When this research was performed the authors were with the Department of Physics, the LIGO Project, California Institute of Technology, Pasadena, California 91125.
J. E. Mason is now with Lockheed Martin Advanced Technology Center, B201 L9-23, 3251 Hanover Street, Palo Alto, California 94304.
James E. Mason and Phil A. Willems, "Signal extraction and optical design for an advanced gravitational-wave interferometer," Appl. Opt. 42, 1269-1282 (2003)
We present an experimental demonstration of a locking and control scheme for an interferometer using a power-recycled resonant sideband extraction configuration and show that the measured response to mirror vibrations matches an optical model. We discuss some aspects of resonant sideband extraction that are relevant to gravitational-wave detection.
Kenneth A. Strain, Guido Müller, Tom Delker, David H. Reitze, David B. Tanner, James E. Mason, Phil A. Willems, Daniel A. Shaddock, Malcolm B. Gray, Conor Mow-Lowry, and David E. McClelland Appl. Opt. 42(7) 1244-1256 (2003)
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Matrix of Discriminants for an Optimized Broadband Interferometera
Signal Port (MHz)
Φ+
Φ-
ϕ+
ϕ-
ϕs
Reflection 81
2400
0
-1.7
-0.51
0.37
2400
-0.0006
-1.7
-0.51
0.34
Pick 81
96000
0
54
-71
51
96000
-0.09
54
-71
47
Dark 81
0
-77
0
-0.097
0
0
-77
0
-0.097
0
Reflection 54
0
0
-0.25
-0.014
-0.35
0
0
-0.25
-0.015
-0.35
Pick 54
0
0
-6.3
-0.057
9.6
0
0
-6.4
-0.055
9.7
Numbers in bold are predictions from Twiddle, whereas lightface numbers are generated from approximate analytical formulas; 81 MHz is the PM frequency, and 54 MHz is the SSB frequency.
Table 2
Demodulation Phase Changes for the DRM Relative to the FPM
Experimental numbers are in lightface; Twiddle numbers are in bold. This is a relative measurement because the OSA output is not reliably calibrated. Hence all modeled and measured powers are scaled to the -81-MHz (PM) rf sideband.
Measured values are in lightface; the predicted Twiddle values are in bold.
Table 5
Matrix of Discriminants for the RSE Interferometera
Signal Port (MHz)
Φ+
ϕ+
ϕ-
ϕs
Pickoff 81
410 ± 55
0.50 ± 0.11
-1.06 ± 0.29
-0.10 ± 0.046
(ϕ-)
310 ± 25
0.46 ± 0.16
-0.60 ± 0.14
-0.16 ± 0.03
Reflected 54
0
0.090 ± 0.010
-0.029 ± 0.0041
-0.11 ± 0.039
(ϕ+)
0
0.13 ± 0.010
-0.060 ± 0.013
-0.12 ± 0.0084
Pickoff 54
0
0.13 ± 0.031
0.041 ± 0.016
0.35 ± 0.092
(ϕs)
0
0.070 ± 0.0058
0.011 ± 0.037
0.34 ± 0.024
Measured values are in lightface; the predicted Twiddle values are in bold. The ϕ+, ϕ-, and ϕs elements in the pickoff 81 row are actually the cross-coupled matrix elements predicted by relation (17).
Tables (5)
Table 1
Matrix of Discriminants for an Optimized Broadband Interferometera
Signal Port (MHz)
Φ+
Φ-
ϕ+
ϕ-
ϕs
Reflection 81
2400
0
-1.7
-0.51
0.37
2400
-0.0006
-1.7
-0.51
0.34
Pick 81
96000
0
54
-71
51
96000
-0.09
54
-71
47
Dark 81
0
-77
0
-0.097
0
0
-77
0
-0.097
0
Reflection 54
0
0
-0.25
-0.014
-0.35
0
0
-0.25
-0.015
-0.35
Pick 54
0
0
-6.3
-0.057
9.6
0
0
-6.4
-0.055
9.7
Numbers in bold are predictions from Twiddle, whereas lightface numbers are generated from approximate analytical formulas; 81 MHz is the PM frequency, and 54 MHz is the SSB frequency.
Table 2
Demodulation Phase Changes for the DRM Relative to the FPM
Experimental numbers are in lightface; Twiddle numbers are in bold. This is a relative measurement because the OSA output is not reliably calibrated. Hence all modeled and measured powers are scaled to the -81-MHz (PM) rf sideband.
Measured values are in lightface; the predicted Twiddle values are in bold.
Table 5
Matrix of Discriminants for the RSE Interferometera
Signal Port (MHz)
Φ+
ϕ+
ϕ-
ϕs
Pickoff 81
410 ± 55
0.50 ± 0.11
-1.06 ± 0.29
-0.10 ± 0.046
(ϕ-)
310 ± 25
0.46 ± 0.16
-0.60 ± 0.14
-0.16 ± 0.03
Reflected 54
0
0.090 ± 0.010
-0.029 ± 0.0041
-0.11 ± 0.039
(ϕ+)
0
0.13 ± 0.010
-0.060 ± 0.013
-0.12 ± 0.0084
Pickoff 54
0
0.13 ± 0.031
0.041 ± 0.016
0.35 ± 0.092
(ϕs)
0
0.070 ± 0.0058
0.011 ± 0.037
0.34 ± 0.024
Measured values are in lightface; the predicted Twiddle values are in bold. The ϕ+, ϕ-, and ϕs elements in the pickoff 81 row are actually the cross-coupled matrix elements predicted by relation (17).