Abstract

We have tested a new kind of Fabry–Perot long-baseline optical resonator proposed to reduce the thermal noise sensitivity of gravitational wave interferometric detectors—the “mesa beam” cavity—whose flat top beam shape is achieved by means of an aspherical end mirror. We present the fundamental mode intensity pattern for this cavity and its distortion due to surface imperfections and tilt misalignments, and contrast the higher order mode patterns to the Gauss–Laguerre modes of a spherical mirror cavity. We discuss the effects of mirror tilts on cavity alignment and locking and present measurements of the mesa beam tilt sensitivity.

© 2007 Optical Society of America

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  1. P. Fritschel, "Advanced LIGO systems design," LIGO Tech. Note T-010075-00-D, http://docuserv.ligo.caltech.edu/.
  2. P. A. Belanger and C. Paré, "Optical resonators using graded-phase mirrors," Opt. Lett. 16, 1057-1059 (1991).
    [CrossRef] [PubMed]
  3. P. A. Belanger, R. L. Lachance, and C. Paré, "Super-Gaussian output from a CO2 laser by using a graded-phase mirror resonator," Opt. Lett. 17, 739-741 (1992).
    [CrossRef] [PubMed]
  4. E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. S. Thorne, and S. Vyatchanin, "Reducing thermoelastic noise in gravitational-wave interferometers by flattening the light beams," arXiv.org e-Print archive, gr-qc/0409075, 2004, http://arxiv.org/archive/gr-qc.
  5. R. O'Shaughnessy, S. Strigin, and S. Vyatchanin, "The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for the Mexican-hat-mirror proposal for advanced LIGO," arXiv.org e-Print archive, gr-qc/0409050, 2004, http://arxiv.org/archive/gr-qc.
  6. E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. Thorne, and S. Vyatchanin, "Status report on Mexican-hat flat-topped beams for advanced LIGO," LIGO Tech. Note T-030009-00, http://docuserv.ligo.caltech.edu/.
  7. J. Agresti and R. DeSalvo, "Flat beam profile to depress thermal noise," presented at Aspen Winter Conference on Gravitational Waves, Gravitational Wave Advanced Detectors Workshop (GWADW), Aspen, Colo., USA, 16-22 January 2005, e-Print LIGO-G050041-00-Z, http://docuserv.ligo.caltech.edu/.
  8. J.-Y. Vinet, "Mirror thermal noise in flat-beam cavities for advanced gravitational wave interferometers," Class. Quantum Grav. 22, 1395-1404 (2005).
    [CrossRef]
  9. J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
    [CrossRef]
  10. E. D'Ambrosio, R. O'Shaughnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, "Advanced LIGO: non-Gaussian beams," Class. Quantum Grav. 21, S867-S873 (2004).
    [CrossRef]
  11. E. D'Ambrosio, "Non-spherical mirrors to reduce thermoelastic noise in advanced gravity wave interferometers," Phys. Rev. D 67, 102004 (2003).
    [CrossRef]
  12. P. Beyersdorf, S. Zappe, M. M. Fejer, and M. Burkhardt, "Cavity with a deformable mirror for tailoring the shape of the eigenmode," Appl. Opt. 45, 6723-6728 (2006).
    [CrossRef] [PubMed]
  13. S. Avino, E. Calloni, L. Milano, L. Di Fiore, R. De Rosa, and A. Tierno, "Generation of non-Gaussian flat laser beams," Phys. Lett. A 355, 258-261 (2006).
    [CrossRef]
  14. G. Cella, R. DeSalvo, V. Sannibale, H. Tariq, N. Viboud, and A. Takamori, "Seismic attenuation performance of the first prototype of a geometric anti-spring filter," Nucl. Instrum. Methods Phys. Res. A 487, 652-660 (2002).
    [CrossRef]
  15. M. G. Tarallo, "Experimental study of a non Gaussian optical resonator to reduce mirror thermal noise for graviatational waves detectors," Ph.D. disseration (University of Pisa, 2005), e-Print LIGO-P050032-00-R, http://docuserv.ligo.caltech.edu/.
  16. J. M. Spinhirne, D. Anafi, R. H. Freeman, and H. R. Garcia, "Intracavity adaptive optics. 1: Astigmatism correction performance," Appl. Opt. 20, 976-984 (1981).
    [CrossRef] [PubMed]
  17. S. Makki and J. Leger, "Solid-state laser resonators with diffractive optic thermal aberration correction," IEEE J. Quantum Electron. 35, 1075-1085 (1999).
    [CrossRef]
  18. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

