Abstract

The transmission of a plane-mirror Fabry–Perot (PFP) interferometer is theoretically modeled and investigated by treating the spatial and spectral features in a unified manner. A spatiospectral transfer function is formulated and utilized to describe the beam propagation and the multiple-beam interference occurring in an ideal one-dimensional strip PFP interferometer with no diffraction loss. The spatial-frequency filtration of a finite-size beam input not only determines the transmitted spatial beam profile but also plays a crucial role in affecting the overall spectral transmittance. The inherent deviations of the spectral transmittance from what we know as the standard Airy’s formula are revealed in diverse aspects, including the less-than-unity peak transmittance, the displacement of a resonance peak frequency, and the asymmetric detuning profile. Our theoretical analysis extends to the misaligned PFP interferometers, such as the cases in which non-normal-incidence beams or wedge-aligned mirrors are used that could severely degrade the effective interferometer finesse.

© 2002 Optical Society of America

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    [CrossRef]
  38. K. An, C. Yang, R. R. Dasari, M. S. Feld, “Cavity ring-down technique and its application to the measurement of ultraslow velocities,” Opt. Lett. 20, 1068–1070 (1995).
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    [CrossRef]

2001

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Spatial domain realization of the cavity ringdown technique in a plane Fabry–Perot cavity,” Appl. Phys. Lett. 78, 1481–1483 (2001).
[CrossRef]

1999

E. Inbar, A. Arie, “High-sensitivity CW Fabry–Pérot en-hanced spectroscopy of CO2 and C2H2 using a 1064-nm Nd:YAG laser,” Appl. Phys. B 68, 99–105 (1999).
[CrossRef]

P. La Penna, A. Di Virgilio, M. Fiorentino, A. Porzio, S. Solimeno, “Transmittivity profile of high finesse plane parallel Fabry–Perot cavities illuminated by Gaussian beams,” Opt. Commun. 162, 267–279 (1999).
[CrossRef]

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Time domain study on cavity ring-down signals from a Fabry–Pérot cavity under pulsed laser excitations,” Jpn. J. Appl. Phys., Part 1 38, 6287–6297 (1999).
[CrossRef]

M. J. Lawrence, B. Willke, M. E. Husman, E. K. Gustafson, R. L. Byer, “Dynamic response of a Fabry–Perot interferometer,” J. Opt. Soc. Am. B 16, 523–532 (1999).
[CrossRef]

1998

J. K. Brasseur, K. S. Repasky, J. L. Carlsten, “Continuous-wave Raman laser in H2,” Opt. Lett. 23, 367–369 (1998).
[CrossRef]

B. Willke, N. Uehara, E. K. Gustafson, R. L. Byer, P. J. King, S. U. Seel, R. L. Savage, “Spatial and temporal filtering of a 10-W Nd:YAG laser with a Fabry–Perot ring-cavity premode cleaner,” Opt. Lett. 23, 1704–1706 (1998).
[CrossRef]

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

1997

1996

K. S. Repasky, J. G. Wessel, J. L. Carlsten, “Frequency stability of high-finesse interferometers,” Appl. Opt. 35, 609–611 (1996).
[CrossRef] [PubMed]

K. Ait-Ameur, “Reflection and transmission of the first two Laguerre–Gauss modes incident on a Fabry–Perot interferometer,” J. Mod. Opt. 43, 99–104 (1996).

J. T. Hodges, J. P. Looney, R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

1995

N. Uehara, K. Ueda, “Accurate measurement of ultralow loss in a high-finesse Fabry–Perot interferometer using the frequency response functions,” Appl. Phys. B. 61, 9–15 (1995).
[CrossRef]

K. An, C. Yang, R. R. Dasari, M. S. Feld, “Cavity ring-down technique and its application to the measurement of ultraslow velocities,” Opt. Lett. 20, 1068–1070 (1995).
[CrossRef] [PubMed]

1994

H. Abu-Safia, R. Al-Tahtamouni, I. Abu-Aljarayesh, N. A. Yusuf, “Transmission of a Gaussian beam through a Fabry–Perot interferometer,” Appl. Opt. 33, 3805–3811 (1994).
[CrossRef] [PubMed]

