Abstract

In this paper, we analytically prove a unique duality relation between the eigenspectra of paraxial optical cavities with nonspherical mirrors: a one-to-one mapping between eigenmodes and eigenvalues of cavities deviating from flat mirrors by h(r⃗) and cavities deviating from concentric mirrors by −h(r⃗), where h need not be a small perturbation. We then illustrate its application to optical cavities, proposed for advanced interferometric gravitational-wave detectors, where the mirrors are designed to support beams with rather flat intensity profiles over the mirror surfaces. This unique mapping might be very useful in future studies of alternative optical designs for advanced gravitational wave interferometers or experiments employing optical cavities with nonstandard mirrors.

© 2012 Optical Society of America

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  2. Advanced LIGO https://www.advancedligo.mit.edu .
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  5. 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:gr-qc/0409075v1.
  6. R. O’Shaughnessy, S. Strigin, and S. Vyatchanin, “The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for Mexican-hat mirror proposal for advanced LIGO,” arXiv:gr-qc/0409050v1.
  7. E. D’Ambrosio, “Non-spherical mirrors to reduce thermoelastic noise in advanced gravity wave interferometers,” Phys. Rev. D 67, 102004 (2003).
    [CrossRef]
  8. M. G. Tarallo, J. Miller, J. Agresti, E. D’Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remilleux, B. Simoni, and P. Willems, “Generation of a flat-top laser beam for gravitational-wave detectors by means of a non-spherical Fabry–Perot resonator,” Appl. Opt. 46, 6648–6654 (2007).
    [CrossRef]
  9. M. Bondarescu, O. Kogan, and Y. Chen, “Optimal light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 78, 082002 (2008).
    [CrossRef]
  10. B. Mours, E. Tournefier, and J. Y. Vinet, “Thermal noise reduction in interferometric gravitational wave antennas: using high order TEM modes,” Classical Quantum Gravity 23, 5777–5784 (2006).
    [CrossRef]
  11. J. Y. Vinet, “On special optical modes and thermal issues in advanced gravitational wave interferometric detectors,” Living Rev. Relativity 12, 5 (2009).
  12. V. Pierro, V. Galdi, G. Castaldi, I. M. Pinto, J. Agresti, and R. DeSalvo, “Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: bounds, profiles, and critical parameters,” Phys. Rev. D 76, 122003 (2007).
    [CrossRef]
  13. J. Agresti and R. DeSalvo, “Thermal noises calculations: Gaussian vs. Mesa beams,” LIGO technical note, LIGO-T050269-00-R available at http://admdbsrv.ligo.caltech.edu/dcc/ .
  14. P. Savov and S. Vyatchanin, “Estimate of tilt instability of Mesa-beam and Gaussian-beam modes for advanced LIGO,” Phys. Rev. D 74, 082002 (2006).
    [CrossRef]
  15. D. Sigg, “Angular instability in high power FP cavities,” LIGO technical note, LIGO-T030120-00, (2003); available at http://admdbsrv.ligo.caltech.edu/dcc/ .
  16. J. Sidles and D. Sigg, “Optical torques in suspended Fabry–Perot interferometers,” Phys. Lett. A 354, 167–172 (2006).
    [CrossRef]
  17. M. Bondarescu and K. S. Thorne, “A new family of light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 74, 082003 (2006).
    [CrossRef]
  18. V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006).
    [CrossRef]
  19. A. P. Lundgren, R. Bondarescu, D. Tsang, and M. Bondarescu, “Finite mirror effects in advanced interferometric gravitational wavedetectors,” Phys. Rev. D 77, 042003(2008).
    [CrossRef]
  20. A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
  21. J. P. Gordon and H. Kogelnik, “Equivalence relations among spherical mirror optical resonators,” Bell Syst. Tech. J. 43, 2873–2886 (1964).
  22. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef]
  23. G. Herziger and H. Weber, “Equivalent optical resonators,” Appl. Opt. 23, 1450–1452 (1984).
    [CrossRef]
  24. A. Siegman, Lasers (University Science Books, 1996), Ch. 19.
  25. P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20, 1098–1130 (2003).
    [CrossRef]
  26. V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric oscillatory instability in Fabry–Perot interferometer,” Phys. Lett. A 287, 331–338 (2001).
    [CrossRef]
  27. S. Gras, D. G. Blair, and L. Ju, “Opto-acoustic interactions in gravitational wave detectors: comparing flat-top beams with Gaussian beams,” Phys. Rev. D 81, 042001 (2010).
    [CrossRef]
  28. Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10–16-level laser stabilization,” Nat. Photon. 5, 158161 (2011).
  29. R. Grimm, M. Weidenmüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atomic Molec. Opt. Phys. 42, 95–170 (2000).

