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LASER INTERFEROMETER GRAVITATIONAL WAVE OBSERVATORY
LIGO Laboratory / LIGO Scientific Collaboration
LIGO-T080131-02-E LIGO July 17, 2008
Pedestrian’s guide of MIT FFT 08
Hiroaki Yamamoto
Distribution of this document: LIGO Science Collaboration
This is an internal working note
of the LIGO Project.
California Institute of Technology LIGO Project – MS 18-34 1200
E. California Blvd.
Pasadena, CA 91125 Phone (626) 395-2129 Fax (626) 304-9834
E-mail: [email protected]
Massachusetts Institute of Technology LIGO Project –
NW17-161
175 Albany St Cambridge, MA 02139 Phone (617) 253-4824 Fax (617)
253-7014
E-mail: [email protected]
LIGO Hanford Observatory P.O. Box 1970
Mail Stop S9-02 Richland WA 99352 Phone 509-372-8106 Fax
509-372-8137
LIGO Livingston Observatory
P.O. Box 940 Livingston, LA 70754
Phone 225-686-3100 Fax 225-686-7189
http://www.ligo.caltech.edu/
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1 What’ new in the latest release
1.1 Release July 17, 2008
The input beam can be specified either by a mask on a nominal
Gaussian beam or by the amplitude of a Gaussian beam itself.
In the IFO specification file, one can specify the mask or beam
by the file name where input beam characteristics is defined.
Postion & angle error of excitation laser beam:
dx,dy,theta(microrad),phi(deg) 0.0d0 0.0d0 0.0d0 0.0d0 FLDDATA.dat
or MSKDATA.dat or keep it blank to use the original Gaussian
beam
2 Introduction
This is a documentation explaining how to use MIT FFT 08. MIT
FFT 08 is based on the static IFO simulation using FFT originally
developed by B. Bachner at MIT mainly for designing LIGO I IFO. The
code was modified by H. Yamamoto mainly to make the program capable
of simulating IFO with thermal deformation.
This document does not cover details of the code nor does not
cover all possible options of customization. This covers minimal
information how to study the mode (mis)matching effects and thermal
deformation and TCS designs.
MIT FFT 08 will be taken over by SIS, a new stationary IFO
simulation code, by the end of 2008. At this time, Spring of 2008,
studies of mode matching and thermal deformation of LIGO I and
eLIGO need full IFO simulations, and SIS is not capable of
simulating an entire IFO. This document is to fulfill that temporal
needs.
3 How to run
The source code is written in standard Fortran. The code,
ffttW08.f, was tested to be compiled by gfortran, part of the gnu
compiler collection, version 4.1.2. Only additional package needed
is FFTW, fft library developed at MIT. The link command is given at
the top of the source code. A binary executable is available on a
Caltech LIGO machine at /home/hiro/bin/FFTW08.go, which runs on 64
bit machines, like menkar.ligo.caltech.edu. To use the program, you
need the definition package MITFFT08.tar.gz. That package has the
following files. FFTrun, LLO4K_IFO.dat, CR.dat, SBP.dat, SBM.dat,
thermal/refl.dat, trans.dat, ann_trans.dat.
LLO4K_IFO.dat contains the definition of an IFO, and this file
is setup for L1 IFO. CR, SBP and SBM are files specific to CR,
upper and lower SB. Directory “thermal” contains data files needed
for thermal deformation simulation prepared by Phil Willems. FFTrun
is a short script to run the program in sequence for CR and two
sidebands. It is necessary that CR simulation is done first. During
this run, the IFO is locked, and the cavity lengths are stored in
res0.dat. This result is used for SB runs.
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To execute the code, type source FFTrun
4 Outputs
The field distributions are stored in xxx.re and xxx.im files.
Xxx.re contains the real part and xxx.im contains the imaginary
part of the field. To use the data, the following is an example
using matlab ref = load(‘eref_unbal_carr.re’) +
i*load(‘eref_unbal_carr.im’);
ref = rehape( ref, 128, 128 ).’;
dx = 0.35/128; xl = (-0.35/2+dx/2):dx:(0.35/2-dx/2);
Once loaded like this, ref(ix,iy) is the field at x = xl(ix) and
y = xl(iy).
Three files, dcr1.out, dsbp1.out and sdbm1.out, contain summary
information for each frequency. ModalInfo.out has the beam size and
the inverse of the field radius of curvature used for the mode
decomposition in the following order.