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

K. An, J. J. Childs, R. R. Dasari, M. S. Feld, “The microlaser: a laser with one atom in an optical resonator,” Phys. Rev. Lett. 73, 3375–3378 (1994).
[CrossRef] [PubMed]

1993

Z. Li, G. E. Stedman, H. R. Bilger, “Asymmetric response profile of a scanning Fabry–Perot interferometer,” Opt. Commun. 100, 240–246 (1993).
[CrossRef]

1992

E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, “Mode theory of plane Fabry–Pérot resonator with inhomogeneous active medium,” Opt. Commun. 90, 381–390 (1992).
[CrossRef]

F. Moreno, F. González, “Transmission of a Gaussian beam of low divergence through a high-finesse Fabry–Perot device,” J. Opt. Soc. Am. A 9, 2173–2175 (1992).
[CrossRef]

1990

H. Jager, M. Musso, C. Neureiter, L. Windholz, “Optical measurement of the free spectral range and spacing of plane and confocal Fabry–Perot interferometers,” Opt. Eng. 29, 42–46 (1990).
[CrossRef]

1980

1975

N. B. Kolinko, D. A. Solomakha, “Checking deviations from plane-parallelism of a Fabry–Perot interferometer by means of laser radiations,” Izmer. Tekh. 18, 92 (1975).

W. Schreiber, “Influence of diffraction on multi-beam interference in the plane-mirror Fabry–Perot interferometer,” Feingeraetetechnik 24, 121–127 (1975).

L. Ronchi, “Asymptotic behavior of an infinite-strip tilted-mirror resonator,” Appl. Opt. 14, 274–276 (1975).
[CrossRef]

1971

1970

L. Ronchi, “The asymptotic expression for the resonant mode losses of a Fabry–Perot open resonator,” Appl. Opt. 9, 733–736 (1970).
[CrossRef] [PubMed]

V. P. Koronkevich, D. A. Solomakha, “Effect of the lack of plane-parallelism of the interferometer in the optical multiplication of lengths,” Opt. Spektrosk. 28, 309–312 (1970).

1966

1963

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51, 80–89 (1963).
[CrossRef]

Abu-Aljarayesh, I.

Abu-Safia, H.

Ait-Ameur, K.

K. Ait-Ameur, “Reflection and transmission of the first two Laguerre–Gauss modes incident on a Fabry–Perot interferometer,” J. Mod. Opt. 43, 99–104 (1996).

Al-Tahtamouni, R.

An, K.

K. An, C. Yang, R. R. Dasari, M. S. Feld, “Cavity ring-down technique and its application to the measurement of ultraslow velocities,” Opt. Lett. 20, 1068–1070 (1995).
[CrossRef] [PubMed]

K. An, J. J. Childs, R. R. Dasari, M. S. Feld, “The microlaser: a laser with one atom in an optical resonator,” Phys. Rev. Lett. 73, 3375–3378 (1994).
[CrossRef] [PubMed]

Arie, A.

E. Inbar, A. Arie, “High-sensitivity CW Fabry–Pérot en-hanced spectroscopy of CO2 and C2H2 using a 1064-nm Nd:YAG laser,” Appl. Phys. B 68, 99–105 (1999).
[CrossRef]

Bernardini, M.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Bilger, H. R.

Z. Li, G. E. Stedman, H. R. Bilger, “Asymmetric response profile of a scanning Fabry–Perot interferometer,” Opt. Commun. 100, 240–246 (1993).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), pp. 351–360.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), pp. 323–329.

Braccini, S.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Bradaschia, C.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Brasseur, J. K.

Bretenaker, F.

Byer, R. L.

Carlsten, J. L.

Cella, G.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Childs, J. J.

K. An, J. J. Childs, R. R. Dasari, M. S. Feld, “The microlaser: a laser with one atom in an optical resonator,” Phys. Rev. Lett. 73, 3375–3378 (1994).
[CrossRef] [PubMed]

Cuoco, E.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

D’Ambrosio, E.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Dasari, R. R.

