Abstract

We describe and verify the dynamic behavior of a novel technique to optimize and actively control the optical impedance matching condition of a coupled resonator system. The technique employs radio frequency modulation and demodulation to interrogate the reflection amplitude response of the coupled cavity system. The sign and magnitude of the demodulated signal is used in a closed loop feedback system which controls the coupling condition of a three-mirror resonator. This was done by actuating on the spacing between two of mirrors, effectively using the pair as a variable reflectivity compound mirror. We propose that this technique can be used for controlling the signal bandwidth of next-generation gravitational wave detectors, as well as optimizing circulating optical carrier power in the instrument.

© 2010 Optical Society of America

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References

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  1. P. R. Saulson, Fundamentals of interferometric gravitational wave detectors, 1st ed., (World Scientific, Singapore, 1994).
  2. K. A. Strain, G. M¨uller, T. Delker, D. H. Reitze, D. B. Tanner, J. E. Mason, P. A. Willems, D. A. Shaddock, M. B. Gray, C. Mow-Lowry, and D. E. McClelland, "Sensing and Control in Dual-Recycling Laser Interferometer Gravitational-Wave Detectors," Appl. Opt. 42, 7, 1244-1256 (2003).
    [CrossRef] [PubMed]
  3. R. W. P. Drever, "Interferometric detectors for gravitational radiation," in Gravitational Radiation (North-Holland, Amsterdam, 1983), pp. 321-338.
  4. B. J. Meers, "Recycling in laser-interferometric gravitational wave detectors," Phys. Rev. D 38, 2317-2326 (1988).
    [CrossRef]
  5. K. A. Strain and J. Hough, "Experimental demonstration of the use of a Fabry-Perot cavity as a mirror of variable reflectivity," Rev. Sci. Instrum. 65(4), 799-802 (1994).
    [CrossRef]
  6. G. de Vine, D. A. Shaddock, and D. E. McClelland, "Experimental demonstration of variable-reflectivity signal recycling for interferometric gravitational-wave detectors," Opt. Lett. 27(17), 1507-1509 (2002).
    [CrossRef]
  7. D. S. Rabeling, S. Goßler, J. Cumpston, M. B. Gray, and D. E. McClelland, "A new topology for the control of complex interferometers," Class. Quantum Grav. 23, S267-S275, (2006), doi:10.1088/0264-9381/23/8/S34.
    [CrossRef]
  8. J. H. Chow, I. C.M. Littler, D. S. Rabeling, D. E. McClelland, andM. B. Gray, "Using active resonator impedance matching for shot-noise limited, cavity enhanced amplitude modulated laser absorption spectroscopy," Opt. Express 16(11), 7726-7738 (2008).
    [CrossRef] [PubMed]
  9. J. H. Chow, M. B. Gray, I. C. M. Littler, and D. E. McClelland, "Spectroscopic detection system and method," Australian Patent Application, No. 2007906639.
  10. P. Kwee, B. Willke, and K. Danzmann, "Optical ac coupling to overcome limitations in the detection of optical power fluctuations," Opt. Lett. 33(13), 1509-1511 (2008).
    [CrossRef] [PubMed]
  11. P. Kwee, B. Willke, and K. Danzmann, "Laser power stabilization using optical ac coupling and its quantum and technical limits," Appl. Opt. 48(28), 5423-5431 (2009).
    [CrossRef] [PubMed]
  12. A. E. Siegman, Lasers (University Science, Mill Valley Calif., 1986).
  13. R. W. P. Drever, J. L. Hall, F. W. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
    [CrossRef]
  14. S. H. Huttner, B. W. Barr, M. V. Plissi, J. R. Taylor, B. Sorazu, and K. A. Strain, "Novel sensing and control schemes for a three-mirror coupled cavity," Class. Quantum Grav. 24, 3825-3836 (2007), doi:10.1088/0264-9381/24/15/004.
    [CrossRef]
  15. G. de Vine, D. E. McClelland, and M. B. Gray, "Differential cavity mode spectroscopy: A new cavity enhanced technique for the detection of weak transitions," Phys. Lett. A 372(25), 4650-4653 (2008).
    [CrossRef]
  16. G. de Vine, D. A. Shaddock, and D. E. McClelland, "Variable reflectivity signal mirrors and signal response measurements," Class. Quantum Grav. 191561-1568 (2002), doi:10.1088/0264-9381/19/7/345.
    [CrossRef]

