Transcript Preliminary length sensing system for Advanced Virgo

Automated simulations:
choosing modulation frequencies
à la Advanced LIGO
Stefan Hild, M.Mantovani, A.Perreca and A. Freise
Advanced Virgo meeting, August 2008
Outline
 Context and Motivation for automated detector design.
 A preliminary length sensing and control scheme for
Advanced Virgo a la Advanced Ligo
 OSD-Tool functions: an easy way to get an optimized detector
configuration.
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S. Hild
Optimizing the mirror ROCs
Choosing the optimal modulation frequencies
Finding the optimal length of the Power Recycling cavity
Choosing the Schnupp length
Finding the optimal length of the Signal Recycling cavity
Advanced Virgo, 15th of August 2008
Slide 2
The context of this work
 THE FACT: One deliverable of
my postdoc position is a
preliminary length sensing
and control scheme.
 THE HISTORY: When my
project was granted and
started … there were no
subsystems and no Advanced
Virgo ISC group.
 THE STATUS: The work I
show here should NOT be
seen as competition to ISC,
but rather as potential
supplement.
S. Hild
Advanced Virgo, 15th of August 2008
Slide 3
Introduction: Why to do automated design
of the Ad-Virgo configuration
 We need to do plenty of simulations for Advanced Virgo
 Many of these simulation task are fairly big constructs (for instance
producing control matrix)
 Many parameters are not fixed and might change several times within
the next year or so
 For instance: mod frequencies, beam size, ...
 Many design options are available which might completely change
everything
 For instance degenerate recycling cavities
 We will have to do the simulations many times, with several parameter
set, several optimization criteria …
S. Hild
Advanced Virgo, 15th of August 2008
Slide 4
OSD-Tools
 OSD-tools are a collection of Matlab functions and scripts:
 Providing the possibility of an automated parameter optimization
of an Advanced Virgo detector configuration.
 OSD-Tools work together with Finesse
 Reading in parameters from Finesse input files.
 Running Finesse simulations within Matlab
 Writing the optimised parameters back to Finesse input Files.
 Please note: Finesse is just one tool. We can also use analytical
calculations or other simulation software such as Optickle or GWINC
with the OSD_tools. (We choose Finesse for convenience).
S. Hild
Advanced Virgo, 15th of August 2008
Slide 5
Definition of lengths
 Lengths are macroscopic
distances (with a maximal
accuracy of millimeter).
 Length of PR cavity:
 Length of SR cavity:
 Schnupp length:
S. Hild
Advanced Virgo, 15th of August 2008
Slide 6
Definition of the interferometer
degrees of freedom
 Degrees of freedom correspond to
microscopic mirror positions, i.e. their
tunings.
 For DC-readout we need a dark
fringe offset => transmit TEM00
carrier to output port.
S. Hild
Advanced Virgo, 15th of August 2008
Slide 7
Our preliminary length sensing scheme:
Copying the ALIGO approach
 The LSC spend years of
R&D (simulations, table
top experiments, 40m
prototype) to develop
the ALIGO ISC.
 For simplicity we copied
their approach for our
preliminary length
sensing and control
scheme.
 Some aspects of higher
order modes are
included.
 We do not take lock acquisition into account.
(We start from a locked system)
S. Hild
Advanced Virgo, 15th of August 2008
Slide 8
What order do use for parameter
optimization ??
 There is natural order in which the optimization has to be carried out !!
Primary optimisation
Full control matrix (5xNmatrix)
Calculate Figure of merit:
Controlability of the system
Fine tuning
Quadratic control
matrix (5x5)
S. Hild
Advanced Virgo, 15th of August 2008
Slide 9
Optimising the mirror ROCs
 The actual beam size at the
mirrors is determined by the
radii of curvature (ROC) of
the mirrors.
 For a given beam size we
calculate the required mirror
ROCs.
 Input: Beam size
 Output: new ROCs of IMX,
EMX, IMY, EMY, PRM and
SRM.
 Function: OSD_ROC.m
S. Hild
Advanced Virgo, 15th of August 2008
Slide 10
Choosing optimal modulation
frequencies (I)
 Requirement 1: Modulations should not be resonant inside the arm
cavities.
 Requirement 2: Higher order optical modes of the modulation
sidebands should also not be resonant inside the arm cavities. (For
our analysis we consider all orders up to 6)
 Requirement 3: We want 2 modulation frequencies. One to readout
the PRC, one two read out the SR cavity.
 Both frequencies have to be resonant in the PRC.
 If we choose f1 to be at the 1st FSR of the PRC, then f2 has to
be a harmonic of f1:
S. Hild
Advanced Virgo, 15th of August 2008
Slide 11
Choosing optimal modulation
frequencies (II)
 Requirement 4: The modulations
sidebands should not be exactly
anti-resonant inside the arm
cavities.
 For modulation indicies of 0.2 to 0.3
about 10% of the modulation
appears in the first harmonic (2f)
 If f is chosen to be exactly antiresonant, then 2f will be exactly
resonant inside the arm cavities !!
 Requirement 5: Also all optical
higher order modes should not be
anti resonant inside the arm
cavities.
S. Hild
Advanced Virgo, 15th of August 2008
Slide 12
Choosing optimal modulation
frequencies (III)
 For each potential set of
f1 and f2 we calculate
the distance of +f1, -f1,
+f2 and -f2 to
resonance and antiresoance inside the arm
cavity (8 values)
 We do the same for all
higher order optimal
modes up to 6th order
((1+6)x8 = 56 values)
S. Hild
Advanced Virgo, 15th of August 2008
Slide 13
Choosing optimal modulation
frequencies (III)
Modulation sideband of optical higher order mode (l+m) has
the frequency:
With transversal mode spacing given by
(Note: TMS changes with the mirror ROCs)
28 distances to resonance:
28 distances to anti-resonance:
S. Hild
Take the minimum distance out of
this 56 values as figure of merit.
Advanced Virgo, 15th of August 2008
Slide 14
Choosing optimal modulation
frequencies (V)
Minimum distance
1. Find minimum distance
for each modulation
frequency.
2. Scan over a certain
range of frequencies.
3. Choose the one with
the largest minimal
distance
 Input: Freq range,
M (f2 = M x f1)
 Output: f1, f2.
 Function:
OSD_modfreq.m
S. Hild
Advanced Virgo, 15th of August 2008
Slide 15
Choosing the length of PRC
 The length of PRC is chosen to make both modulation sidebands
resonant inside the PRC:
 Input: N, f1, rough
length of PRC.
 Output: L_prc,
readjusted ROC of PRM
 Function:
OSD_PRC_length.m
S. Hild
Advanced Virgo, 15th of August 2008
Slide 16
Choosing Schnupp length and SRC length
Optical power inside the SRC
 Requirement: f2 resonant inside
SRC, while f1 not resonant in
SRC (maximum decoupling).
 We find f2 resonant for two
different Schnupp lengths (short
and long option). Need to decide
for one option.
 Finally we choose the SRC length
to make f2 resonant inside the
SRC.
Short
S. Hild
Advanced Virgo, 15th of August 2008
long Schnupp length
Slide 17
Choosing Schnupp length and SRC length
Optical power inside the SRC
 Input: Schnupp option
(short or long), rough
length of SRC.
 Output: L_Schnupp,
length of SRC,
readjusted ROC of SRM
 Function:
OSD_SR_Schnupp.m
Short
S. Hild
Advanced Virgo, 15th of August 2008
long Schnupp length
Slide 18
Building a chain of
OSD-tool functions
 The first OSD-function
(OSD_ROC) reads in a full
Advanced Virgo parameter
set from a FINESSE input file.
 The optimized parameters are
written back to a new Finesse
file, which is then read in by
the next function. And so on
and so on…
 The last function finally writes
the fully optimised parameter
set.
S. Hild
Advanced Virgo, 15th of August 2008
Slide 19
Primary Optimisation
Primary optimisation
 Using the OSD-tool function we can perform
the full primary optimization with a Matlab
script of 4 Lines.
 Example 1: In case we decide to change the
beam size … you only have to change one
number in the script and run it again.
 Example 2: In case we change the thickness
of the BS … you only change it in the Finesse
input file and rerun the script
S. Hild
Advanced Virgo, 15th of August 2008
Slide 20
Primary Optimisation
Primary optimisation

