band 5 goes from frequency value 0.56 to *0.635* (as
> explicitly mentioned in explanation of Fig. 6 in the same paper) but in my
> calculated values using mpb i get them in the range 0.56 - *0.615* (the
> upper frequency value doesn't match).
>
> As far as i know the results of said paper were not calculated using mpb
> then is this discrepancy arising because of that ? If so, then how to make
> sure which result is more accurate ?
>
> I'm just putting my .ctl file below for all to have a look and suggest if i
> made any mistake in setting up .ctl file itself or i'm missing out on
> something which may improve my result.
>
> Any help in this will be much appreciated.
>
> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
> (set! num-bands 8)
>
> (set! geometry-lattice (make lattice (size 1 1 no-size)
>                           (basis1 (/ (sqrt 3) 2) 0.5)
>                           (basis2 (/ (sqrt 3) 2) -0.5)))
> (set! geometry (list (make cylinder
>                         (center 0 0 0) (radius 0.35) (height infinity)
>                         (material (make dielectric (epsilon 12.96))))))
>
> (set! k-points (list
>                       (vector3 (/ -3) (/ 3) 0) ; K
>               (vector3 0 0.5 0)        ; M
>                       (vector3 0 0 0)          ; Gamma
>               (vector3 (/ -3) (/ 3) 0) ; K
>               ))
> (set! k-points (interpolate 4 k-points))
>
> (set! resolution 64)
>
> (run-te)
>
> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
>
>
>
> On 11 August 2012 05:18, Rafael Gonzalez <[email protected]> wrote:
>
>> Hello
>>
>> I'm trying to reproduce a paper on bandgaps for 2D lattices. These
>> authors report using a FEM method. I understand this approach is
>> different from the one that MPB uses. And so are the results. I get
>> very similar in shape dispersion diagrams but the bandgaps reported by
>> them are completely different. I thought it could be provoked for ther
>> lack of resolution of the simulation I ran, but the same results were
>> obtained. I also changed the cell size for the averaging and the block
>> size of the eigen solver but none of these parameters seemed to be the
>> reason of the discrepancy. I also thought it could be the difference
>> of the approaches to solve the eigenvalue problem, but I guess that a
>> given geometry must have a unique dispersion diagram. Numeric errors
>> are to be expected but I guess either one of us is doing something
>> wrong. Anyone has any clue?
>>
>> Best regards
>>
>> _______________________________________________
>> mpb-discuss mailing list
>> [email protected]
>> http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
>>
>
>

-- 
Dr. Sebastian Schulz
Postdoctoral Fellow
Department of Physics
University of Ottawa
[email protected]
Tel: 613 562 5800 7139