2006 (3)

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

S. Avino, E. Calloni, L. Milano, L. Di Fiore, R. De Rosa, and A. Tierno, "Generation of non-Gaussian flat laser beams," Phys. Lett. A 355, 258-261 (2006).
[CrossRef]

P. Beyersdorf, S. Zappe, M. M. Fejer, and M. Burkhardt, "Cavity with a deformable mirror for tailoring the shape of the eigenmode," Appl. Opt. 45, 6723-6728 (2006).
[CrossRef] [PubMed]

2005 (3)

M. G. Tarallo, "Experimental study of a non Gaussian optical resonator to reduce mirror thermal noise for graviatational waves detectors," Ph.D. disseration (University of Pisa, 2005), e-Print LIGO-P050032-00-R, http://docuserv.ligo.caltech.edu/.

J. Agresti and R. DeSalvo, "Flat beam profile to depress thermal noise," presented at Aspen Winter Conference on Gravitational Waves, Gravitational Wave Advanced Detectors Workshop (GWADW), Aspen, Colo., USA, 16-22 January 2005, e-Print LIGO-G050041-00-Z, http://docuserv.ligo.caltech.edu/.

J.-Y. Vinet, "Mirror thermal noise in flat-beam cavities for advanced gravitational wave interferometers," Class. Quantum Grav. 22, 1395-1404 (2005).
[CrossRef]

2004 (3)

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. S. Thorne, and S. Vyatchanin, "Reducing thermoelastic noise in gravitational-wave interferometers by flattening the light beams," arXiv.org e-Print archive, gr-qc/0409075, 2004, http://arxiv.org/archive/gr-qc.

R. O'Shaughnessy, S. Strigin, and S. Vyatchanin, "The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for the Mexican-hat-mirror proposal for advanced LIGO," arXiv.org e-Print archive, gr-qc/0409050, 2004, http://arxiv.org/archive/gr-qc.

E. D'Ambrosio, R. O'Shaughnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, "Advanced LIGO: non-Gaussian beams," Class. Quantum Grav. 21, S867-S873 (2004).
[CrossRef]

2003 (1)

E. D'Ambrosio, "Non-spherical mirrors to reduce thermoelastic noise in advanced gravity wave interferometers," Phys. Rev. D 67, 102004 (2003).
[CrossRef]

2002 (1)

G. Cella, R. DeSalvo, V. Sannibale, H. Tariq, N. Viboud, and A. Takamori, "Seismic attenuation performance of the first prototype of a geometric anti-spring filter," Nucl. Instrum. Methods Phys. Res. A 487, 652-660 (2002).
[CrossRef]

1999 (2)

S. Makki and J. Leger, "Solid-state laser resonators with diffractive optic thermal aberration correction," IEEE J. Quantum Electron. 35, 1075-1085 (1999).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

1992 (1)

1991 (1)

1981 (1)

Agresti, J.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

J. Agresti and R. DeSalvo, "Flat beam profile to depress thermal noise," presented at Aspen Winter Conference on Gravitational Waves, Gravitational Wave Advanced Detectors Workshop (GWADW), Aspen, Colo., USA, 16-22 January 2005, e-Print LIGO-G050041-00-Z, http://docuserv.ligo.caltech.edu/.

Anafi, D.

Avino, S.

S. Avino, E. Calloni, L. Milano, L. Di Fiore, R. De Rosa, and A. Tierno, "Generation of non-Gaussian flat laser beams," Phys. Lett. A 355, 258-261 (2006).
[CrossRef]

Belanger, P. A.

Beyersdorf, P.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Burkhardt, M.

Calloni, E.

