Abstract

The current LIGO detectors will undergo an upgrade which is expected to improve their sensitivity and bandwidth significantly. These advanced gravitational-wave detectors will employ stable recycling cavities to better confine their spatial eigenmodes instead of the currently installed marginally stable power recycling cavity. In this letter we describe the general layout of the recycling cavities and give specific values for a first possible design. We also address the issue of mode mismatch due to manufacturing tolerance of optical elements and present a passive compensation scheme based upon optimizing the distances between optical elements.

© 2008 Optical Society of America

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References

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  1. S. J. Waldman et al., "Status of LIGO at the start of the fifth science run," Class. Quantum Grav. 23, S267-S269 (1999).
  2. R. Adhikari, P. Fritschel, and S. Waldman, "Enhanced LIGO," LIGO document, LIGO-T060156-01, http://www.ligo.caltech.edu/docs/T/T060156-01.pdf.
  3. A. Weinstein, "Advanced LIGO optical configuration and prototyping effort," Class. Quantum Grav. 19, 1575- 1584 (2002).
    [CrossRef]
  4. C. Wilkinson, "Plans for Advanced LIGO Instruments," presented at the 2005 APS April Meeting, Tampa, Florida, USA, 16-19 April 2005.
  5. A. M. Gretarsson, E. D�??Ambrosio, V. Frolov, B. O�??Reilly, and P. K. Fritschel, "Effects of mode degeneracy in the LIGO Livingston Observatory recycling cavity," J. Opt. Soc. Am. B 24, 2821-2828 (1999).
    [CrossRef]
  6. S. Ballmer et al., "Thermal Compensation System Description," LIGO document, LIGO- T050064-00-R, http://www.ligo.caltech.edu/docs/T/T050064-00.pdf.
  7. H. Armandula et al., "Core Optics Components Preliminary Design," LIGO document LIGO- E080033-00-D, http://www.ligo.caltech.edu/ gari/LIGOII/E080033-00PreliminaryDesign.pdf.
  8. H. Armandula et al., "Core Optics Components Preliminary Design," LIGO document LIGO- E080033-00-D, http://www.ligo.caltech.edu/ gari/LIGOII/E080033-00PreliminaryDesign.pdf.
  9. P. Fritschel, "Second generation instruments for the Laser Interferometer Gravitational Wave Observatory (LIGO)," Proc. SPIE 4856, 282-291 (2003).
    [CrossRef]
  10. H. Yamamoto, "Scattering Loss," presented at the LIGO-Virgo meeting, Hannover, Germany, October 2007, www.ligo.caltech.edu/docs/G/G070657.pdf.
  11. D. A. Shaddock et al., "Power-recycled Michelson interferometer with resonant sideband extraction," Appl. Opt. 42, 1283-1295 (2003).
    [CrossRef] [PubMed]
  12. M. A. Arain et al., "Input Optics Subsystem Preliminary Design Document," LIGO document, LIGO-T060269- 02-D, http://www.ligo.caltech.edu/docs/T/T060269-02.pdf.
  13. Y. Pan, "Optimal degeneracy for the signal-recycling cavity in advanced LIGO," http://arxiv.org/PS cache/gr-qc/pdf/0608/0608128v1.pdf.
  14. G. Mueller, "Stable Recycling Cavities for Advanced LIGO," LIGO document LIGO-G050423-00-Z, http://www.ligo.caltech.edu/docs/G/G050423-00/G050423-00.pdf.
  15. M. A. Arain, "Thermal Compensation in Stable Recycling Cavity," presented at the LSC March meeting, Louisiana, USA, March 2006, http://www.ligo.caltech.edu/docs/G/G060155-00/G060155-00.pdf.
  16. G. Mueller, "Stable recycling cavities for Advanced LIGO," presented at the LIGO-Virgo meeting, Hannover, Germany, October 2007, available at www.ligo.caltech.edu/docs/G/G070691-00.pdf.
  17. G. Heinzel et al, "Dual recycling for GEO 600," Class. Quantum Grav. 19,1547-1553 (2002).
    [CrossRef]
  18. G. Heinzel et al, "Experimental Demonstration of a Suspended Dual Recycling Interferometer for Gravitational Wave Detection," Phys. Rev. Lett. 81, 5493-5496 (1998).
    [CrossRef]
  19. F Acernese et al, "Status of Virgo," Class. Quantum Grav. 22, S869-S880 (2002).
    [CrossRef]
  20. R. Takahashi et al., "Status of TAMA300," Class. Quantum Grav. 22, S403-S408 (2004).
    [CrossRef]
  21. G. Mueller, "Parametric Instabilities and the geometry of the recycling cavities," presented at the Parametric Instability Workshop, Perth, Australia, 16-18 July, 2007, www.ligo.caltech.edu/docs/G/G070441-00.pdf.
  22. N. Mavalvala, D. Sigg, and D. Shoemaker, "Experimental Test of an Alignment-Sensing Scheme for a Gravitational-Wave Interferometer," Appl. Opt. 37, 7743-7746 (2005).
    [CrossRef]
  23. G. Mueller, "Beam jitter coupling in advanced LIGO," Opt. Express 13,7118-7132 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-7118.
    [CrossRef] [PubMed]
  24. E. Siegman, Lasers (University Science Books 1986).
  25. R. Lawrence, "Active Wavefront Correction in Laser Interferometric Gravitational Wave Detectors," PhD Dissertation, Massachusetts Institute of Technology, (2003).