K. An, C. Yang, R. R. Dasari, M. S. Feld, “Cavity ring-down technique and its application to the measurement of ultraslow velocities,” Opt. Lett. 20, 1068–1070 (1995).
[CrossRef] [PubMed]

K. An, J. J. Childs, R. R. Dasari, M. S. Feld, “The microlaser: a laser with one atom in an optical resonator,” Phys. Rev. Lett. 73, 3375–3378 (1994).
[CrossRef] [PubMed]

Dattilo, V.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

de Labachelerie, M.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

De Salvo, R.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Di Virgilio, A.

P. La Penna, A. Di Virgilio, M. Fiorentino, A. Porzio, S. Solimeno, “Transmittivity profile of high finesse plane parallel Fabry–Perot cavities illuminated by Gaussian beams,” Opt. Commun. 162, 267–279 (1999).
[CrossRef]

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Eberly, J. H.

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 469–531.

Feld, M. S.

K. An, C. Yang, R. R. Dasari, M. S. Feld, “Cavity ring-down technique and its application to the measurement of ultraslow velocities,” Opt. Lett. 20, 1068–1070 (1995).
[CrossRef] [PubMed]

K. An, J. J. Childs, R. R. Dasari, M. S. Feld, “The microlaser: a laser with one atom in an optical resonator,” Phys. Rev. Lett. 73, 3375–3378 (1994).
[CrossRef] [PubMed]

Fidecaro, F.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Fiorentino, M.

P. La Penna, A. Di Virgilio, M. Fiorentino, A. Porzio, S. Solimeno, “Transmittivity profile of high finesse plane parallel Fabry–Perot cavities illuminated by Gaussian beams,” Opt. Commun. 162, 267–279 (1999).
[CrossRef]

Floch, A. L.

Fox, A. G.

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51, 80–89 (1963).
[CrossRef]

Gaddi, A.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Gennai, A.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Giassi, A.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Giazotto, A.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

González, F.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 46–61.

Gustafson, E. K.

Hahn, J. W.

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Spatial domain realization of the cavity ringdown technique in a plane Fabry–Perot cavity,” Appl. Phys. Lett. 78, 1481–1483 (2001).
[CrossRef]

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Time domain study on cavity ring-down signals from a Fabry–Pérot cavity under pulsed laser excitations,” Jpn. J. Appl. Phys., Part 1 38, 6287–6297 (1999).
[CrossRef]

Hauck, R.

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, New York, 1987), pp. 368–372.

Hernandez, G.

G. Hernandez, Fabry–Perot Interferometers, 1st ed. (Cambridge U. Press, Cambridge, UK, 1986).

Hodges, J. T.

J. T. Hodges, J. P. Looney, R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

Hofstetter, D.

Husman, M. E.

Inbar, E.

E. Inbar, A. Arie, “High-sensitivity CW Fabry–Pérot en-hanced spectroscopy of CO2 and C2H2 using a 1064-nm Nd:YAG laser,” Appl. Phys. B 68, 99–105 (1999).
[CrossRef]

Jager, H.

H. Jager, M. Musso, C. Neureiter, L. Windholz, “Optical measurement of the free spectral range and spacing of plane and confocal Fabry–Perot interferometers,” Opt. Eng. 29, 42–46 (1990).
[CrossRef]

Katsuda, T.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

King, P. J.

Kogelnik, H.

Kolinko, N. B.

N. B. Kolinko, D. A. Solomakha, “Checking deviations from plane-parallelism of a Fabry–Perot interferometer by means of laser radiations,” Izmer. Tekh. 18, 92 (1975).

Koronkevich, V. P.

V. P. Koronkevich, D. A. Solomakha, “Effect of the lack of plane-parallelism of the interferometer in the optical multiplication of lengths,” Opt. Spektrosk. 28, 309–312 (1970).

Korta, H. P.

La Penna, P.

P. La Penna, A. Di Virgilio, M. Fiorentino, A. Porzio, S. Solimeno, “Transmittivity profile of high finesse plane parallel Fabry–Perot cavities illuminated by Gaussian beams,” Opt. Commun. 162, 267–279 (1999).
[CrossRef]

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Lawrence, M. J.

