## Design of the Advanced LIGO recycling cavities

Optics Express, Vol. 16, Issue 14, pp. 10018-10032 (2008)

http://dx.doi.org/10.1364/OE.16.010018

Acrobat PDF (360 KB)

### 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

## 1. Introduction

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]

## 2. LIGO Configuration

*T*=2.7% and a radius of curvature (ROC)

_{I}*R*of about 15km and the end mirrors (ETMs) have a transmission of about 5–10ppm and a ROC

_{ITM}*R*of about 7km. Consequently, each arm cavity is highly over-coupled and on resonance the reflected field will be dominated by the field leaking out of the cavity. This changes the phase of the reflected field by 180° compared to the case where the arm cavity would be non-resonant. Each Fabry Perot cavity resonates on the same fundamental Gaussian mode. This mode has a beam radius at the ITM of 3.7cm and a Rayleigh range of 4000m inside the arm cavities and of 3700m inside the short Michelson interferometer. These modes (red) interfere again at the beamsplitter such that virtually all the light is sent back towards the Faraday rotator.

_{ETM}*T*=2.7% and increases the circulating power by about 50. This transmissivity was chosen based on the expected losses for the carrier field which resonates in the arm cavities. The goal was to create a slightly over-coupled PRC for the carrier field.

_{PR}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.

## 3. Advanced LIGO

*w*=5.55cm (1/

_{ITM}*e*

^{2}intensity beam radius) on the ITMs and of

*w*=6.2cm on the ETMs [7

_{ETM}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.

*R*=

_{ITM}*R*=2076m and beamsizes of 6cm to reduce diffraction losses inside the recycling cavities and to take into account the scaling of the thermo-elastic noise with the number of coating layers [9

_{ETM}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.

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]

*R*

_{3}(

*PR*

_{3}or

*SR*

_{3}) mirror. The convergence angle between

*R*

_{3}and

*R*

_{2}(

*PR*

_{2}or

*SR*

_{2}) will be in the order of a few mrad (see also Appendix). This highly converging beam propagates over a distance of about 16m to

*R*

_{2}. Before this mode reaches its own Rayleigh range,

*R*

_{2}reduces the convergence angle and sends the light to

*R*

_{1}(

*PR*

_{1}or

*SR*

_{1}). As

*R*

_{2}changes the modal parameters before the mode reaches its own Rayleigh range, the accumulated Gouy phase between the mirrors

*R*

_{2}and

*R*

_{3}is very small. The location of the waist of the mode between

*R*

_{1}and

*R*

_{2}with respect to the location of

*R*

_{1}is responsible for the accumulated Gouy phase and consequently for the transversal mode spacing and the stability of the recycling cavities. This location depends on the ROC of

*R*

_{2}. Figure 3 shows the accumulated Gouy phase and the beam size on

*R*

_{1}as a function of the ROC of

*R*

_{2}for a typical fixed distance between

*R*

_{2}and

*R*

_{1}and a typical ROC of

*R*

_{3}.

*R*

_{1}. But by decreasing the (negative) ROC of

*R*

_{2}, the waist location can be pushed closer and closer to

*R*

_{1}. Once the distance between the waist and

*R*

_{1}is smaller than the Rayleigh range, the mode will start to accumulate Gouy phase inside the SRC and the transversal mode spacing will become larger than the linewidth of the recycling cavity. Our current design of the SRC is similar to this case and the one-way Gouy phase in the SRC is currently set to Ψ

*=0.51rad. For the PRC, we further decrease the ROC of*

^{SR}_{G}*PR*

_{2}and move the waist into the PRC. Once the waist is inside the cavity, the Gouy phase is larger than π/2. Our current design of the power recycling cavity is similar to this case and the one-way Gouy phase in the PRC is currently set to Ψ

*=2.08rad.*

^{PR}_{G}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.