S. Avino, E. Calloni, L. Milano, L. Di Fiore, R. De Rosa, and A. Tierno, "Generation of non-Gaussian flat laser beams," Phys. Lett. A 355, 258-261 (2006).
[CrossRef]

Cella, G.

G. Cella, R. DeSalvo, V. Sannibale, H. Tariq, N. Viboud, and A. Takamori, "Seismic attenuation performance of the first prototype of a geometric anti-spring filter," Nucl. Instrum. Methods Phys. Res. A 487, 652-660 (2002).
[CrossRef]

D'Ambrosio, E.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. S. Thorne, and S. Vyatchanin, "Reducing thermoelastic noise in gravitational-wave interferometers by flattening the light beams," arXiv.org e-Print archive, gr-qc/0409075, 2004, http://arxiv.org/archive/gr-qc.

E. D'Ambrosio, R. O'Shaughnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, "Advanced LIGO: non-Gaussian beams," Class. Quantum Grav. 21, S867-S873 (2004).
[CrossRef]

E. D'Ambrosio, "Non-spherical mirrors to reduce thermoelastic noise in advanced gravity wave interferometers," Phys. Rev. D 67, 102004 (2003).
[CrossRef]

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. Thorne, and S. Vyatchanin, "Status report on Mexican-hat flat-topped beams for advanced LIGO," LIGO Tech. Note T-030009-00, http://docuserv.ligo.caltech.edu/.

De Rosa, R.

S. Avino, E. Calloni, L. Milano, L. Di Fiore, R. De Rosa, and A. Tierno, "Generation of non-Gaussian flat laser beams," Phys. Lett. A 355, 258-261 (2006).
[CrossRef]

DeSalvo, R.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

J. Agresti and R. DeSalvo, "Flat beam profile to depress thermal noise," presented at Aspen Winter Conference on Gravitational Waves, Gravitational Wave Advanced Detectors Workshop (GWADW), Aspen, Colo., USA, 16-22 January 2005, e-Print LIGO-G050041-00-Z, http://docuserv.ligo.caltech.edu/.

G. Cella, R. DeSalvo, V. Sannibale, H. Tariq, N. Viboud, and A. Takamori, "Seismic attenuation performance of the first prototype of a geometric anti-spring filter," Nucl. Instrum. Methods Phys. Res. A 487, 652-660 (2002).
[CrossRef]

Di Fiore, L.

S. Avino, E. Calloni, L. Milano, L. Di Fiore, R. De Rosa, and A. Tierno, "Generation of non-Gaussian flat laser beams," Phys. Lett. A 355, 258-261 (2006).
[CrossRef]

Fejer, M. M.

Forest, D.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

Freeman, R. H.

Fritschel, P.

P. Fritschel, "Advanced LIGO systems design," LIGO Tech. Note T-010075-00-D, http://docuserv.ligo.caltech.edu/.

Garcia, H. R.

Lachance, R. L.

Lagrange, B.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

Leger, J.

S. Makki and J. Leger, "Solid-state laser resonators with diffractive optic thermal aberration correction," IEEE J. Quantum Electron. 35, 1075-1085 (1999).
[CrossRef]

Mackowski, J. M.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

Makki, S.

S. Makki and J. Leger, "Solid-state laser resonators with diffractive optic thermal aberration correction," IEEE J. Quantum Electron. 35, 1075-1085 (1999).
[CrossRef]

Michel, C.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

Milano, L.

S. Avino, E. Calloni, L. Milano, L. Di Fiore, R. De Rosa, and A. Tierno, "Generation of non-Gaussian flat laser beams," Phys. Lett. A 355, 258-261 (2006).
[CrossRef]

Montorio, J. L.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

Morgado, N.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

O'Shaughnessy, R.

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. S. Thorne, and S. Vyatchanin, "Reducing thermoelastic noise in gravitational-wave interferometers by flattening the light beams," arXiv.org e-Print archive, gr-qc/0409075, 2004, http://arxiv.org/archive/gr-qc.

R. O'Shaughnessy, S. Strigin, and S. Vyatchanin, "The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for the Mexican-hat-mirror proposal for advanced LIGO," arXiv.org e-Print archive, gr-qc/0409050, 2004, http://arxiv.org/archive/gr-qc.