Lee, H.-W.

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Spatial domain realization of the cavity ringdown technique in a plane Fabry–Perot cavity,” Appl. Phys. Lett. 78, 1481–1483 (2001).
[CrossRef]

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Time domain study on cavity ring-down signals from a Fabry–Pérot cavity under pulsed laser excitations,” Jpn. J. Appl. Phys., Part 1 38, 6287–6297 (1999).
[CrossRef]

Lee, J. Y.

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Spatial domain realization of the cavity ringdown technique in a plane Fabry–Perot cavity,” Appl. Phys. Lett. 78, 1481–1483 (2001).
[CrossRef]

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Time domain study on cavity ring-down signals from a Fabry–Pérot cavity under pulsed laser excitations,” Jpn. J. Appl. Phys., Part 1 38, 6287–6297 (1999).
[CrossRef]

Li, T.

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

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51, 80–89 (1963).
[CrossRef]

Li, Z.

Z. Li, G. E. Stedman, H. R. Bilger, “Asymmetric response profile of a scanning Fabry–Perot interferometer,” Opt. Commun. 100, 240–246 (1993).
[CrossRef]

Looney, J. P.

J. T. Hodges, J. P. Looney, R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

Losurdo, G.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Lyablin, M.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Maggiore, M.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Mancini, S.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Milonni, P. W.

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 469–531.

Moreno, F.

Musso, M.

H. Jager, M. Musso, C. Neureiter, L. Windholz, “Optical measurement of the free spectral range and spacing of plane and confocal Fabry–Perot interferometers,” Opt. Eng. 29, 42–46 (1990).
[CrossRef]

Nakagawa, K.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Neureiter, C.

H. Jager, M. Musso, C. Neureiter, L. Windholz, “Optical measurement of the free spectral range and spacing of plane and confocal Fabry–Perot interferometers,” Opt. Eng. 29, 42–46 (1990).
[CrossRef]

Ohtsu, M.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Pan, H. B.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Pasqualetti, A.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Pasqualetti, F.

Passuello, D.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Poggiani, R.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Poirson, J.

Popolizio, P.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Porzio, A.

P. La Penna, A. Di Virgilio, M. Fiorentino, A. Porzio, S. Solimeno, “Transmittivity profile of high finesse plane parallel Fabry–Perot cavities illuminated by Gaussian beams,” Opt. Commun. 162, 267–279 (1999).
[CrossRef]

Remo, J. L.

Repasky, K. S.

Ronchi, L.

Saldin, E. L.

E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, “Mode theory of plane Fabry–Pérot resonator with inhomogeneous active medium,” Opt. Commun. 90, 381–390 (1992).
[CrossRef]

Savage, R. L.

Schneidmiller, E. A.

E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, “Mode theory of plane Fabry–Pérot resonator with inhomogeneous active medium,” Opt. Commun. 90, 381–390 (1992).
[CrossRef]

Schreiber, W.

W. Schreiber, “Influence of diffraction on multi-beam interference in the plane-mirror Fabry–Perot interferometer,” Feingeraetetechnik 24, 121–127 (1975).

Seel, S. U.

Shabalin, D.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Shelkovnikov, A. S.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 744–913.

Solimeno, S.

P. La Penna, A. Di Virgilio, M. Fiorentino, A. Porzio, S. Solimeno, “Transmittivity profile of high finesse plane parallel Fabry–Perot cavities illuminated by Gaussian beams,” Opt. Commun. 162, 267–279 (1999).
[CrossRef]

Solomakha, D. A.

N. B. Kolinko, D. A. Solomakha, “Checking deviations from plane-parallelism of a Fabry–Perot interferometer by means of laser radiations,” Izmer. Tekh. 18, 92 (1975).

V. P. Koronkevich, D. A. Solomakha, “Effect of the lack of plane-parallelism of the interferometer in the optical multiplication of lengths,” Opt. Spektrosk. 28, 309–312 (1970).

Stedman, G. E.