*T*≈7% when the SRC is resonant for the carrier (resonant sideband extraction). However, it has to be realized that it is impossible to fullfil this condition for all possible tunings of the signal recycling cavity. Additional optimization will require identification of a certain (hopefully small) number of potential tunings for the SRC and then optimization of the Gouy phases for these specific points of operation. Note that the difference between the Gouy phases Ψ

_{SR}*-Ψ*

^{PR}_{G}*=π/2causes degeneracy in the transversal mode spectrum which reduces the problem to some degree. This specific difference has another advantage as long as the SRC is tuned on or near the resonant sideband extraction tuning. The Michelson interferometer formed by the two recycling cavities reflects all odd modes and transmits all even modes generated in one of the arms. Although the visibility is not perfect because the reflectivities of the two recycling cavity mirrors are not equal, the amplitude of an odd mode will be much higher in the arm where it is generated compared to the other arm where it is not generated. The odd modes include the (1,0) and (0,1) Hermite Gauss modes which are generated by alignment errors of the mirrors. The amplitudes of these modes are measured at various ports to generate alignment signals for all optical components. With this specific Gouy phase difference it is possible to differentiate between alignment errors in the X and the Y-arm of the main interferometer by using spurious reflections in each arm to generate the alignment sensing signals. The signals in the X-arm are fairly independent from any misalignments in the Y-arm and vice versa. This choice of Gouy phases also allows to track modes which are generated for example by parametric instabilities better which could help during commissioning to identify their source and to suppress them.*

^{SR}_{G}## 4. Requirements on Mode matching

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. Express13, 7118–7132 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-7118. [CrossRef] [PubMed]

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]

### 4.1. Signal recycling cavity

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

### 4.2. Power recycling cavity

### 4.3. General properties of both designs

*PR*

_{2}or

*SR*

_{2}and of the distance between the first and the second mirror. The mode matching between each recycling cavity and the arm cavities can be changed by changing the distances between the three mirrors and also the distance to the arm cavity. However, the change scales in general with the Rayleigh range of the Gaussmode which is received or send out by the mirror that is repositioned. The Rayleigh range in the part between the ITM and

*R*

_{3}will be around 200m in Advanced LIGO. Any substantial change in mode matching in this part would require to move the mirrors with respect to each other by several 10m. This is impossible given the vacuum contraints in LIGO. On the other hand, this also means that even changes in the distance of up to a few meter will not affect the mode matching. The Rayleigh range in the part between

*R*

_{2}and

*R*

_{1}is on the order of a few meters (≈4.1m in the power recycling cavity and ≈7.7m in the signal recycling cavity). Any substantial change in the mode matching in this part would also require to move the mirrors by at least several 10cm. Although possible, this would still require major additional changes as the overall length of the recycling cavities has to be preserved to ensure that the RF-sidebands are resonant in the recycling cavities.

*R*

_{2}and

*R*

_{3}. The Rayleigh range of the mode propagating between these two mirrors is only ≈3.3cm in the PRC and ≈3.1cm in the SRC. Consequently, any change in the ROCs or distances on scales of a few cm will change the mode matching significantly. The fact that the mode matching is rather insensitive to the other distances allows us to optimize the mode matching without changing the overall lengths of the recycling cavities. Any change in the distance between

*R*

_{2}and

*R*

_{3}will simply be compensated by also changing the distance between

*R*

_{2}and

*R*

_{1}by twice that much; changing the distance between

*R*

_{3}and the ITMs would be even better from a mode matching point of view but

*R*

_{3}is a much larger mirror and would require much more available real estate for this move than the smaller

*R*

_{1}mirror.

*R*

_{2}and

*R*

_{3}can also be understood in terms of ray optics. The field coming from

*R*

_{2}appears to orginate from a virtual point source behind

*R*

_{2}. The distance between this virtual source is roughly half of the ROC of

*R*

_{2}.

*R*

_{3}is then placed close to half of its ROC away from the virtual focus and creates an image of the focus several km away. A small change of δ

*R*

_{2}in the ROC of

*R*

_{2}will change the location of the virtual point source by about δ

*R*

_{2}/2. A change of δ

*R*

_{3}in the ROC of

*R*

_{3}will change where the location of the virtual source should be to focus the beam to the right spot by δ

*R*

_{3}/2. As the image of the focus is several km away, a small change in any of the two radii curvatures in the wrong direction pushes the image even further out leading to an unstable mode inside the recycling cavities. However, both changes or deviations in the radii of curvatures can be compensated by changing the distance between

*R*

_{2}and

*R*

_{3}by δ

*L*

_{23}≈δ

*R*

_{3}/2+δ

*R*

_{2}/2 creating again a very stable recycling cavity. Although this will also affect the beamsizes and reduce the mode matching again, the change in beamsizes are rather small and, as we will see in the following chapter, will not reduce the modematching significantly.