2005 (2)

2004 (1)

R. Takahashi et al., "Status of TAMA300," Class. Quantum Grav. 22, S403-S408 (2004).
[CrossRef]

2003 (2)

D. A. Shaddock et al., "Power-recycled Michelson interferometer with resonant sideband extraction," Appl. Opt. 42, 1283-1295 (2003).
[CrossRef] [PubMed]

P. Fritschel, "Second generation instruments for the Laser Interferometer Gravitational Wave Observatory (LIGO)," Proc. SPIE 4856, 282-291 (2003).
[CrossRef]

2002 (3)

G. Heinzel et al, "Dual recycling for GEO 600," Class. Quantum Grav. 19,1547-1553 (2002).
[CrossRef]

A. Weinstein, "Advanced LIGO optical configuration and prototyping effort," Class. Quantum Grav. 19, 1575- 1584 (2002).
[CrossRef]

F Acernese et al, "Status of Virgo," Class. Quantum Grav. 22, S869-S880 (2002).
[CrossRef]

1999 (2)

1998 (1)

G. Heinzel et al, "Experimental Demonstration of a Suspended Dual Recycling Interferometer for Gravitational Wave Detection," Phys. Rev. Lett. 81, 5493-5496 (1998).
[CrossRef]

Acernese, F

F Acernese et al, "Status of Virgo," Class. Quantum Grav. 22, S869-S880 (2002).
[CrossRef]

D???Ambrosio, E.

Fritschel, P.

P. Fritschel, "Second generation instruments for the Laser Interferometer Gravitational Wave Observatory (LIGO)," Proc. SPIE 4856, 282-291 (2003).
[CrossRef]

Fritschel, P. K.

Frolov, V.

Gretarsson, A. M.

Heinzel, G.

G. Heinzel et al, "Dual recycling for GEO 600," Class. Quantum Grav. 19,1547-1553 (2002).
[CrossRef]

G. Heinzel et al, "Experimental Demonstration of a Suspended Dual Recycling Interferometer for Gravitational Wave Detection," Phys. Rev. Lett. 81, 5493-5496 (1998).
[CrossRef]

Mavalvala, N.

Mueller, G.

O???Reilly, B.

Shaddock, D. A.

Shoemaker, D.

Sigg, D.

Takahashi, R.

R. Takahashi et al., "Status of TAMA300," Class. Quantum Grav. 22, S403-S408 (2004).
[CrossRef]

Waldman, S. J.

S. J. Waldman et al., "Status of LIGO at the start of the fifth science run," Class. Quantum Grav. 23, S267-S269 (1999).

Weinstein, A.