E. D'Ambrosio, R. O'Shaughnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, "Advanced LIGO: non-Gaussian beams," Class. Quantum Grav. 21, S867-S873 (2004).
[CrossRef]

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. Thorne, and S. Vyatchanin, "Status report on Mexican-hat flat-topped beams for advanced LIGO," LIGO Tech. Note T-030009-00, http://docuserv.ligo.caltech.edu/.

Paré, C.

Pinard, L.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

Remillieux, A.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

Sannibale, V.

G. Cella, R. DeSalvo, V. Sannibale, H. Tariq, N. Viboud, and A. Takamori, "Seismic attenuation performance of the first prototype of a geometric anti-spring filter," Nucl. Instrum. Methods Phys. Res. A 487, 652-660 (2002).
[CrossRef]

Simoni, B.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

Spinhirne, J. M.

Strigin, S.

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. S. Thorne, and S. Vyatchanin, "Reducing thermoelastic noise in gravitational-wave interferometers by flattening the light beams," arXiv.org e-Print archive, gr-qc/0409075, 2004, http://arxiv.org/archive/gr-qc.

R. O'Shaughnessy, S. Strigin, and S. Vyatchanin, "The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for the Mexican-hat-mirror proposal for advanced LIGO," arXiv.org e-Print archive, gr-qc/0409050, 2004, http://arxiv.org/archive/gr-qc.

E. D'Ambrosio, R. O'Shaughnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, "Advanced LIGO: non-Gaussian beams," Class. Quantum Grav. 21, S867-S873 (2004).
[CrossRef]

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. Thorne, and S. Vyatchanin, "Status report on Mexican-hat flat-topped beams for advanced LIGO," LIGO Tech. Note T-030009-00, http://docuserv.ligo.caltech.edu/.

Takamori, A.

G. Cella, R. DeSalvo, V. Sannibale, H. Tariq, N. Viboud, and A. Takamori, "Seismic attenuation performance of the first prototype of a geometric anti-spring filter," Nucl. Instrum. Methods Phys. Res. A 487, 652-660 (2002).
[CrossRef]

Tarallo, M.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

Tarallo, M. G.

M. G. Tarallo, "Experimental study of a non Gaussian optical resonator to reduce mirror thermal noise for graviatational waves detectors," Ph.D. disseration (University of Pisa, 2005), e-Print LIGO-P050032-00-R, http://docuserv.ligo.caltech.edu/.

Tariq, H.

G. Cella, R. DeSalvo, V. Sannibale, H. Tariq, N. Viboud, and A. Takamori, "Seismic attenuation performance of the first prototype of a geometric anti-spring filter," Nucl. Instrum. Methods Phys. Res. A 487, 652-660 (2002).
[CrossRef]

Thorne, K.

E. D'Ambrosio, R. O'Shaughnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, "Advanced LIGO: non-Gaussian beams," Class. Quantum Grav. 21, S867-S873 (2004).
[CrossRef]

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. Thorne, and S. Vyatchanin, "Status report on Mexican-hat flat-topped beams for advanced LIGO," LIGO Tech. Note T-030009-00, http://docuserv.ligo.caltech.edu/.

Thorne, K. S.

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. S. Thorne, and S. Vyatchanin, "Reducing thermoelastic noise in gravitational-wave interferometers by flattening the light beams," arXiv.org e-Print archive, gr-qc/0409075, 2004, http://arxiv.org/archive/gr-qc.

Tierno, A.

S. Avino, E. Calloni, L. Milano, L. Di Fiore, R. De Rosa, and A. Tierno, "Generation of non-Gaussian flat laser beams," Phys. Lett. A 355, 258-261 (2006).
[CrossRef]

Viboud, N.

G. Cella, R. DeSalvo, V. Sannibale, H. Tariq, N. Viboud, and A. Takamori, "Seismic attenuation performance of the first prototype of a geometric anti-spring filter," Nucl. Instrum. Methods Phys. Res. A 487, 652-660 (2002).
[CrossRef]

Vinet, J.-Y.