Z. Li, G. E. Stedman, H. R. Bilger, “Asymmetric response profile of a scanning Fabry–Perot interferometer,” Opt. Commun. 100, 240–246 (1993).
[CrossRef]

Thornton, R. L.

Ueda, K.

N. Uehara, K. Ueda, “Accurate measurement of ultralow loss in a high-finesse Fabry–Perot interferometer using the frequency response functions,” Appl. Phys. B. 61, 9–15 (1995).
[CrossRef]

Uehara, N.

B. Willke, N. Uehara, E. K. Gustafson, R. L. Byer, P. J. King, S. U. Seel, R. L. Savage, “Spatial and temporal filtering of a 10-W Nd:YAG laser with a Fabry–Perot ring-cavity premode cleaner,” Opt. Lett. 23, 1704–1706 (1998).
[CrossRef]

N. Uehara, K. Ueda, “Accurate measurement of ultralow loss in a high-finesse Fabry–Perot interferometer using the frequency response functions,” Appl. Phys. B. 61, 9–15 (1995).
[CrossRef]

Vallet, M.

van Zee, R. D.

J. T. Hodges, J. P. Looney, R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

Vicere, A.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Weber, H.

Weinstein, L. A.

L. A. Weinstein, Open Resonators and Open Waveguides (Golem, Boulder, Colo., 1969).

Wessel, J. G.

Willke, B.

Windholz, L.

H. Jager, M. Musso, C. Neureiter, L. Windholz, “Optical measurement of the free spectral range and spacing of plane and confocal Fabry–Perot interferometers,” Opt. Eng. 29, 42–46 (1990).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), pp. 323–329.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), pp. 351–360.

Yang, C.

Yurkov, M. V.

E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, “Mode theory of plane Fabry–Pérot resonator with inhomogeneous active medium,” Opt. Commun. 90, 381–390 (1992).
[CrossRef]

Yusuf, N. A.

Zhang, Z.

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Appl. Opt.

Appl. Phys. B

E. Inbar, A. Arie, “High-sensitivity CW Fabry–Pérot en-hanced spectroscopy of CO2 and C2H2 using a 1064-nm Nd:YAG laser,” Appl. Phys. B 68, 99–105 (1999).
[CrossRef]

Appl. Phys. B.

N. Uehara, K. Ueda, “Accurate measurement of ultralow loss in a high-finesse Fabry–Perot interferometer using the frequency response functions,” Appl. Phys. B. 61, 9–15 (1995).
[CrossRef]

Appl. Phys. Lett.

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Spatial domain realization of the cavity ringdown technique in a plane Fabry–Perot cavity,” Appl. Phys. Lett. 78, 1481–1483 (2001).
[CrossRef]

Feingeraetetechnik

W. Schreiber, “Influence of diffraction on multi-beam interference in the plane-mirror Fabry–Perot interferometer,” Feingeraetetechnik 24, 121–127 (1975).

Izmer. Tekh.

N. B. Kolinko, D. A. Solomakha, “Checking deviations from plane-parallelism of a Fabry–Perot interferometer by means of laser radiations,” Izmer. Tekh. 18, 92 (1975).

J. Chem. Phys.

J. T. Hodges, J. P. Looney, R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

J. Mod. Opt.

K. Ait-Ameur, “Reflection and transmission of the first two Laguerre–Gauss modes incident on a Fabry–Perot interferometer,” J. Mod. Opt. 43, 99–104 (1996).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys., Part 1

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Time domain study on cavity ring-down signals from a Fabry–Pérot cavity under pulsed laser excitations,” Jpn. J. Appl. Phys., Part 1 38, 6287–6297 (1999).
[CrossRef]

Opt. Commun.

Z. Li, G. E. Stedman, H. R. Bilger, “Asymmetric response profile of a scanning Fabry–Perot interferometer,” Opt. Commun. 100, 240–246 (1993).
[CrossRef]

E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, “Mode theory of plane Fabry–Pérot resonator with inhomogeneous active medium,” Opt. Commun. 90, 381–390 (1992).
[CrossRef]

P. La Penna, A. Di Virgilio, M. Fiorentino, A. Porzio, S. Solimeno, “Transmittivity profile of high finesse plane parallel Fabry–Perot cavities illuminated by Gaussian beams,” Opt. Commun. 162, 267–279 (1999).
[CrossRef]

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Opt. Eng.