2011 (1)

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10–16-level laser stabilization,” Nat. Photon. 5, 158161 (2011).

2010 (1)

S. Gras, D. G. Blair, and L. Ju, “Opto-acoustic interactions in gravitational wave detectors: comparing flat-top beams with Gaussian beams,” Phys. Rev. D 81, 042001 (2010).
[CrossRef]

2009 (1)

J. Y. Vinet, “On special optical modes and thermal issues in advanced gravitational wave interferometric detectors,” Living Rev. Relativity 12, 5 (2009).

2008 (2)

M. Bondarescu, O. Kogan, and Y. Chen, “Optimal light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 78, 082002 (2008).
[CrossRef]

A. P. Lundgren, R. Bondarescu, D. Tsang, and M. Bondarescu, “Finite mirror effects in advanced interferometric gravitational wavedetectors,” Phys. Rev. D 77, 042003(2008).
[CrossRef]

2007 (2)

V. Pierro, V. Galdi, G. Castaldi, I. M. Pinto, J. Agresti, and R. DeSalvo, “Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: bounds, profiles, and critical parameters,” Phys. Rev. D 76, 122003 (2007).
[CrossRef]

M. G. Tarallo, J. Miller, J. Agresti, E. D’Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remilleux, B. Simoni, and P. Willems, “Generation of a flat-top laser beam for gravitational-wave detectors by means of a non-spherical Fabry–Perot resonator,” Appl. Opt. 46, 6648–6654 (2007).
[CrossRef]

2006 (5)

P. Savov and S. Vyatchanin, “Estimate of tilt instability of Mesa-beam and Gaussian-beam modes for advanced LIGO,” Phys. Rev. D 74, 082002 (2006).
[CrossRef]

J. Sidles and D. Sigg, “Optical torques in suspended Fabry–Perot interferometers,” Phys. Lett. A 354, 167–172 (2006).
[CrossRef]

M. Bondarescu and K. S. Thorne, “A new family of light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 74, 082003 (2006).
[CrossRef]

V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006).
[CrossRef]

B. Mours, E. Tournefier, and J. Y. Vinet, “Thermal noise reduction in interferometric gravitational wave antennas: using high order TEM modes,” Classical Quantum Gravity 23, 5777–5784 (2006).
[CrossRef]

2003 (2)

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

P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20, 1098–1130 (2003).
[CrossRef]

2001 (1)

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric oscillatory instability in Fabry–Perot interferometer,” Phys. Lett. A 287, 331–338 (2001).
[CrossRef]

2000 (1)

R. Grimm, M. Weidenmüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atomic Molec. Opt. Phys. 42, 95–170 (2000).

1984 (1)

1966 (1)

1964 (1)

J. P. Gordon and H. Kogelnik, “Equivalence relations among spherical mirror optical resonators,” Bell Syst. Tech. J. 43, 2873–2886 (1964).

1961 (1)

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

Agresti, J.

V. Pierro, V. Galdi, G. Castaldi, I. M. Pinto, J. Agresti, and R. DeSalvo, “Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: bounds, profiles, and critical parameters,” Phys. Rev. D 76, 122003 (2007).
[CrossRef]

M. G. Tarallo, J. Miller, J. Agresti, E. D’Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remilleux, B. Simoni, and P. Willems, “Generation of a flat-top laser beam for gravitational-wave detectors by means of a non-spherical Fabry–Perot resonator,” Appl. Opt. 46, 6648–6654 (2007).
[CrossRef]

V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006).
[CrossRef]

J. Agresti and R. DeSalvo, “Thermal noises calculations: Gaussian vs. Mesa beams,” LIGO technical note, LIGO-T050269-00-R available at http://admdbsrv.ligo.caltech.edu/dcc/ .