2009 (1)

2008 (3)

2007 (1)

S. H. Huttner, B. W. Barr, M. V. Plissi, J. R. Taylor, B. Sorazu, and K. A. Strain, "Novel sensing and control schemes for a three-mirror coupled cavity," Class. Quantum Grav. 24, 3825-3836 (2007), doi:10.1088/0264-9381/24/15/004.
[CrossRef]

2006 (1)

D. S. Rabeling, S. Goßler, J. Cumpston, M. B. Gray, and D. E. McClelland, "A new topology for the control of complex interferometers," Class. Quantum Grav. 23, S267-S275, (2006), doi:10.1088/0264-9381/23/8/S34.
[CrossRef]

2003 (1)

2002 (2)

G. de Vine, D. A. Shaddock, and D. E. McClelland, "Experimental demonstration of variable-reflectivity signal recycling for interferometric gravitational-wave detectors," Opt. Lett. 27(17), 1507-1509 (2002).
[CrossRef]

G. de Vine, D. A. Shaddock, and D. E. McClelland, "Variable reflectivity signal mirrors and signal response measurements," Class. Quantum Grav. 191561-1568 (2002), doi:10.1088/0264-9381/19/7/345.
[CrossRef]

1994 (1)

K. A. Strain and J. Hough, "Experimental demonstration of the use of a Fabry-Perot cavity as a mirror of variable reflectivity," Rev. Sci. Instrum. 65(4), 799-802 (1994).
[CrossRef]

1988 (1)

B. J. Meers, "Recycling in laser-interferometric gravitational wave detectors," Phys. Rev. D 38, 2317-2326 (1988).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. W. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Barr, B. W.

S. H. Huttner, B. W. Barr, M. V. Plissi, J. R. Taylor, B. Sorazu, and K. A. Strain, "Novel sensing and control schemes for a three-mirror coupled cavity," Class. Quantum Grav. 24, 3825-3836 (2007), doi:10.1088/0264-9381/24/15/004.
[CrossRef]

Chow, J. H.

Cumpston, J.

D. S. Rabeling, S. Goßler, J. Cumpston, M. B. Gray, and D. E. McClelland, "A new topology for the control of complex interferometers," Class. Quantum Grav. 23, S267-S275, (2006), doi:10.1088/0264-9381/23/8/S34.
[CrossRef]

Danzmann, K.

de Vine, G.

G. de Vine, D. E. McClelland, and M. B. Gray, "Differential cavity mode spectroscopy: A new cavity enhanced technique for the detection of weak transitions," Phys. Lett. A 372(25), 4650-4653 (2008).
[CrossRef]

G. de Vine, D. A. Shaddock, and D. E. McClelland, "Variable reflectivity signal mirrors and signal response measurements," Class. Quantum Grav. 191561-1568 (2002), doi:10.1088/0264-9381/19/7/345.
[CrossRef]

G. de Vine, D. A. Shaddock, and D. E. McClelland, "Experimental demonstration of variable-reflectivity signal recycling for interferometric gravitational-wave detectors," Opt. Lett. 27(17), 1507-1509 (2002).
[CrossRef]

Delker, T.

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. W. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. W. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Goßler, S.

D. S. Rabeling, S. Goßler, J. Cumpston, M. B. Gray, and D. E. McClelland, "A new topology for the control of complex interferometers," Class. Quantum Grav. 23, S267-S275, (2006), doi:10.1088/0264-9381/23/8/S34.
[CrossRef]

Gray, M. B.