H. Jager, M. Musso, C. Neureiter, L. Windholz, “Optical measurement of the free spectral range and spacing of plane and confocal Fabry–Perot interferometers,” Opt. Eng. 29, 42–46 (1990).
[CrossRef]

Opt. Lett.

Opt. Spektrosk.

V. P. Koronkevich, D. A. Solomakha, “Effect of the lack of plane-parallelism of the interferometer in the optical multiplication of lengths,” Opt. Spektrosk. 28, 309–312 (1970).

Phys. Lett. A

M. Bernardini, S. Braccini, C. Bradaschia, G. Cella, E. Cuoco, E. D’Ambrosio, V. Dattilo, R. De Salvo, A. di Virgilio, F. Fidecaro, A. Gaddi, A. Gennai, A. Giassi, A. Giazotto, P. La Penna, M. Lyablin, G. Losurdo, M. Maggiore, S. Mancini, H. B. Pan, A. Pasqualetti, D. Passuello, R. Poggiani, P. Popolizio, D. Shabalin, A. Vicere, Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
[CrossRef]

Phys. Rev. Lett.

K. An, J. J. Childs, R. R. Dasari, M. S. Feld, “The microlaser: a laser with one atom in an optical resonator,” Phys. Rev. Lett. 73, 3375–3378 (1994).
[CrossRef] [PubMed]

Proc. IEEE

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51, 80–89 (1963).
[CrossRef]

Other

G. Hernandez, Fabry–Perot Interferometers, 1st ed. (Cambridge U. Press, Cambridge, UK, 1986).

E. Hecht, Optics, 2nd ed. (Addison-Wesley, New York, 1987), pp. 368–372.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 744–913.

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 469–531.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 46–61.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), pp. 323–329.

L. A. Weinstein, Open Resonators and Open Waveguides (Golem, Boulder, Colo., 1969).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), pp. 351–360.

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Figures (10)

Fig. 1
Fig. 1

Modification of the angular spectrum of a beam being transmitted through a plane-mirror Fabry–Perot (PFP) interferometer.

Fig. 2
Fig. 2

Optical geometry of a misaligned PFP interferometer.

Fig. 3
Fig. 3

Spatiospectral contours of resonance transmission through a PFP interferometer. Solid curves represent the resonance contours, and dotted curves represent the contours with a finite detuning (Δm=±0.1) from each nearest resonance. The curves are shown for resonance orders m near N=20,000.

Fig. 4
Fig. 4

Transmission curves of a PFP interferometer as a function of (a)–(c) spatial frequency and (a)–(c) wave number. The curves are obtained from sectioning the transmission function along several (a)–(c) constant k’s and (a)–(c) constant kx’s, which are indicated. A PFP interferometer is considered with mirror reflectivity R=0.9 and resonances of order m near N=20,000. Dotted curves represent the spatial-frequency distribution for a collimated Gaussian input beam with transverse dimension D=100λ in full width at half-maximum (FWHM).

Fig. 5
Fig. 5

Spectral transmission of a PFP interferometer for Gaussian (q=1) beam inputs of different beam sizes. The transmittance curves are plotted based on (a) the whole beam power and (b) the peak intensity. The discrepancy between the two transmission plots is evidence of the fact that the transmitted beams are spatially distorted and dispersed from the original profile of the input beams. The results shown are for a PFP interferometer comprising mirrors of reflectivity R=0.99 and separation L=10 mm, with the input beam wavelength assumed to be at 632.8 nm and the FWHM beam width D of each input indicated.