Blair, D. G.

S. Gras, D. G. Blair, and L. Ju, “Opto-acoustic interactions in gravitational wave detectors: comparing flat-top beams with Gaussian beams,” Phys. Rev. D 81, 042001 (2010).
[CrossRef]

Bondarescu, M.

M. Bondarescu, O. Kogan, and Y. Chen, “Optimal light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 78, 082002 (2008).
[CrossRef]

A. P. Lundgren, R. Bondarescu, D. Tsang, and M. Bondarescu, “Finite mirror effects in advanced interferometric gravitational wavedetectors,” Phys. Rev. D 77, 042003(2008).
[CrossRef]

M. Bondarescu and K. S. Thorne, “A new family of light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 74, 082003 (2006).
[CrossRef]

Bondarescu, R.

A. P. Lundgren, R. Bondarescu, D. Tsang, and M. Bondarescu, “Finite mirror effects in advanced interferometric gravitational wavedetectors,” Phys. Rev. D 77, 042003(2008).
[CrossRef]

Braginsky, V. B.

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric oscillatory instability in Fabry–Perot interferometer,” Phys. Lett. A 287, 331–338 (2001).
[CrossRef]

Castaldi, G.

V. Pierro, V. Galdi, G. Castaldi, I. M. Pinto, J. Agresti, and R. DeSalvo, “Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: bounds, profiles, and critical parameters,” Phys. Rev. D 76, 122003 (2007).
[CrossRef]

V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006).
[CrossRef]

Chen, Y.

M. Bondarescu, O. Kogan, and Y. Chen, “Optimal light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 78, 082002 (2008).
[CrossRef]

D’Ambrosio, E.

M. G. Tarallo, J. Miller, J. Agresti, E. D’Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remilleux, B. Simoni, and P. Willems, “Generation of a flat-top laser beam for gravitational-wave detectors by means of a non-spherical Fabry–Perot resonator,” Appl. Opt. 46, 6648–6654 (2007).
[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. S. Thorne, and S. Vyatchanin, “Reducing thermoelastic noise in gravitational-wave interferometers by flattening the light beams,” arXiv:gr-qc/0409075v1.

DAmbrosio, E.

V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006).
[CrossRef]

DeSalvo, R.

M. G. Tarallo, J. Miller, J. Agresti, E. D’Ambrosio, R. DeSalvo, D. Forest, B. Lagrange, J. M. Mackowski, C. Michel, J. L. Montorio, N. Morgado, L. Pinard, A. Remilleux, B. Simoni, and P. Willems, “Generation of a flat-top laser beam for gravitational-wave detectors by means of a non-spherical Fabry–Perot resonator,” Appl. Opt. 46, 6648–6654 (2007).
[CrossRef]

V. Pierro, V. Galdi, G. Castaldi, I. M. Pinto, J. Agresti, and R. DeSalvo, “Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: bounds, profiles, and critical parameters,” Phys. Rev. D 76, 122003 (2007).
[CrossRef]

V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006).
[CrossRef]

J. Agresti and R. DeSalvo, “Thermal noises calculations: Gaussian vs. Mesa beams,” LIGO technical note, LIGO-T050269-00-R available at http://admdbsrv.ligo.caltech.edu/dcc/ .

Domokos, P.

Forest, D.

Fox, A. G.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

Fox, R. W.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10–16-level laser stabilization,” Nat. Photon. 5, 158161 (2011).

Galdi, V.

V. Pierro, V. Galdi, G. Castaldi, I. M. Pinto, J. Agresti, and R. DeSalvo, “Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: bounds, profiles, and critical parameters,” Phys. Rev. D 76, 122003 (2007).
[CrossRef]

V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006).
[CrossRef]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “Equivalence relations among spherical mirror optical resonators,” Bell Syst. Tech. J. 43, 2873–2886 (1964).

Gras, S.

S. Gras, D. G. Blair, and L. Ju, “Opto-acoustic interactions in gravitational wave detectors: comparing flat-top beams with Gaussian beams,” Phys. Rev. D 81, 042001 (2010).
[CrossRef]

Grimm, R.

