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Stefan Hild, M.Mantovani, A.Perreca and A. Freise Advanced Virgo meeting, August 2008 Automated simulations: choosing modulation frequencies à la Advanced LIGO

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S. HildAdvanced Virgo, 15th of August 2008 Slide 2 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. 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

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S. HildAdvanced Virgo, 15th of August 2008 Slide 3 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.

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S. HildAdvanced Virgo, 15th of August 2008 Slide 4 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 …

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S. HildAdvanced Virgo, 15th of August 2008 Slide 5 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).

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S. HildAdvanced Virgo, 15th of August 2008 Slide 6 Definition of lengths Lengths are macroscopic distances (with a maximal accuracy of millimeter). Length of PR cavity: Length of SR cavity: Schnupp length:

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S. HildAdvanced Virgo, 15th of August 2008 Slide 7 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 TEM 00 carrier to output port.

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S. HildAdvanced Virgo, 15th of August 2008 Slide 8 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)

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S. HildAdvanced Virgo, 15th of August 2008 Slide 9 What order do use for parameter optimization ?? There is natural order in which the optimization has to be carried out !! Fine tuning Primary optimisation Full control matrix (5xN- matrix) Calculate Figure of merit: Controlability of the system Quadratic control matrix (5x5)

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S. HildAdvanced Virgo, 15th of August 2008 Slide 10 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

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S. HildAdvanced Virgo, 15th of August 2008 Slide 11 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:

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S. HildAdvanced Virgo, 15th of August 2008 Slide 12 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 anti- resonant, 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.

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S. HildAdvanced Virgo, 15th of August 2008 Slide 13 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 anti- resoance 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)

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S. HildAdvanced Virgo, 15th of August 2008 Slide 14 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: Take the minimum distance out of this 56 values as figure of merit.

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S. HildAdvanced Virgo, 15th of August 2008 Slide 15 Choosing optimal modulation frequencies (V) 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 Minimum distance Input: Freq range, M (f2 = M x f1) Output: f1, f2. Function: OSD_modfreq.m

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S. HildAdvanced Virgo, 15th of August 2008 Slide 16 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

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S. HildAdvanced Virgo, 15th of August 2008 Slide 17 Choosing Schnupp length and SRC length 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. Optical power inside the SRC Short long Schnupp length

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S. HildAdvanced Virgo, 15th of August 2008 Slide 18 Choosing Schnupp length and SRC length Optical power inside the SRC Short long Schnupp length 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

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S. HildAdvanced Virgo, 15th of August 2008 Slide 19 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.

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S. HildAdvanced 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

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S. HildAdvanced Virgo, 15th of August 2008 Slide 21 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 OSD-tools provide an easy and automated way to calculate an optimized Advanced Virgo detector configuration.

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S. HildAdvanced Virgo, 15th of August 2008 Slide 22 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. VIR-066A-08

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S. HildAdvanced Virgo, 15th of August 2008 Slide 23 … Nearly the E N D…

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S. HildAdvanced Virgo, 15th of August 2008 Slide 24 Final remarks Fine tuning Primary optimisation Full control matrix (5xN- matrix) Calculate Figure of merit: Controlability of the system Quadratic control matrix (5x5)

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S. HildAdvanced Virgo, 15th of August 2008 Slide 25 Producing the control matrix Full control matrix (5xN- matrix) Calculate Figure of merit: Controlability of the system Quadratic control matrix (5x5) OSD_fullcontrolmatrix.m OSD_submatrix.m 5 x 35 matrix

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S. HildAdvanced Virgo, 15th of August 2008 Slide 26 Final remarks Fine tuning Primary optimisation Full control matrix (5xN- matrix) Calculate Figure of merit: Controlability of the system Quadratic control matrix (5x5)

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S. HildAdvanced Virgo, 15th of August 2008 Slide 27 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). 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 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

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S. HildAdvanced Virgo, 15th of August 2008 Slide 28 E N D…

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