J.-Y. Vinet, "Mirror thermal noise in flat-beam cavities for advanced gravitational wave interferometers," Class. Quantum Grav. 22, 1395-1404 (2005).
[CrossRef]

Vyatchanin, S.

R. O'Shaughnessy, S. Strigin, and S. Vyatchanin, "The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for the Mexican-hat-mirror proposal for advanced LIGO," arXiv.org e-Print archive, gr-qc/0409050, 2004, http://arxiv.org/archive/gr-qc.

E. D'Ambrosio, R. O'Shaughnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, "Advanced LIGO: non-Gaussian beams," Class. Quantum Grav. 21, S867-S873 (2004).
[CrossRef]

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. S. Thorne, and S. Vyatchanin, "Reducing thermoelastic noise in gravitational-wave interferometers by flattening the light beams," arXiv.org e-Print archive, gr-qc/0409075, 2004, http://arxiv.org/archive/gr-qc.

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. Thorne, and S. Vyatchanin, "Status report on Mexican-hat flat-topped beams for advanced LIGO," LIGO Tech. Note T-030009-00, http://docuserv.ligo.caltech.edu/.

Willems, P.

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

E. D'Ambrosio, R. O'Shaughnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, "Advanced LIGO: non-Gaussian beams," Class. Quantum Grav. 21, S867-S873 (2004).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Zappe, S.

Appl. Opt. (2)

Class. Quantum Grav. (2)

J.-Y. Vinet, "Mirror thermal noise in flat-beam cavities for advanced gravitational wave interferometers," Class. Quantum Grav. 22, 1395-1404 (2005).
[CrossRef]

E. D'Ambrosio, R. O'Shaughnessy, K. Thorne, P. Willems, S. Strigin, and S. Vyatchanin, "Advanced LIGO: non-Gaussian beams," Class. Quantum Grav. 21, S867-S873 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Makki and J. Leger, "Solid-state laser resonators with diffractive optic thermal aberration correction," IEEE J. Quantum Electron. 35, 1075-1085 (1999).
[CrossRef]

J. Phys.: Conf. Ser. (1)

J. Agresti, E. D'Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remillieux, B. Simoni, M. Tarallo, and P. Willems, "Design and construction of a prototype of a flat top beam interferometer and initial tests," J. Phys.: Conf. Ser. 32, 301-308 (2006).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

G. Cella, R. DeSalvo, V. Sannibale, H. Tariq, N. Viboud, and A. Takamori, "Seismic attenuation performance of the first prototype of a geometric anti-spring filter," Nucl. Instrum. Methods Phys. Res. A 487, 652-660 (2002).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

S. Avino, E. Calloni, L. Milano, L. Di Fiore, R. De Rosa, and A. Tierno, "Generation of non-Gaussian flat laser beams," Phys. Lett. A 355, 258-261 (2006).
[CrossRef]

Phys. Rev. D (1)

E. D'Ambrosio, "Non-spherical mirrors to reduce thermoelastic noise in advanced gravity wave interferometers," Phys. Rev. D 67, 102004 (2003).
[CrossRef]

Other (7)

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. S. Thorne, and S. Vyatchanin, "Reducing thermoelastic noise in gravitational-wave interferometers by flattening the light beams," arXiv.org e-Print archive, gr-qc/0409075, 2004, http://arxiv.org/archive/gr-qc.

R. O'Shaughnessy, S. Strigin, and S. Vyatchanin, "The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for the Mexican-hat-mirror proposal for advanced LIGO," arXiv.org e-Print archive, gr-qc/0409050, 2004, http://arxiv.org/archive/gr-qc.

E. D'Ambrosio, R. O'Shaughnessy, S. Strigin, K. Thorne, and S. Vyatchanin, "Status report on Mexican-hat flat-topped beams for advanced LIGO," LIGO Tech. Note T-030009-00, http://docuserv.ligo.caltech.edu/.

J. Agresti and R. DeSalvo, "Flat beam profile to depress thermal noise," presented at Aspen Winter Conference on Gravitational Waves, Gravitational Wave Advanced Detectors Workshop (GWADW), Aspen, Colo., USA, 16-22 January 2005, e-Print LIGO-G050041-00-Z, http://docuserv.ligo.caltech.edu/.