G. de Vine, D. E. McClelland, and M. B. Gray, "Differential cavity mode spectroscopy: A new cavity enhanced technique for the detection of weak transitions," Phys. Lett. A 372(25), 4650-4653 (2008).
[CrossRef]

D. S. Rabeling, S. Goßler, J. Cumpston, M. B. Gray, and D. E. McClelland, "A new topology for the control of complex interferometers," Class. Quantum Grav. 23, S267-S275, (2006), doi:10.1088/0264-9381/23/8/S34.
[CrossRef]

K. A. Strain, G. M¨uller, T. Delker, D. H. Reitze, D. B. Tanner, J. E. Mason, P. A. Willems, D. A. Shaddock, M. B. Gray, C. Mow-Lowry, and D. E. McClelland, "Sensing and Control in Dual-Recycling Laser Interferometer Gravitational-Wave Detectors," Appl. Opt. 42, 7, 1244-1256 (2003).
[CrossRef] [PubMed]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. W. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Hough, J.

K. A. Strain and J. Hough, "Experimental demonstration of the use of a Fabry-Perot cavity as a mirror of variable reflectivity," Rev. Sci. Instrum. 65(4), 799-802 (1994).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. W. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Huttner, S. H.

S. H. Huttner, B. W. Barr, M. V. Plissi, J. R. Taylor, B. Sorazu, and K. A. Strain, "Novel sensing and control schemes for a three-mirror coupled cavity," Class. Quantum Grav. 24, 3825-3836 (2007), doi:10.1088/0264-9381/24/15/004.
[CrossRef]

Kowalski, F. W.

R. W. P. Drever, J. L. Hall, F. W. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Kwee, P.

Littler, I. C.M.

M¨uller, G.

Mason, J. E.

McClelland, D. E.

G. de Vine, D. E. McClelland, and M. B. Gray, "Differential cavity mode spectroscopy: A new cavity enhanced technique for the detection of weak transitions," Phys. Lett. A 372(25), 4650-4653 (2008).
[CrossRef]

J. H. Chow, I. C.M. Littler, D. S. Rabeling, D. E. McClelland, andM. B. Gray, "Using active resonator impedance matching for shot-noise limited, cavity enhanced amplitude modulated laser absorption spectroscopy," Opt. Express 16(11), 7726-7738 (2008).
[CrossRef] [PubMed]

D. S. Rabeling, S. Goßler, J. Cumpston, M. B. Gray, and D. E. McClelland, "A new topology for the control of complex interferometers," Class. Quantum Grav. 23, S267-S275, (2006), doi:10.1088/0264-9381/23/8/S34.
[CrossRef]

K. A. Strain, G. M¨uller, T. Delker, D. H. Reitze, D. B. Tanner, J. E. Mason, P. A. Willems, D. A. Shaddock, M. B. Gray, C. Mow-Lowry, and D. E. McClelland, "Sensing and Control in Dual-Recycling Laser Interferometer Gravitational-Wave Detectors," Appl. Opt. 42, 7, 1244-1256 (2003).
[CrossRef] [PubMed]

G. de Vine, D. A. Shaddock, and D. E. McClelland, "Experimental demonstration of variable-reflectivity signal recycling for interferometric gravitational-wave detectors," Opt. Lett. 27(17), 1507-1509 (2002).
[CrossRef]

G. de Vine, D. A. Shaddock, and D. E. McClelland, "Variable reflectivity signal mirrors and signal response measurements," Class. Quantum Grav. 191561-1568 (2002), doi:10.1088/0264-9381/19/7/345.
[CrossRef]

Meers, B. J.

B. J. Meers, "Recycling in laser-interferometric gravitational wave detectors," Phys. Rev. D 38, 2317-2326 (1988).
[CrossRef]

Mow-Lowry, C.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. W. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Plissi, M. V.

S. H. Huttner, B. W. Barr, M. V. Plissi, J. R. Taylor, B. Sorazu, and K. A. Strain, "Novel sensing and control schemes for a three-mirror coupled cavity," Class. Quantum Grav. 24, 3825-3836 (2007), doi:10.1088/0264-9381/24/15/004.
[CrossRef]

Rabeling, D. S.

J. H. Chow, I. C.M. Littler, D. S. Rabeling, D. E. McClelland, andM. B. Gray, "Using active resonator impedance matching for shot-noise limited, cavity enhanced amplitude modulated laser absorption spectroscopy," Opt. Express 16(11), 7726-7738 (2008).
[CrossRef] [PubMed]

D. S. Rabeling, S. Goßler, J. Cumpston, M. B. Gray, and D. E. McClelland, "A new topology for the control of complex interferometers," Class. Quantum Grav. 23, S267-S275, (2006), doi:10.1088/0264-9381/23/8/S34.
[CrossRef]

Reitze, D. H.

Shaddock, D. A.

Sorazu, B.

S. H. Huttner, B. W. Barr, M. V. Plissi, J. R. Taylor, B. Sorazu, and K. A. Strain, "Novel sensing and control schemes for a three-mirror coupled cavity," Class. Quantum Grav. 24, 3825-3836 (2007), doi:10.1088/0264-9381/24/15/004.
[CrossRef]

Strain, K. A.

S. H. Huttner, B. W. Barr, M. V. Plissi, J. R. Taylor, B. Sorazu, and K. A. Strain, "Novel sensing and control schemes for a three-mirror coupled cavity," Class. Quantum Grav. 24, 3825-3836 (2007), doi:10.1088/0264-9381/24/15/004.
[CrossRef]

K. A. Strain, G. M¨uller, T. Delker, D. H. Reitze, D. B. Tanner, J. E. Mason, P. A. Willems, D. A. Shaddock, M. B. Gray, C. Mow-Lowry, and D. E. McClelland, "Sensing and Control in Dual-Recycling Laser Interferometer Gravitational-Wave Detectors," Appl. Opt. 42, 7, 1244-1256 (2003).
[CrossRef] [PubMed]

K. A. Strain and J. Hough, "Experimental demonstration of the use of a Fabry-Perot cavity as a mirror of variable reflectivity," Rev. Sci. Instrum. 65(4), 799-802 (1994).
[CrossRef]

Tanner, D. B.

Taylor, J. R.

S. H. Huttner, B. W. Barr, M. V. Plissi, J. R. Taylor, B. Sorazu, and K. A. Strain, "Novel sensing and control schemes for a three-mirror coupled cavity," Class. Quantum Grav. 24, 3825-3836 (2007), doi:10.1088/0264-9381/24/15/004.
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. W. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Willems, P. A.

Willke, B.

Appl. Opt. (2)

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. W. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Class. Quantum Grav. (3)

S. H. Huttner, B. W. Barr, M. V. Plissi, J. R. Taylor, B. Sorazu, and K. A. Strain, "Novel sensing and control schemes for a three-mirror coupled cavity," Class. Quantum Grav. 24, 3825-3836 (2007), doi:10.1088/0264-9381/24/15/004.
[CrossRef]

G. de Vine, D. A. Shaddock, and D. E. McClelland, "Variable reflectivity signal mirrors and signal response measurements," Class. Quantum Grav. 191561-1568 (2002), doi:10.1088/0264-9381/19/7/345.
[CrossRef]

D. S. Rabeling, S. Goßler, J. Cumpston, M. B. Gray, and D. E. McClelland, "A new topology for the control of complex interferometers," Class. Quantum Grav. 23, S267-S275, (2006), doi:10.1088/0264-9381/23/8/S34.
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

G. de Vine, D. E. McClelland, and M. B. Gray, "Differential cavity mode spectroscopy: A new cavity enhanced technique for the detection of weak transitions," Phys. Lett. A 372(25), 4650-4653 (2008).
[CrossRef]

