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Automated simulations: choosing modulation frequencies à la Advanced LIGO

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

  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 Advanced Virgo, 15th of August 2008

  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. Advanced Virgo, 15th of August 2008

  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 … Advanced Virgo, 15th of August 2008

  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). Advanced Virgo, 15th of August 2008

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

  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 TEM00 carrier to output port. Advanced Virgo, 15th of August 2008

  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) Advanced Virgo, 15th of August 2008

  9. 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 (5xN-matrix) Calculate Figure of merit: Controlability of the system Fine tuning Quadratic control matrix (5x5) Advanced Virgo, 15th of August 2008

  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 Advanced Virgo, 15th of August 2008

  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: Advanced Virgo, 15th of August 2008

  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. Advanced Virgo, 15th of August 2008

  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) Advanced Virgo, 15th of August 2008

  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: Take the minimum distance out of this 56 values as figure of merit. 28 distances to anti-resonance: Advanced Virgo, 15th of August 2008

  15. Choosing optimal modulation frequencies (V) Minimum distance • Find minimum distance for each modulation frequency. • Scan over a certain range of frequencies. • Choose the one with the largest minimal distance • Input:Freq range, M (f2 = M x f1) • Output: f1, f2. • Function:OSD_modfreq.m Advanced Virgo, 15th of August 2008

  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 Advanced Virgo, 15th of August 2008

  17. 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 long Schnupp length Advanced Virgo, 15th of August 2008

  18. 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 long Schnupp length Advanced Virgo, 15th of August 2008

  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. Advanced Virgo, 15th of August 2008

  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 Advanced Virgo, 15th of August 2008

  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. Advanced Virgo, 15th of August 2008

  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. Advanced Virgo, 15th of August 2008

  23. … Nearly the E N D… Advanced Virgo, 15th of August 2008

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

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

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

  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 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 Fine tuning 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 Advanced Virgo, 15th of August 2008

  28. E N D… Advanced Virgo, 15th of August 2008