Using the OSD-tool function we can perform the full
primary optimization with a Matlab script of 4 Lines.

Example 1: In case we decide to change the beam size
… you only have to change one number in the script
and run it again.

Example 2: In case we change the thickness of the BS
… you only change it in the Finesse input file and rerun
the script
S. Hild
Advanced Virgo, 15th of August 2008
Slide 21
Availability and Documentation
 All OSD-tool functions and input files are stored in a subversion
repository including backup and version control.
 This svn is accessible to everyone:
 Server: svn://lnx0.sr.bham.ac.uk
 Repository: adv-osd
 If there is interest we can build OSD-tools for working with
Optickle or other simulation software of interest.
 For more detailed information please have a look at: S.Hild et al
“Advanced Virgo design: The Advanced LIGO approach for
choosing modulation frequencies”, Virgo note, VIR-066A-08.
S. Hild
Advanced Virgo, 15th of August 2008
Slide 22
… Nearly the
S. Hild
E N D…
Advanced Virgo, 15th of August 2008
Slide 23
Final remarks
Primary optimisation
Full control matrix (5xNmatrix)
Calculate Figure of merit:
Controlability of the system
Fine tuning
Quadratic control
matrix (5x5)
S. Hild
Advanced Virgo, 15th of August 2008
Slide 24
Producing the control matrix
OSD_fullcontrolmatrix.m
Full control matrix (5xNmatrix)
Calculate Figure of merit:
Controlability of the system
Quadratic control
matrix (5x5)
5 x 35 matrix
S. Hild
OSD_submatrix.m
Advanced Virgo, 15th of August 2008
Slide 25
Final remarks
Primary optimisation
Full control matrix (5xNmatrix)
Calculate Figure of merit:
Controlability of the system
Fine tuning
Quadratic control
matrix (5x5)
S. Hild
Advanced Virgo, 15th of August 2008
Slide 26
Fine tuning
Trade-off between noise couplings (increase
with dfo) and higher order mode content at
output port (need to make dfo large enough to
dominate the output port).
Fine tuning
Need to optimize demodulation phases.
Especially with detuned SR one cannot expect
to have maximum signal for demodulation
phase equal 0 or 90 deg.
Function available: OSD_optimization.m
OSD_submatrix.m
Need to provide sufficient Signal to shot noise
ratio at all detection ports. Might need to
increase modulation index and/or reflectivity of
pick-off AR coatings
S. Hild
Advanced Virgo, 15th of August 2008
Slide 27
E N D…
S. Hild
Advanced Virgo, 15th of August 2008
Slide 28