## 5. Tolerances on the radii of curvatures

### 5.1. ROC Tolerance of PRC and SRC

*PR*

_{2}(

*SR*

_{2}) and

*R*

_{3}(

*SR*

_{3}) form relatively fast telescopes inside the recycling cavities. Consequently, the spatial eigenmode inside the recycling cavities is very sensitive to any ROC error in these mirrors. Comparatively, the remaining mirror, i.e.,

*PR*

_{1}(

*SR*

_{1}) has much relaxed ROC error tolerances. For simplicity, we will discuss PRC in the remainig of the section as the behavior of SRC is very silimar. The blue curve in the left graph in Figure 4 shows the mode matching between the recycling cavity eigenmode and the arm cavity eigenmode as a function of the error in

*PR*

_{3}ROC. It shows two maxima where the modematching is 100%. The reason for the two maxima lies in the dependence of the ROC of a Gaussmode from the distance to its waist:

*z*=

*z*. A change in the ROC of

_{R}*PR*

_{3}will move the waist further away from

*PR*

_{1}. During the change the ROC of the mode at

*PR*

_{1}will run through the minima and increase again. Consequently, it will match twice to the ROC of the

*PR*

_{1}mirror. The first solution corresponds to the design Gouy phase of 2.08rad while the second solution has a one-way Gouy phase of π-2.08=1.06rad. Although the ROCs match, the beam sizes are quite different for these two solutions. Therefore, the mode matching from the MC is only good for first solution. Changes in the ROC of

*PR*

_{2}shows a similar behavior but as the ROC is smaller the normalized error tolerance is larger. The SRC shows essentially the same behavior.

*PR*

_{3}of only 0.1% destabilizes the spatial eigenmodes of the recycling cavities. However, adjusting the distance between

*PR*

_{2}and

*PR*

_{3}while maintaining the recycling cavity length by moving

*PR*

_{1}by twice the distance allows to regain the stable recycling cavity modes and improve the mode matching back to 99.998% for deviations up to ±15cm in the recycling cavity mirrors ROCs. Figure 5 shows the mode matching sensitivity to the position of

*PR*

_{2}. The blue curve shows themodematching as a function of

*PR*

_{2}position from its nominal position when

*PR*

_{2}and

*PR*

_{3}are at their nominal ROC values. The curve has two maximums, i.e, one at the nominal position and the other 40 mm from its nominal position. The reason for the two maxima is again the hyperbolic behaviour of the ROC of the phasefront as a function of the distance to the waist. The same behavior can be observed even when the ROCs of

*PR*

_{2}and

*PR*

_{3}differ from their nominal values as shown by the green curve. The red and golden curves show the product ofmode matching betweenMC to recycling cvaity and recycling cavity to arm cavityas a function of the position of

*PR*

_{2}. Again, only one of the maxima in the mode matching between the recycling cavity and the arm cavity eigenmodes coincides with a good modematching of the input beam. In any case, as the Fig. 5 suggests the expected polishing error in ROCs of

*PR*

_{2}and

*PR*

_{3}can be corrected by appropriately repositioning the

*PR*

_{2}and

*PR*

_{1}mirror.

*PR*

_{3}and

*SR*

_{3}. Much tighter tolerances have to be put on our knowledge of the ROCs before the mirrors can be installed or installation procedures have to be developed which allow to place the mirrors in the appropriate position for the as-build ROCs.

### 5.2. Test masses

*PR*

_{2}and

*PR*

_{3}makes the mode matching between recycling cavity and arm cavity to virtually 100%. However, the mode matching fromMC to the recycling cavity remains greater than 99.1% as shown in the right graph of Fig. 6. This assumes that the input mode is fixed. However, we can adjust the input mode by adjusting the mirrors present before

*PR*

_{1}or by increasing the power from the laser. A 1% decrease can easily by adjusted by increasing the laser power without worrying about any additinal thermal effects. Similarly, for SRC, the output MC can be adjusted to the new SRC mode.

## 6. Summary

## 7. Appendix

*PR*

_{2}) which could be polished either into the substrate of the ITM or in the substrate of a compensation plate which will be located directly in front of the ITM. This lens would focus the beam over the length of the recycling cavity. The second element

*PR*

_{1}would then be placed inside the Rayleigh range near the waist of the mode to accumulate a reasonable Gouy phase. An alternative design simply replaces the lens with a curved mirror similar to the curved mirror used in the three-mirror design.