Fig. 6
Fig. 6

Spectral transmission of a PFP interferometer for super-Gaussian beam inputs of different orders q. The transmittance curves are plotted on a logarithmic scale based on (a) the whole beam power and (b) the peak intensity. The discrepancy between the two transmission plots reflects the fact that the transmitted beams are spatially distorted and dispersed from the original profile of the input beams. The results shown are for a PFP interferometer comprising mirrors of reflectivity R=0.99 and separation L=10 mm, with the input beam wavelength assumed to be at 632.8 nm and a FWHM beam width D=1.0 mm.

Fig. 7
Fig. 7

Spectral transmission of a misaligned PFP interferometer with a tilt to the normal incidence of an input beam. The results shown are for a 10-mm-long PFP interferometer comprising mirrors of reflectivity R=0.99 with tilt angles θ indicated, illuminated by a Gaussian beam input at the wavelength of 632.8 nm having FWHM width D=1.0 mm.

Fig. 8
Fig. 8

Transmitted-beam profiles through a tilted PFP interferometer with frequency detunings Ω. The results are for the frequency detunings (a) 0, (b) 0.02 FSR, and (c) 0.5 FSR. In the inset of each plot, the transmittance curve of the tilted PFP interferometer (solid curve) and the input beam distribution (dotted curve) are illustrated as a function of spatial frequency. A 10-mm-long PFP interferometer comprising mirrors of reflectivity R=0.99 with tilt angle θ=2.0 mrad was considered for the calculation with a Gaussian beam input at wavelength 632.8 nm having FWHM width D=1.0 mm.

Fig. 9
Fig. 9

Spectral transmission of a misaligned PFP interferometer suffering nonparallelism of mirrors. The results shown are for a 10-mm-long PFP interferometer comprising mirrors of reflectivity R=0.99 with mirror wedge angles indicated, illuminated by a Gaussian beam input at wavelength 632.8 nm having FWHM width D=1.0 mm.

Fig. 10
Fig. 10

Transmitted-beam profiles through a nonparallel mirror PFP interferometer with frequency detunings Ω. A 10-mm-long PFP interferometer comprising two nonparallel mirrors of reflectivity R=0.99 with wedge angle =15 µrad was considered for the calculation with a normally incident Gaussian input beam at wavelength 632.8 nm having FWHM width D=5.0 mm, which is illustrated as a dotted curve with an arbitrary intensity scale.

Equations (20)

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E˜(kx; z)|k=H(kx; z-z0)|kE˜(kx; z0)|k,
E(x; z)|k=12πdkx exp(ikxx)E˜(kx; z)|k.
HFP(kx; z)|k=T2 exp(izk2-kx2)1-R2 exp(izrk2-kx2),
Etrm(x; z)|k=n=0T 2R2nE(x; z+nzr)|k,
Etrm(x; z)|k=n=0T2R2n12πdkx×exp(ikxx)E˜(kx; z+nzr)|k=12πdkx exp(ikxx)E˜(kx; z0)|k×n=0T2R2nH(kx; z-z0+nzr)|k=12πdkx exp(ikxx)E˜trm(kx; z)|k.
E˜trm(kx; z)|k=HFP(kx; z-z0)|kE˜(kx; z0)|k,
Etrm(x; z)|k=n=0T2R2nE(x-nxr; z+nzr)|k,
HFP(kx; z)|k=T2 exp(izk2-kx2)1-R2 exp[i(zrk2-kx2-xrkx)].
Etrm(x; z)=n=0T2R2nEn(x-xn(z); z+zn(z)),
xn(L)=Ltan 1cos 2n-1,
zn(L)=Ltan tan 2n.
k2-kx2=Km2,
E(x; z)|k=A(x; z)|k exp-ln 22xwhw2qexp(ikz),
E(ρ; z)|k=E0w0w(z)exp-ρ2w2(z)expikρ22R(z)×expikz-tan-1zzR,
k=k-12L[ϕ(z+2L)-ϕ(z)],
Ωc12π11+(zeff/zR)22LzR(FSR),
|HFP(kx; L)|2(T/xr)214[2(1-R)/xr]2+kx2,
θ[λ(1-R)/2πL]1/2,
Ωc=L sin2 θλ-1+1-2 ln 2π2 sin2 θλ2D21/2(FSR),
I(x)I01xexp-xL/2(1-R)21/2.

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