OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 3 — Mar. 1, 2014
  • pp: 652–660

Accelerated convergence method for fast Fourier transform simulation of coupled cavities

R. A. Day, G. Vajente, and M. Pichot du Mezeray  »View Author Affiliations

JOSA A, Vol. 31, Issue 3, pp. 652-660 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (1084 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Fast Fourier transform (FFT) simulation was used to calculate the power and spatial distribution of resonant fields in optical cavities. This is an important tool when characterizing the effect of imperfect geometry and mirror aberrations. This method is, however, intrinsically slow when the cavities are of relatively high finesse. When this is the case, an accelerated convergence scheme may be used to calculate the steady-state cavity field with a speed that is orders of magnitude faster. The rate of convergence of this method, however, is unpredictable, as many different factors may detrimentally affect its performance. In addition, its use in multiple cavity configurations is not well understood. An in-depth study of the limitations and optimization of this method is presented, together with a formulation of its use in multiple cavity configurations. This work has not only resulted in consistent improvement in performance and stability of the accelerated convergence method but also allows the simulation of optical configurations, which would not previously have been possible.

© 2014 Optical Society of America

OCIS Codes
(070.5753) Fourier optics and signal processing : Resonators
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: December 10, 2013
Revised Manuscript: January 17, 2014
Manuscript Accepted: January 23, 2014
Published: February 27, 2014

R. A. Day, G. Vajente, and M. Pichot du Mezeray, "Accelerated convergence method for fast Fourier transform simulation of coupled cavities," J. Opt. Soc. Am. A 31, 652-660 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. E. Siegman, Lasers (University Science, 1986).
  2. A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency-domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067–S1074 (2004). [CrossRef]
  3. G. Vajente, “Fast modal simulation of paraxial optical systems: the MIST open source toolbox,” Class. Quantum Grav. 30, 075014 (2013). [CrossRef]
  4. W. Winkler, R. Schilling, K. Danzmann, J. Mizuno, A. Rüdiger, and K. A. Strain, “Light scattering described in the mode picture,” Appl. Opt. 33, 7547–7550 (1994). [CrossRef]
  5. J.-Y. Vinet, P. Hello, C. N. Man, and A. Brillet, “A high accuracy method for the simulation of non-ideal optical cavities,” J. Phys. I 2, 1287–1303 (1992). [CrossRef]
  6. C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990). [CrossRef]
  7. P. Saha, “Fast estimation of transverse fields in high-finesse optical cavities,” J. Opt. Soc. Am. A 14, 2195–2202 (1997). [CrossRef]
  8. B. Bochner and Y. Hefetz, “Grid-based simulation program for gravitational wave interferometers with realistically imperfect optics,” Phys. Rev. D 68, 082001 (2003). [CrossRef]
  9. B. Bochner, “Modelling the performance of interferometric gravitational-wave detectors with realistically imperfect optics,” Ph.D. dissertation (Massachussets Institute of Technology, 1998).
  10. MATLAB, The MathWorks, Inc., Natick, Massachusetts, USA.
  11. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983). [CrossRef]
  12. Multiprecision Computing Toolbox, Advanpix, Yokohama, Japan.
  13. K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17, 19662–19673 (2009). [CrossRef]
  14. A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008). [CrossRef]

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