A. Weinstein, "Advanced LIGO optical configuration and prototyping effort," Class. Quantum Grav. 19, 1575- 1584 (2002).
[CrossRef]

Appl. Opt. (2)

Class. Quantum Grav. (5)

A. Weinstein, "Advanced LIGO optical configuration and prototyping effort," Class. Quantum Grav. 19, 1575- 1584 (2002).
[CrossRef]

S. J. Waldman et al., "Status of LIGO at the start of the fifth science run," Class. Quantum Grav. 23, S267-S269 (1999).

G. Heinzel et al, "Dual recycling for GEO 600," Class. Quantum Grav. 19,1547-1553 (2002).
[CrossRef]

F Acernese et al, "Status of Virgo," Class. Quantum Grav. 22, S869-S880 (2002).
[CrossRef]

R. Takahashi et al., "Status of TAMA300," Class. Quantum Grav. 22, S403-S408 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Phys. Rev. Lett. (1)

G. Heinzel et al, "Experimental Demonstration of a Suspended Dual Recycling Interferometer for Gravitational Wave Detection," Phys. Rev. Lett. 81, 5493-5496 (1998).
[CrossRef]

Proc. SPIE (1)

P. Fritschel, "Second generation instruments for the Laser Interferometer Gravitational Wave Observatory (LIGO)," Proc. SPIE 4856, 282-291 (2003).
[CrossRef]

Other (14)

H. Yamamoto, "Scattering Loss," presented at the LIGO-Virgo meeting, Hannover, Germany, October 2007, www.ligo.caltech.edu/docs/G/G070657.pdf.

M. A. Arain et al., "Input Optics Subsystem Preliminary Design Document," LIGO document, LIGO-T060269- 02-D, http://www.ligo.caltech.edu/docs/T/T060269-02.pdf.

Y. Pan, "Optimal degeneracy for the signal-recycling cavity in advanced LIGO," http://arxiv.org/PS cache/gr-qc/pdf/0608/0608128v1.pdf.

G. Mueller, "Stable Recycling Cavities for Advanced LIGO," LIGO document LIGO-G050423-00-Z, http://www.ligo.caltech.edu/docs/G/G050423-00/G050423-00.pdf.

M. A. Arain, "Thermal Compensation in Stable Recycling Cavity," presented at the LSC March meeting, Louisiana, USA, March 2006, http://www.ligo.caltech.edu/docs/G/G060155-00/G060155-00.pdf.

G. Mueller, "Stable recycling cavities for Advanced LIGO," presented at the LIGO-Virgo meeting, Hannover, Germany, October 2007, available at www.ligo.caltech.edu/docs/G/G070691-00.pdf.

C. Wilkinson, "Plans for Advanced LIGO Instruments," presented at the 2005 APS April Meeting, Tampa, Florida, USA, 16-19 April 2005.

S. Ballmer et al., "Thermal Compensation System Description," LIGO document, LIGO- T050064-00-R, http://www.ligo.caltech.edu/docs/T/T050064-00.pdf.

H. Armandula et al., "Core Optics Components Preliminary Design," LIGO document LIGO- E080033-00-D, http://www.ligo.caltech.edu/ gari/LIGOII/E080033-00PreliminaryDesign.pdf.

H. Armandula et al., "Core Optics Components Preliminary Design," LIGO document LIGO- E080033-00-D, http://www.ligo.caltech.edu/ gari/LIGOII/E080033-00PreliminaryDesign.pdf.

R. Adhikari, P. Fritschel, and S. Waldman, "Enhanced LIGO," LIGO document, LIGO-T060156-01, http://www.ligo.caltech.edu/docs/T/T060156-01.pdf.

G. Mueller, "Parametric Instabilities and the geometry of the recycling cavities," presented at the Parametric Instability Workshop, Perth, Australia, 16-18 July, 2007, www.ligo.caltech.edu/docs/G/G070441-00.pdf.

E. Siegman, Lasers (University Science Books 1986).

R. Lawrence, "Active Wavefront Correction in Laser Interferometric Gravitational Wave Detectors," PhD Dissertation, Massachusetts Institute of Technology, (2003).