R. Grimm, M. Weidenmüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atomic Molec. Opt. Phys. 42, 95–170 (2000).

Herziger, G.

Jiang, Y. Y.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10–16-level laser stabilization,” Nat. Photon. 5, 158161 (2011).

Ju, L.

S. Gras, D. G. Blair, and L. Ju, “Opto-acoustic interactions in gravitational wave detectors: comparing flat-top beams with Gaussian beams,” Phys. Rev. D 81, 042001 (2010).
[CrossRef]

Kogan, O.

M. Bondarescu, O. Kogan, and Y. Chen, “Optimal light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 78, 082002 (2008).
[CrossRef]

Kogelnik, H.

H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
[CrossRef]

J. P. Gordon and H. Kogelnik, “Equivalence relations among spherical mirror optical resonators,” Bell Syst. Tech. J. 43, 2873–2886 (1964).

Lagrange, B.

Lemke, N. D.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10–16-level laser stabilization,” Nat. Photon. 5, 158161 (2011).

Li, T.

H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
[CrossRef]

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).

Ludlow, A. D.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10–16-level laser stabilization,” Nat. Photon. 5, 158161 (2011).

Lundgren, A. P.

A. P. Lundgren, R. Bondarescu, D. Tsang, and M. Bondarescu, “Finite mirror effects in advanced interferometric gravitational wavedetectors,” Phys. Rev. D 77, 042003(2008).
[CrossRef]

Ma, L. S.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10–16-level laser stabilization,” Nat. Photon. 5, 158161 (2011).

Mackowski, J. M.

Michel, C.

Miller, J.

Montorio, J. L.

Morgado, N.

Mours, B.

B. Mours, E. Tournefier, and J. Y. Vinet, “Thermal noise reduction in interferometric gravitational wave antennas: using high order TEM modes,” Classical Quantum Gravity 23, 5777–5784 (2006).
[CrossRef]

O’Shaughnessy, R.

R. O’Shaughnessy, S. Strigin, and S. Vyatchanin, “The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for Mexican-hat mirror proposal for advanced LIGO,” arXiv:gr-qc/0409050v1.

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:gr-qc/0409075v1.

Oates, C. W.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10–16-level laser stabilization,” Nat. Photon. 5, 158161 (2011).

Ovchinnikov, Y. B.

R. Grimm, M. Weidenmüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atomic Molec. Opt. Phys. 42, 95–170 (2000).

Pierro, V.

V. Pierro, V. Galdi, G. Castaldi, I. M. Pinto, J. Agresti, and R. DeSalvo, “Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: bounds, profiles, and critical parameters,” Phys. Rev. D 76, 122003 (2007).
[CrossRef]

V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006).
[CrossRef]

Pinard, L.

Pinto, I. M.

V. Pierro, V. Galdi, G. Castaldi, I. M. Pinto, J. Agresti, and R. DeSalvo, “Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: bounds, profiles, and critical parameters,” Phys. Rev. D 76, 122003 (2007).
[CrossRef]

V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006).
[CrossRef]

Remilleux, A.

Ritsch, H.

Savov, P.

P. Savov and S. Vyatchanin, “Estimate of tilt instability of Mesa-beam and Gaussian-beam modes for advanced LIGO,” Phys. Rev. D 74, 082002 (2006).
[CrossRef]

Sherman, J. A.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10–16-level laser stabilization,” Nat. Photon. 5, 158161 (2011).

Sidles, J.

J. Sidles and D. Sigg, “Optical torques in suspended Fabry–Perot interferometers,” Phys. Lett. A 354, 167–172 (2006).
[CrossRef]

Siegman, A.

A. Siegman, Lasers (University Science Books, 1996), Ch. 19.

Sigg, D.

J. Sidles and D. Sigg, “Optical torques in suspended Fabry–Perot interferometers,” Phys. Lett. A 354, 167–172 (2006).
[CrossRef]

D. Sigg, “Angular instability in high power FP cavities,” LIGO technical note, LIGO-T030120-00, (2003); available at http://admdbsrv.ligo.caltech.edu/dcc/ .

Simoni, B.

Strigin, 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 Mexican-hat mirror proposal for advanced LIGO,” arXiv:gr-qc/0409050v1.