AR side of RM
HR side of RM
RM side of BS
Dark port side of BS
AR side of ITMX
HR side of ITMX
AR side of ETMX
AR side of ITMY
HR side of ITMY
AR side of ETMY
res0.dat, created by CR run, has the information of locked
lengths. This data is used when simulating the IFO without
locking.
5 Thermal effect and thermal compensation
When an ITM is heated either by the main NdYAG laser or by TCS
CO2 laser, a lens is induced by the spatial non uniformity of the
refractive index. The ROCs of LIGO I mirrors were chosen assuming a
certain absorption rate in ITMs. It turned out that the point
choice does not work well.
The mode in the arm is well defined by ROCs of ITM and ETM,
which is affected little by the thermal effect. When there is no
thermal effect, the ROC of the field coming out of the arm is
ROC(ITM) / 1.45 ~ 10km. ROC(RM) is ~15km, so the mode does not
match. When the thermal effect induces the lens in the ITM, the net
lens effect changes as follows:
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�
ϕ(r) = − n0 −12RITM
r2 + 12Rthermal
r2
= −nthermal −12RITM
r2
nthermal = n0 −RITMRthermal
The first term on the rhs in first line is the lens effect of
the cold ITM, and the second term is the thermal effect. As is
written in the second line, the thermal effect can be interpreted
as the change of the refractive index. The role of TCS is to
properly adjust the effective refractive index to match the ROC of
the field on the AR side of ITM to match with ROC(RM). Because LIGO
I Michelson cavity is short, using a near field approximation, the
requirement of TCS is
�
ROC(ITM) /neffective = ROC(RM)orneffective = ROC(ITM)
/ROC(RM)
The thermal effect, Rthermal, is induced by both NdYAG and CO2
heating. Because ROC(ITM) is nearly equal to ROC(RM), the purpose
of TCS is to adjust ITM transparent, neffective = 1. The input beam
should be set to match to this mode defined by RM and ITM with
thermal effect. The package has three thermal data files,
trans.dat, ann_trans.dat and refl.dat.
Figure 1 Thermal deformation data created by Phil Willems.
trans.dat is the transmission optical phase induced by a
Gaussian beam, either by NdYAG or CO2, ann_trans.dat is the one
induced by an annular heating. refl.dat is the surface deformation
by a Gaussian beam. They should be multiplied by the power actually
absorbed. The thermal effect, both NdYAG and CO2, will be included
in the simulation using these maps with proper weights.
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The dashed line in the figure is a second order polynomial fit
of the transmission phase by an Gaussian beam within radius <
4.5cm. Reffective = 1700 / Pabsorbed, so
�
neffective = n0 −RITMRthermal
= n0 −RITM1700
Pabsorb
In order to make neffective to be close to 1, Pabsorb ~ 0.05W.
This is just a guide.
The thermal deformation is not a pure lens as is seen in the
figure, i.e., the transmission deformation cannot be fit by a
simple power term. But, for a simple case study, it is a reasonably
approximation.
6 How to configure
In the following, red letters are important ones and
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res0.dat Read from/Do (for lenchange/fixedlen case) Asymm.
Length Optim. Run (Y=1,N=0)? 0
6.3 LLO4K_IFO.dat
Relevant lines related to item N is marked by “ 7cm before the
beam center is offset.
for ix = 1 , 128 x = -0.35/2+0.35/128*(ix-0.5); for iy = 1 , 128
if x > 0.07 Data(ix,iy) = 0; else Data(ix,iy) = 1; end end
end
The data file contains the real and imaginary part of the
amplitude in one line as follows. dataReal(1,1) dataImag(1,1)
dataReal(1,2) dataImag(1,2)
… dataReal(1,n) dataImag(1,n)
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dataReal(2,1) dataImag(2,1) dataReal(2,2) dataImag(2,2)
… dataReal(n,n) dataImag(n,n)
(7) The beam offset is applied to these input data as well.
I.e., if the above clipping is used, and if
dx is set to be 1cm, the slipping region moves toward +x by 1cm.
So the incoming beam becomes a Gaussian beam with the center at
x=1cm and the clipped at x = 8cm.
