OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 5 — May. 1, 2002
  • pp: 973–984

Spatiospectral transmission of a plane-mirror Fabry–Perot interferometer with nonuniform finite-size diffraction beam illuminations

Jae Yong Lee, Jae Won Hahn, and Hai-Woong Lee  »View Author Affiliations

JOSA A, Vol. 19, Issue 5, pp. 973-984 (2002)

View Full Text Article

Acrobat PDF (265 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.6110) Fourier optics and signal processing : Spatial filtering
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
(260.3160) Physical optics : Interference

Jae Yong Lee, Jae Won Hahn, and Hai-Woong Lee, "Spatiospectral transmission of a plane-mirror Fabry–Perot interferometer with nonuniform finite-size diffraction beam illuminations," J. Opt. Soc. Am. A 19, 973-984 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. G. Hernandez, Fabry–Perot Interferometers, 1st ed. (Cambridge U. Press, Cambridge, UK, 1986).
  2. K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
  3. E. Inbar and 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).
  4. J. K. Brasseur, K. S. Repasky, and J. L. Carlsten, “Continuous-wave Raman laser in H2,” Opt. Lett. 23, 367–369 (1998).
  5. K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, “The microlaser: a laser with one atom in an optical resonator,” Phys. Rev. Lett. 73, 3375–3378 (1994).
  6. B. Willke, N. Uehara, E. K. Gustafson, R. L. Byer, P. J. King, S. U. Seel, and R. L. Savage, Jr., “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).
  7. E. Hecht, Optics, 2nd ed. (Addison-Wesley, New York, 1987), pp. 368–372.
  8. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 744–913.
  9. P. W. Milonni and J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 469–531.
  10. H. Jager, M. Musso, C. Neureiter, and L. Windholz, “Optical measurement of the free spectral range and spacing of plane and confocal Fabry–Perot interferometers,” Opt. Eng. 29, 42–46 (1990).
  11. J. Y. Lee, H.-W. Lee, and J. W. Hahn, “Spatial domain realization of the cavity ringdown technique in a plane Fabry–Perot cavity,” Appl. Phys. Lett. 78, 1481–1483 (2001).
  12. 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, and Z. Zhang, “Plane parallel mirrors Fabry–Perot cavity to improve Virgo superattenuators,” Phys. Lett. A 243, 187–194 (1998).
  13. A. G. Fox and T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51, 80–89 (1963).
  14. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
  15. L. Ronchi, “The asymptotic expression for the resonant mode losses of a Fabry–Perot open resonator,” Appl. Opt. 9, 733–736 (1970).
  16. F. Pasqualetti and L. Ronchi, “Quasi-stationary wave patterns inside infinite-strip open resonators,” Appl. Opt. 10, 2488–2494 (1971).
  17. W. Schreiber, “Influence of diffraction on multi-beam interference in the plane-mirror Fabry–Perot interferometer,” Feingeraetetechnik 24, 121–127 (1975).
  18. L. A. Weinstein, Open Resonators and Open Waveguides (Golem, Boulder, Colo., 1969).
  19. E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, “Mode theory of plane Fabry–Pérot resonator with inhomogeneous active medium,” Opt. Commun. 90, 381–390 (1992).
  20. P. La Penna, A. Di Virgilio, M. Fiorentino, A. Porzio, and S. Solimeno, “Transmittivity profile of high finesse plane parallel Fabry–Perot cavities illuminated by Gaussian beams,” Opt. Commun. 162, 267–279 (1999).
  21. F. Moreno and 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).
  22. H. Abu-Safia, R. Al-Tahtamouni, I. Abu-Aljarayesh, and N. A. Yusuf, “Transmission of a Gaussian beam through a Fabry–Perot interferometer,” Appl. Opt. 33, 3805–3811 (1994).
  23. 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).
  24. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 46–61.
  25. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), pp. 323–329.
  26. K. S. Repasky, J. G. Wessel, and J. L. Carlsten, “Frequency stability of high-finesse interferometers,” Appl. Opt. 35, 609–611 (1996).
  27. R. Hauck, H. P. Korta, and H. Weber, “Misalignment sensitivity of optical resonators,” Appl. Opt. 19, 598–601 (1980).
  28. V. P. Koronkevich and 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).
  29. N. B. Kolinko and D. A. Solomakha, “Checking deviations from plane-parallelism of a Fabry–Perot interferometer by means of laser radiations,” Izmer. Tekh. 18, 92 (1975).
  30. L. Ronchi, “Asymptotic behavior of an infinite-strip tilted-mirror resonator,” Appl. Opt. 14, 274–276 (1975).
  31. J. L. Remo, “Diffraction losses for symmetrically tilted plane reflectors in open resonators,” Appl. Opt. 19, 774–777 (1980).
  32. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), pp. 351–360.
  33. N. Uehara and 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).
  34. D. Hofstetter and R. L. Thornton, “Theory of loss measurements of Fabry–Perot resonators by Fourier analysis of the transmission spectra,” Opt. Lett. 22, 1831–1833 (1997).
  35. J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
  36. J. Y. Lee, H.-W. Lee, and 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).
  37. Z. Li, G. E. Stedman, and H. R. Bilger, “Asymmetric response profile of a scanning Fabry–Perot interferometer,” Opt. Commun. 100, 240–246 (1993).
  38. K. An, C. Yang, R. R. Dasari, and M. S. Feld, “Cavity ring-down technique and its application to the measurement of ultraslow velocities,” Opt. Lett. 20, 1068–1070 (1995).
  39. J. Poirson, F. Bretenaker, M. Vallet, and A. L. Floch, “Analytical and experimental study of ringing effects in a Fabry–Perot cavity. Application to the measurement of high finesses,” J. Opt. Soc. Am. B 14, 2811–2817 (1997).
  40. M. J. Lawrence, B. Willke, M. E. Husman, E. K. Gustafson, and R. L. Byer, “Dynamic response of a Fabry–Perot interferometer,” J. Opt. Soc. Am. B 16, 523–532 (1999).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited