Author Contributions
Conceptualization, M.M.; methodology, D.B., M.B., J.C.D., A.F., R.M., M.M. and M.V.; software, D.B., M.B., J.C.D., A.F., R.M. and M.V.; validation, D.B., M.B., J.C.D. and M.M.; formal analysis, D.B., M.B., J.C.D., R.M. and M.V.; investigation, D.B., M.B., J.C.D., R.M., M.M. and M.V.; resources, A.F.; writing—original draft preparation, D.B., M.B., J.C.D., R.M. and M.V.; writing—review and editing, D.B., J.C.D., M.M. and M.V.; visualization, D.B., M.B., R.M., M.M. and M.V.; supervision, M.M. All authors have read and agreed to the published version of the manuscript.
Acknowledgments
The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS) and the Netherlands Organization for Scientific Research (NWO), for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies as well as by the Spanish Agencia Estatal de Investigación, the Consellera d’Innovació, Universitats, Ciència i Societat Digital de la Generalitat Valenciana and the CERCA Programme Generalitat de Catalunya, Spain, the National Science Centre of Poland and the European Union—European Regional Development Fund; Foundation for Polish Science (FNP), the Hungarian Scientific Research Fund (OTKA), the French Lyon Institute of Origins (LIO), the Belgian Fonds de la Recherche Scientifique (FRS-FNRS), Actions de Recherche Concertées (ARC) and Fonds Wetenschappelijk Onderzoek–Vlaanderen (FWO), Belgium, the European Commission. The authors gratefully acknowledge the support of the NSF, STFC, INFN, CNRS and Nikhef for provision of computational resources. A particular acknowledgment goes to Priyanka Giri, Manuel Pinto and Enzo Tapia, who extensively contributed to the DRMI commissioning activities.
Figure 1.
Simplified optical layout of AdV+, including the DRMI. The DRMI is circled in orange and includes the Power Recycling (PR), Signal Recycling (SR), North-Input (NI) and West-Input (WI) mirrors, and the Beam-Splitter (BS). The full interferometer, in its Dual-Recycled Fabry-Pérot Michelson Interferometer (DRFPMI) configuration, would also include the 3 -long Fabry-Pérot arm cavities by the addition of the North-End (NE) and West-End (WE) mirrors. The figure also includes the position of the main photodetectors monitoring the DRMI beams: B2 (reflection from the PRC), B4 (intra-cavity pickoff of PRC), B1p (antisymmetric port pickoff), B1 (antisymmetric port beam after the output mode cleaner), B5 (stray-beam generated by the BS anti-reflective surface).
Figure 1.
Simplified optical layout of AdV+, including the DRMI. The DRMI is circled in orange and includes the Power Recycling (PR), Signal Recycling (SR), North-Input (NI) and West-Input (WI) mirrors, and the Beam-Splitter (BS). The full interferometer, in its Dual-Recycled Fabry-Pérot Michelson Interferometer (DRFPMI) configuration, would also include the 3 -long Fabry-Pérot arm cavities by the addition of the North-End (NE) and West-End (WE) mirrors. The figure also includes the position of the main photodetectors monitoring the DRMI beams: B2 (reflection from the PRC), B4 (intra-cavity pickoff of PRC), B1p (antisymmetric port pickoff), B1 (antisymmetric port beam after the output mode cleaner), B5 (stray-beam generated by the BS anti-reflective surface).
Figure 2.
Resonance conditions of the control sidebands in the DRMI. The red line shows the path of the carrier beam, while the other colored lines correspond to the field of a specific sideband.
Figure 2.
Resonance conditions of the control sidebands in the DRMI. The red line shows the path of the carrier beam, while the other colored lines correspond to the field of a specific sideband.
Figure 3.
Experimental comparison between “1f” and “3f” error signals used to lock the DRMI. In particular, the comparison is between B2 6 MHz and B2 18 MHz for PRCL, and between B2 56 MHz and B2 169 MHz for SRCL and MICH. One can easily note that in all three cases, a flat shot noise dominates the spectrum above in the “3f” signals. The plotted data has been acquired during the pre-O4 commissioning period, with 33 of input power.
Figure 3.
Experimental comparison between “1f” and “3f” error signals used to lock the DRMI. In particular, the comparison is between B2 6 MHz and B2 18 MHz for PRCL, and between B2 56 MHz and B2 169 MHz for SRCL and MICH. One can easily note that in all three cases, a flat shot noise dominates the spectrum above in the “3f” signals. The plotted data has been acquired during the pre-O4 commissioning period, with 33 of input power.
Figure 4.
(a): Simulated error signal linearization. In red, the PRCL error signal, B2 6 MHz. In black, the linearizing signal, magnitude of B4 12 MHz. In blue, the PRCL error signal divided by the linearizing signal. (b): Experimental comparison, during a free scan of the PRCL DOF, of linearized and non-linearized signals for the control of PRCL in the proximity of the PRC resonance.
Figure 4.
(a): Simulated error signal linearization. In red, the PRCL error signal, B2 6 MHz. In black, the linearizing signal, magnitude of B4 12 MHz. In blue, the PRCL error signal divided by the linearizing signal. (b): Experimental comparison, during a free scan of the PRCL DOF, of linearized and non-linearized signals for the control of PRCL in the proximity of the PRC resonance.
Figure 5.
DRMI triggers: determination of the signals with respect to the DOF working point. This figure (shared x axis among subplots) represents a scan of the three DRMI DOFs, where it is known where the good working point is; in this way, it is possible to determine the value that signals of interest have in such point. During the study, a larger set of signals to be tested has been used to determine the best triggers; in this plot, only the most relevant signals are shown.
Figure 5.
DRMI triggers: determination of the signals with respect to the DOF working point. This figure (shared x axis among subplots) represents a scan of the three DRMI DOFs, where it is known where the good working point is; in this way, it is possible to determine the value that signals of interest have in such point. During the study, a larger set of signals to be tested has been used to determine the best triggers; in this plot, only the most relevant signals are shown.
Figure 6.
DRMI Triggers: this figure (shared x axis among subplots) represents another, different scan of the three DRMI DOFs, where it is known where the good working point is; such knowledge is not used, while instead inverse selection rules, based on the values of the signals of interest, are used to reconstruct the wanted working point; different, more stringent inverse selection rules are stacked from black to red, yellow and finally green until the correct working point is finally reconstructed.
Figure 6.
DRMI Triggers: this figure (shared x axis among subplots) represents another, different scan of the three DRMI DOFs, where it is known where the good working point is; such knowledge is not used, while instead inverse selection rules, based on the values of the signals of interest, are used to reconstruct the wanted working point; different, more stringent inverse selection rules are stacked from black to red, yellow and finally green until the correct working point is finally reconstructed.
Figure 7.
In the first two rows, error signals are plotted against the tuning of pairs of DOFs. At the center of each image is the operating point. Triggering thresholds are exceeded for the points within the black line. In the bottom row, a cross-section of the graphs above.
Figure 7.
In the first two rows, error signals are plotted against the tuning of pairs of DOFs. At the center of each image is the operating point. Triggering thresholds are exceeded for the points within the black line. In the bottom row, a cross-section of the graphs above.
Figure 8.
Example of DRMI lock acquisition during the commissioning of AdV+. In the second row there are, in blue, the three single trigger signals, based on the corresponding signals of the first row; in red, the final global trigger, computed as the product of the single triggers.
Figure 8.
Example of DRMI lock acquisition during the commissioning of AdV+. In the second row there are, in blue, the three single trigger signals, based on the corresponding signals of the first row; in red, the final global trigger, computed as the product of the single triggers.
Figure 9.
DRMI error signals Optical Gain (OG) variation vs. misalignments of the PR mirror. Each line corresponds to the relative optical gain of an error signal used to control the DRMI. (a) shows the “1f” error signals; (b) shows the “3f” error signals. The OGs are relative to the gains in a fully aligned condition. The vertical line marks the lowest angle at which one of the error signals has lost 50% of its OG.
Figure 9.
DRMI error signals Optical Gain (OG) variation vs. misalignments of the PR mirror. Each line corresponds to the relative optical gain of an error signal used to control the DRMI. (a) shows the “1f” error signals; (b) shows the “3f” error signals. The OGs are relative to the gains in a fully aligned condition. The vertical line marks the lowest angle at which one of the error signals has lost 50% of its OG.
Figure 10.
DRMI error signals scans for various PR misalignments. Each plot shows the scan of a different DRMI DOF and its corresponding “3f” error signal (continuous lines). The dashed lines show the “2f” signal magnitude, acquired on B4, corresponding to the resonances of either the 6 MHz (first plot) or 56 MHz (second and third plot).
Figure 10.
DRMI error signals scans for various PR misalignments. Each plot shows the scan of a different DRMI DOF and its corresponding “3f” error signal (continuous lines). The dashed lines show the “2f” signal magnitude, acquired on B4, corresponding to the resonances of either the 6 MHz (first plot) or 56 MHz (second and third plot).
Figure 11.
Simplified scheme of the optical layout of the DRMI with the QPDs used for the automatic alignment sensing.
Figure 11.
Simplified scheme of the optical layout of the DRMI with the QPDs used for the automatic alignment sensing.
Figure 12.
Signals (
left) and compass plot (
right) for B2 NF 6 MHz comparing the signals produced by the misalignment of PR (blue), SR (red), WI (yellow, dashed), and NI (purple, dashed) mirrors [
18].
Figure 12.
Signals (
left) and compass plot (
right) for B2 NF 6 MHz comparing the signals produced by the misalignment of PR (blue), SR (red), WI (yellow, dashed), and NI (purple, dashed) mirrors [
18].
Figure 13.
Example of the engagement of the angular control of the PR mirror after the lock of the DRMI. The top plots show the I and Q projections of the angular error signals for yaw (horizontal) and pitch (vertical) DOFs of the PR mirror. The Q is almost flat, signaling a good tuning of the demodulation phase. The middle plots show the behavior of the global power (left) and the sidebands’ power (12 MHz and 112 MHz, right) picked-off in the PRC. The bottom plots show the pitch (left) and the yaw (right) of the PR mirror as detected by the optical levers for its marionetta.
Figure 13.
Example of the engagement of the angular control of the PR mirror after the lock of the DRMI. The top plots show the I and Q projections of the angular error signals for yaw (horizontal) and pitch (vertical) DOFs of the PR mirror. The Q is almost flat, signaling a good tuning of the demodulation phase. The middle plots show the behavior of the global power (left) and the sidebands’ power (12 MHz and 112 MHz, right) picked-off in the PRC. The bottom plots show the pitch (left) and the yaw (right) of the PR mirror as detected by the optical levers for its marionetta.
Table 1.
Planned error signals for the longitudinal control of the DRMI DOFs.
Table 1.
Planned error signals for the longitudinal control of the DRMI DOFs.
Lock Acquisition Step | PRCL | MICH | SRCL |
---|
Initial lock (“1f”) | B2
6
MHz | B2
56
MHz I | B2
56
MHz Q |
CARM offset reduction (“3f”) | B2
18
MHz | B2
169
MHz I | B2
169
MHz Q |
Table 2.
50% OG loss thresholds for each error signal. Each column shows the respective mirror misalignment at which the error signal loses 50% of its optical gain. For SR misalignments (last column), most of the error signals do not reach the 50% threshold in the simulated range (up to ).
Table 2.
50% OG loss thresholds for each error signal. Each column shows the respective mirror misalignment at which the error signal loses 50% of its optical gain. For SR misalignments (last column), most of the error signals do not reach the 50% threshold in the simulated range (up to ).
DOF | Signal | PR Thr. [Rad] | NI Thr. [Rad] | SR Thr. [Rad] |
---|
PRCL | B2
6
MHz I | | | N.A. |
| B2
18
MHz I | | | N.A. |
MICH | B2
56
MHz I | | | N.A. |
| B2
169
MHz I | | | N.A. |
SRCL | B2
56
MHz Q | | | N.A. |
| B2
169
MHz Q | | | |
Table 3.
Optical gains (in dB, normalized over the smallest) and demodulation phases (in degree) of the simulated signals shown in
Figure 12.
Table 3.
Optical gains (in dB, normalized over the smallest) and demodulation phases (in degree) of the simulated signals shown in
Figure 12.
DOF | Mag | Phase |
---|
PR | 72.80 dB | 89.10 |
SR | 0.00 dB | −78.30 |
NI | 70.02 dB | 89.10 |
WI | 70.05 dB | 89.10 |