Phys. Rev. D (1)

B. J. Meers, "Recycling in laser-interferometric gravitational wave detectors," Phys. Rev. D 38, 2317-2326 (1988).
[CrossRef]

Rev. Sci. Instrum. (1)

K. A. Strain and J. Hough, "Experimental demonstration of the use of a Fabry-Perot cavity as a mirror of variable reflectivity," Rev. Sci. Instrum. 65(4), 799-802 (1994).
[CrossRef]

Other (4)

R. W. P. Drever, "Interferometric detectors for gravitational radiation," in Gravitational Radiation (North-Holland, Amsterdam, 1983), pp. 321-338.

P. R. Saulson, Fundamentals of interferometric gravitational wave detectors, 1st ed., (World Scientific, Singapore, 1994).

J. H. Chow, M. B. Gray, I. C. M. Littler, and D. E. McClelland, "Spectroscopic detection system and method," Australian Patent Application, No. 2007906639.

A. E. Siegman, Lasers (University Science, Mill Valley Calif., 1986).

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Figures (9)

Fig. 1.
Fig. 1.

A simplified dual recycled Michelson interferometer for gravitational wave detection.

Fig. 2.
Fig. 2.

A two-mirror resonant cavity

Fig. 3.
Fig. 3.

Reflected intensity and amplitude response as a function of the input coupler transmission. (a) Normalized reflected intensity as a function of the input coupler transmission; (b) Amplitude response as a function of input coupler transmission. In both plots the output mirror is set to r 2 = √0.9.

Fig. 4.
Fig. 4.

A two-mirror resonant cavity interrogated by an amplitude modulated laser. (a) the schematic of the interrogation and readout setup; (b) the operating spectral condition of the AM sidebands, showing the AM sidebands well outside the resonance FWHM of the cavity, such that they are mostly reflected.

Fig. 5.
Fig. 5.

A three mirror coupled cavity. (a) the two closely spaced mirrors form an etalon, whose reflectivity can be varied by their spacing; (b) if the output coupler reflectivity R 2 is high, then the laser must be well away from resonance of the etalon for the three mirror system to be impedance matched.

Fig. 6.
Fig. 6.

Simplified experimental layout of the impedance matching experiment. The reflected and transmitted signals are measured on Rx and Tx respectively. The carrier laser has two modulation frequencies. One set of 190 MHz PM sidebands and one set of 30 MHz AM sidebands. The signal laser is used to create a single sideband providing a signal frequency to map the frequency response of the cavity system.

Fig. 7.
Fig. 7.

(a) The normalised transmitted intensity for three different etalon phase offsets; (b) The impedance locking error signal for three different etalon phase offsets. As the etalon phase is varied the coupling condition of the cavity changes from over coupled to impedance matched to under coupled.

Fig. 8.
Fig. 8.

The coupled cavity reflection response compared with the impedance locking error signal when the etalon spacing was scanned. (a) the reflection response of the etalon, when m 2 was blocked; (b) the reflection response of the three mirror system while the laser was locked to resonance; (c) the demodulated AM error signal corresponding to (b).

Fig. 9.
Fig. 9.

Magnitude of the coupled cavity signal responses. ‘×’ Signal response fit of an over coupled cavity with a bandwidth γ = 8.8 MHz. ‘○’ Signal response fit of an impedance matched cavity with a bandwidth γ= 2.27 MHz. ‘◇’ Signal response fit of an under coupled cavity with a bandwidth γ = 1.33 MHz.

Equations (7)

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𝓡 res = E refl E inc = r 1 r 2 ( t 1 2 + r 1 2 ) 1 r 1 r 2 .
r 1 > r 2 Under coupled
r 1 < r 2 Over coupled
r 1 = r 2 Impedance matched.
V sig ρβ P opt R pd r 1 r 2 1 r 1 r 2 ,
V sig ρβ P opt R pd r 1 r 2 1 r 1 2
V sig r 1 r 2 .

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