M. G. Tarallo, "Experimental study of a non Gaussian optical resonator to reduce mirror thermal noise for graviatational waves detectors," Ph.D. disseration (University of Pisa, 2005), e-Print LIGO-P050032-00-R, http://docuserv.ligo.caltech.edu/.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

P. Fritschel, "Advanced LIGO systems design," LIGO Tech. Note T-010075-00-D, http://docuserv.ligo.caltech.edu/.

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Figures (11)

Fig. 1
Fig. 1

Schematic of the mechanical structure showing three of the five triangular spacers. (i) Flat input mirror, (ii) MH mirror, (iii) thermal shield (dotted line), (iv) vacuum tank (solid line), (v) spacer plate, (vi) Invar rod, and (vii) flat folding mirror.

Fig. 2
Fig. 2

(Color online) Surface profiles of the MH test mirror. The transverse pixel dimensions are 0.035 cm. (a) MH test mirror: global view. (b) Zoom of the central bump: the pixel colors show the asymmetry of the test mirror. FFT simulations showed a tilt effect of 0.9   μrad .

Fig. 3
Fig. 3

Schematic of the mesa beam cavity prototype experimental setup: the two optical benches, the cavity tank, the control electronics, and the profile acquisition. Solid lines denote optical signals; dotted lines denote electronic signals. (1) Lenses to eliminate astigmatism, (2) Faraday isolator, (3) mode matching lens, (4) flat input mirror, (5) MH mirror, (6) flat folding mirror, (7,10) beam imaging lenses, (8) beam dump, and (9) wedged attenuating pickoff mirror. Unlabeled items are beam-steering mirrors.

Fig. 4
Fig. 4

(Color online) Misaligned modes.

Fig. 5
Fig. 5

Alignment of the fundamental mesa beam with astigmatic flat cavity mirrors: (a) stable, asymmetric single peak, (b) highly sensitive double peak distribution.

Fig. 6
Fig. 6

(Color online) Three-dimensional profile of the mesa fundamental mode.

Fig. 7
Fig. 7

(Color online) One-dimensional profiles of fits to the mesa beam profiles. The top row shows normalized experimental data as they were measured with the CCD camera. The dashed curve is the best fit mesa profile. The bottom row shows profiles extracted from the FFT simulation with the best corrective tilt applied. In this case, the transverse scale is taken at the MH mirror.

Fig. 8
Fig. 8

(Color online) High order mesa beam transverse modes: (a) TEM 10 , (b) TEM 11 , (c) TEM 20 .

Fig. 9
Fig. 9

Mesa TEM 10 profile (thick black curve). The light gray curve shows the theoretical mesa TEM 10 , which better fits the data than a Laguerre–Gauss TEM 10 mode (dashed curve).

Fig. 10
Fig. 10

Apparatus used to measure the tilt sensitivity of the mesa beam cavity: (i) Mephisto laser, (ii) HeNe chopper monitor laser, (iii) mode profiler CCD camera, (iv) chopper wheel, (v) HeNe optical lever laser, (vi) chopper monitor photodiode, (vii) optical lever quadrant photodiode, (viii) mirror dithering PZT, and (ix) function generator.

Fig. 11
Fig. 11

Comparison of FFT simulated (thick curve) and experimental profiles (thin curve) with the same integrated power for various tilts.

Tables (1)

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Table 1 Frequency Spacing between Eigenmodes for the 7.32 m Long MH Cavity Prototype a

Equations (4)

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U ( r ) = r r m e s a exp ( ( r r ) 2 ( 1 i ) 2 w 0 2 ) d 2 r , = 2 π 0 r mesa   exp ( ( r 2 + r 2 ) ( 1 i ) 2 w 0 2 ) × I 0 ( r r ( 1 i ) w 0 2 ) r d r ,
h MH ( r ) = Arg [ U ( r ) ] Arg [ U ( 0 ) ] k .
r mesa = 4 2 π L λ .
L prototype = ( r mesa prototype r mesa AdLIGO ) 2 L AdLIGO .

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