*w*≈5.5cm would be the beam size on

_{ITM}*PR*

_{2},

*L*is the distance to

*PR*

_{1},

*L*+Δ is the distance to the waist,

*w*

_{0}is the waist of this mode, and

*z*is the Rayleigh range. A distance

_{R}*L*that could fit into the LIGO vacuum envelope without folding the recycling cavity furthermore (which makes this a 3 mirror design) is

*L*≈25m. The distance between

*PR*

_{1}and the waist of this mode Δ has to be in the order of the Rayleigh range to have any appreciable Gouy phase or transversal mode spacing inside the recycling cavity:

*w*

_{0}gives:

*PR*

_{1}would then be:

*PR*

_{2}and

*PR*

_{1}, the waist of this mode will also not change when we move it closer to

*PR*

_{1}to change the Gouy phase. In general, any solution which generates a reasonable transversal mode spacing starting with a 5.5cm and having only 25m to work with will have to have a Rayleigh range of about 7cm and beamsizes on

*PR*

_{1}below 250

*µ*m.

*PR*

_{1}inside the power recycling cavity will reach a fewMW/cm

^{2}. Thismight cause life time problems with the coatings. Similar to the three mirror cavity, the short Rayleigh range makes this design very sensitive to ROC mismatches. This can also be compensated by changing the distance between

*PR*

_{1}and

*PR*

_{2}. This length change would have to be compensated by also changing the distance between

*PR*

_{2}and the ITM to maintain the overall length to keep the RF-sidebands resonant. Such a change is impossible when the focusing lens is polished into the ITMsubstrate and virtually impossible when it is polished into the compensation plate (CP) as the CP is suspended from the same suspension system than the ITM. The second design which uses the large curved mirror could accomodate this. However, this design requires to relay the laser beam to the other vacuum chamber and inject the beam from the other side which does not reduce the number of optical components in the entire setup, it tends to increase it.

## Acknowledgments

## References and links

1. | S. J. Waldman et. al., “Status of LIGO at the start of the fifth science run,” Class. Quantum Grav. |

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. |

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 |

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 |

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. |

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. |

18. | G. Heinzel et al, “Experimental Demonstration of a Suspended Dual Recycling Interferometer for Gravitational Wave Detection,” Phys. Rev. Lett. |

19. | F Acernese et al, “Status of Virgo,” Class. Quantum Grav. |

20. | R. Takahashi et al., “Status of TAMA300,” Class. Quantum Grav. |

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. |

23. | G. Mueller, “Beam jitter coupling in advanced LIGO,” Opt. Express13, 7118–7132 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-7118. [CrossRef] [PubMed] |

24. | E. Siegman, |

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

**OCIS Codes**

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(350.4600) Other areas of optics : Optical engineering

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: May 19, 2008

Revised Manuscript: June 17, 2008

Manuscript Accepted: June 17, 2008

Published: June 23, 2008

**Citation**

Muzammil A. Arain and Guido Mueller, "Design of the Advanced LIGO recycling cavities," Opt. Express **16**, 10018-10032 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-14-10018

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### References

- S. J. Waldman et al., "Status of LIGO at the start of the fifth science run," Class. Quantum Grav. 23, S267-S269 (1999).
- R. Adhikari, P. Fritschel, and S. Waldman, "Enhanced LIGO," LIGO document, LIGO-T060156-01, http://www.ligo.caltech.edu/docs/T/T060156-01.pdf.
- A. Weinstein, "Advanced LIGO optical configuration and prototyping effort," Class. Quantum Grav. 19, 1575- 1584 (2002). [CrossRef]
- C. Wilkinson, "Plans for Advanced LIGO Instruments," presented at the 2005 APS April Meeting, Tampa, Florida, USA, 16-19 April 2005.
- 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]
- 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.
- P. Fritschel, "Second generation instruments for the Laser Interferometer Gravitational Wave Observatory (LIGO)," Proc. SPIE 4856, 282-291 (2003). [CrossRef]
- H. Yamamoto, "Scattering Loss," presented at the LIGO-Virgo meeting, Hannover, Germany, October 2007, www.ligo.caltech.edu/docs/G/G070657.pdf.
- D. A. Shaddock et al., "Power-recycled Michelson interferometer with resonant sideband extraction," Appl. Opt. 42, 1283-1295 (2003). [CrossRef] [PubMed]
- 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.
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