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Input data for simulation of full LIGO interferometer
===================================================== -------
^^^ Mrback ^^ | ^^ | L5 | | ^ | E3 | \ | / Mfr --- ----- | Mrecyc
L3 | Mft Mtback | / Ein | / L1 |/ L2 |/ L4 \ | ------->|
|--------------/-------||------------| | Mbs | v Easymm \_/ ***
START HERE ***************************************** Index of
refraction for mirror substrates (depends upon Wavelength &
Materials): RM ITMX ITMY BS 1.45 1.450 1.45000 1.45 0 is Refl-Side
Concave, USE "1.11d+15" to mean "FLAT") for Mrecyc, Mft, Mfr,
Mtback and Mrback: 15780.0d0 14760.0d0 14520.0d0 8730.0d0 8720.0d0
-163.0d3 CARRIER Beam Spot Size, Curvature-Radius, at ON-LINE
FP-Input Mirror: (USE "1.11d+15" to mean "FLAT"; Curv.Rad.>0
means waist INSIDE On-line Arm Cav): 0.0387400 15780
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Propagator Momentum-Space Cutoff & Apodization Info, for
Anti-Aliasing: Highest P-Space Pixel With No Aliasing
(Prop1,Prop2,Prop3,Prop4,Prop5): 1000 1000 1000 9 9 Highest P-Space
Pixel With Real Physics (Prop1,Prop2,Prop3,Prop4,Prop5): 1000 1000
1000 25 25 Initial Reflectivity of Mrecyc, Preliminary DelRef1,
Optimize(lenchange runs)/Use Optim Results(fixed len's)? (Y=1, N=0)
0.9729 0.0 0
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Binary Orientation of Beamsplitter (1 if Ref. Coating faces
On-Line Cav., 0 if Ref. Coating faces Off-Line Cav.): 0 Maximum #
of relaxation iter's, and max. integ. errors (recycling cav,
cav4,5): 1500 6.0D-8 1.5D-8 1.5D-8 Mirror Specification Section:
(max 38 characters for all mirror filenames!)
---------------------------- Names of the files containing mirror
PHASE variations: Reflections from the reflective side:
------------------------------------ (Codes: "+" = all zeroes)
Recycling Mirror : + On-line input mirror : a34, 2f12.7
thermal/refl.dat 0.060
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Beamsplitter Phase Maps: ----------------------- (Code #1: "+" =
all zeroes) Reflection from reflective side: + Transmission from
reflective side: + (Codes #1,#2: "+", "=" = Same T map as from
Refl. Side) Transmission from anti-reflective side: + (Codes #1,#3:
"+", "-" = Make Phase The Appropriate Conjugate of the Other R's
& T's) Reflection from anti-reflective side: - Names of the
files containing mirror AMPLITUDE variations: Reflections from the
reflective side: ------------------------------------ (Codes: "+" =
all unity) Recycling Mirror : + On-line input mirror : + Off-line
input mirror : + On-line FP back mirror : + Off-line FP back mirror
: + Transmissions: ------------- (Codes: "+" = all unity, "L" =
calc T from Rref by making losses constant) Recycling Mirror : +
On-line input mirror : + Off-line input mirror : + Reflections from
the anti-reflective side: -----------------------------------------
(Codes: "+" = all unity, "L" = calc Rar from T by making losses
constant, "=" = make equal to Rref amp variation array (with minus
on antiref)) Recycling Mirror : +
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On-line input mirror : + Off-line input mirror : + Beamsplitter
Amplitude Maps: --------------------------- (Code #1: "+" = all
unity) Reflection from reflective side: + (Codes #1,#2: "+", "L" =
calc Tref from Rref by making losses constant) Transmission from
reflective side: + (Codes #1,#2,#3: "+", "L" = calc Tar from Rref
by making losses constant, "=" = Same T map as from Refl Side)
Transmission from anti-reflective side: + (Codes #1,#2,#3: "+", "L"
= calc Rar from Tar by making losses constant, "=" = Same R map as
from Refl. Side) Reflection from anti-reflective side: + Output
Field Specification Section: ----------------------------------
File names of output fields. First real part, then imaginary. (max
38 chars) For field Ein (see diag. at top): phiin_unbal_*.re
phiin_unbal_*.im For field E1: eins_unbal_*.re eins_unbal_*.im For
field E2: eFPint_unbal_*.re eFPint_unbal_*.im For field E3:
eFPinr_unbal_*.re eFPinr_unbal_*.im For field Esymm:
esymm_unbal_*.re esymm_unbal_*.im For field Easymm:
easymm_unbal_*.re easymm_unbal_*.im For field Eref: eref_unbal_*.re
eref_unbal_*.im For field Epox:
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epox_unbal_*.re epox_unbal_*.im For field Epoy: epoy_unbal_*.re
epoy_unbal_*.im For field Epob: epob_unbal_*.re epob_unbal_*.im