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Figures (7)

Fig. 1.
Fig. 1.

The current LIGO configuration uses two 4km long arm cavities formed between the ITMs and ETMs in each arm of a Michelson interferometer. The PRM and the Michelson interferometer form the PRC. The carrier (red) resonates inside the arm cavities and the PRC, the RF-sdiebands (blue) resonate inside the PRC, and the signal sidebands (green) resonate inside the arm cavities and propagate to the detector in the dark port. The different ‘beam sizes’ symbolize the different spatial modes of the various fields in the various cavities.

Fig. 2.
Fig. 2.

The Advanced LIGO design uses three mirror recycling cavities. Each recycling cavity consists of a beam expanding (or reducing) telescope (PR 3/P R2 or SR 3/SR 2, respectively) and an additional end mirror PR 1 or SR 1. The position of the end mirror with respect to the waist of the mode going to PR 2 or coming from SR 2 determines the final Gouy phase inside each recycling cavity. The red lines indicate the carrier eigenmode, the blue lines the eigenmode of the RF sidebands, and the green line of the signal sidebands. After optimizing the beam expanding and reducing telescopes all spatial modes will be well matched to each other.

Fig. 3.
Fig. 3.

The accumulated Gouy phase (blue, left axis) and the beam size (green, right axis) on R 1 as a function of the ROC of R 2. The minimum spot size is 1.6mm at a Gouy phase of 90°.

Fig. 4.
Fig. 4.

Left graph: The blue line shows the mode matching (in power) between the PRC and the arm cavity eigenmode as a function of the normalized error in PR 3 ROC. The red line shows the mode matching between the input field coming from the mode cleaner and the recycling cavity. Right graph: The ROC plotted on left y-axis and beam size plotted on right y-axis. For two different values of PR 3 ROC, we have the same ROC (and hence a stable solution) at PR 1 with 100% mode matching. The modematching as a function of the ROC of PR 2 behaves similar in terms of absolute error in ROC. The signal recycling cavity shows also the same behavior. Here AC: Arm cavity, RC: Recycling cavity, and MC: Mode cleaner.

Fig. 5.
Fig. 5.

The mode matching (in power) as a function of displacement of R 2 (it applies to both PR 2 and SR 2) from the nominal position. The blue curve shows the mode matching between the recycling cavity and the arm cavity for nominal ROC values of PR 2 and PR 3 while the green curve is for -0.5 percent error in the nominal ROC values of PR 2 and PR 3. The red and the golden curves show the corresponding mode matching product from the input (or output) mode cleaner mode to the PRC (SRC) mode and then from PRC to the arm cavity mode for nominal and -0.5 percent error in the ROCs values of PR 2 and PR 3.

Fig. 6.
Fig. 6.

The mode matching (in power) between the power recycling cavity and the (average) arm cavity as a function of ITM and ETM ROC. The left graph shows the mode matching w/o length adjustments. The mode matching between recycling cavity and arm cavity after adjusting the distances inside the beam expanding telescope becomes essentially 100.00%. The right graph shows the mode matching between the input mode cleaner and the power recycling cavity/arm cavity after adjusting the distances inside the power recycling cavity. These adjustments were made without changing the overall length of the recycling cavity and without changing the mode matching from the input mode. The mode matching between the output mode cleaner, the signal recycling cavity, and the arm cavities shows a similar behavior.

Fig. 7.
Fig. 7.

A two element design for the stable recycling cavities. This design uses a focusing lens (PR2) and one curved mirror (PR1). The focusing lens could be formed inside the thermal compensation plate or inside the ITM substrate. Instead of a focusing lens, it is also possible to use a large curved mirror to focus the beam.

Tables (1)

Tables Icon

Table 1. The current design parameters for the stable PRC and the stable signal recycling cavity. Ri are the radii of curvature of the three mirrors PRi or SRi . Lij are the distances between mirrors ij; Index I stands for the ITM mirror. The one-way Gouy phases in the recycling cavities are: Ψ PR G =2.08rad, Ψ SR G =0.51rad.

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