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, mpb-discuss-requ...@ab-initio.mit.edu wrote:
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Today's Topics:
1. Difference beetween methods (Rafael Gonzalez)
2. Re: Difference beetween methods (Manish Kumar)
----------------------------------------------------------------------
Message: 1
Date: Fri, 10 Aug 2012 15:18:52 -0500
From: Rafael Gonzalez <rafael.g...@gmail.com>
To: mpb-discuss <mpb-discuss@ab-initio.mit.edu>
Subject: [MPB-discuss] Difference beetween methods
Message-ID:
<CAJLkPfT-iq_HK-0T=dygrxxp1pskkkjxu8ycclcfqcxeae8...@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 <mail2manee...@gmail.com>
To: Rafael Gonzalez <rafael.g...@gmail.com>, mpb-discuss
<mpb-discuss@ab-initio.mit.edu>
Subject: Re: [MPB-discuss] Difference beetween methods
Message-ID:
<caostkv7k01a0ukq5rrr80ci-tos4xz4ojzvztzffkbq+p4c...@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/mpb-discuss@ab-initio.mit.edu/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 <rafael.g...@gmail.com> 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
mpb-discuss@ab-initio.mit.edu
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--
Dr. Sebastian Schulz
Postdoctoral Fellow
Department of Physics
University of Ottawa
ssch...@uottawa.ca
Tel: 613 562 5800 7139
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