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:gr-qc/0409075v1.

Strigin, S. E.

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric oscillatory instability in Fabry–Perot interferometer,” Phys. Lett. A 287, 331–338 (2001).
[CrossRef]

Tarallo, M. G.

Thorne, K. S.

M. Bondarescu and K. S. Thorne, “A new family of light beams and mirror shapes for future LIGO interferometers,” Phys. Rev. D 74, 082003 (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:gr-qc/0409075v1.

Tournefier, E.

B. Mours, E. Tournefier, and J. Y. Vinet, “Thermal noise reduction in interferometric gravitational wave antennas: using high order TEM modes,” Classical Quantum Gravity 23, 5777–5784 (2006).
[CrossRef]

Tsang, D.

A. P. Lundgren, R. Bondarescu, D. Tsang, and M. Bondarescu, “Finite mirror effects in advanced interferometric gravitational wavedetectors,” Phys. Rev. D 77, 042003(2008).
[CrossRef]

Vinet, J. Y.

J. Y. Vinet, “On special optical modes and thermal issues in advanced gravitational wave interferometric detectors,” Living Rev. Relativity 12, 5 (2009).

B. Mours, E. Tournefier, and J. Y. Vinet, “Thermal noise reduction in interferometric gravitational wave antennas: using high order TEM modes,” Classical Quantum Gravity 23, 5777–5784 (2006).
[CrossRef]

Vyatchanin, S.

P. Savov and S. Vyatchanin, “Estimate of tilt instability of Mesa-beam and Gaussian-beam modes for advanced LIGO,” Phys. Rev. D 74, 082002 (2006).
[CrossRef]

R. O’Shaughnessy, S. Strigin, and S. Vyatchanin, “The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for Mexican-hat mirror proposal for advanced LIGO,” arXiv:gr-qc/0409050v1.

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:gr-qc/0409075v1.

Vyatchanin, S. P.

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric oscillatory instability in Fabry–Perot interferometer,” Phys. Lett. A 287, 331–338 (2001).
[CrossRef]

Weber, H.

Weidenmüller, M.

R. Grimm, M. Weidenmüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atomic Molec. Opt. Phys. 42, 95–170 (2000).

Willems, P.

Adv. Atomic Molec. Opt. Phys. (1)

R. Grimm, M. Weidenmüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atomic Molec. Opt. Phys. 42, 95–170 (2000).

Appl. Opt. (3)

Bell Syst. Tech. J. (2)

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[CrossRef]

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

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[CrossRef]

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[CrossRef]

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V. Galdi, G. Castaldi, V. Pierro, I. M. Pinto, J. Agresti, E. DAmbrosio, and R. DeSalvo, “Analytic structure of a family of hyperboloidal beams of potential interest for advanced LIGO,” Phys. Rev. D 73, 127101 (2006).
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V. Pierro, V. Galdi, G. Castaldi, I. M. Pinto, J. Agresti, and R. DeSalvo, “Perspectives on beam-shaping optimization for thermal-noise reduction in advanced gravitational-wave interferometric detectors: bounds, profiles, and critical parameters,” Phys. Rev. D 76, 122003 (2007).
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[CrossRef]

Other (9)

A. Siegman, Lasers (University Science Books, 1996), Ch. 19.

J. Agresti and R. DeSalvo, “Thermal noises calculations: Gaussian vs. Mesa beams,” LIGO technical note, LIGO-T050269-00-R available at http://admdbsrv.ligo.caltech.edu/dcc/ .

LIGO http://www.ligo.caltech.edu .

Advanced LIGO https://www.advancedligo.mit.edu .

The name mesa beam was invented by P. Willems.

K. S. Thorne, LIGO-G000068-00-D (2000), available at http://admdbsrv.ligo.caltech.edu/dcc/ .

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:gr-qc/0409075v1.

R. O’Shaughnessy, S. Strigin, and S. Vyatchanin, “The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for Mexican-hat mirror proposal for advanced LIGO,” arXiv:gr-qc/0409050v1.

D. Sigg, “Angular instability in high power FP cavities,” LIGO technical note, LIGO-T030120-00, (2003); available at http://admdbsrv.ligo.caltech.edu/dcc/ .

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