OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8558–8563

Photonic fractional Fourier transformer with a single dispersive device

C. Cuadrado-Laborde, A. Carrascosa, A. Díez, J. L. Cruz, and M. V. Andres  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 8558-8563 (2013)
http://dx.doi.org/10.1364/OE.21.008558


View Full Text Article

Enhanced HTML    Acrobat PDF (1608 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this work we used the temporal analog of spatial Fresnel diffraction to design a temporal fractional Fourier transformer with a single dispersive device, in this way avoiding the use of quadratic phase modulators. We demonstrate that a single dispersive passive device inherently provides the fractional Fourier transform of an incident optical pulse. The relationships linking the fractional Fourier transform order and scaling factor with the dispersion parameters are derived. We first provide some numerical results in order to prove the validity of our proposal, using a fiber Bragg grating as the dispersive device. Next, we experimentally demonstrate the feasibility of this proposal by using a spool of a standard optical fiber as the dispersive device.

© 2013 OSA

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: November 13, 2012
Revised Manuscript: January 28, 2013
Manuscript Accepted: February 7, 2013
Published: April 1, 2013

Citation
C. Cuadrado-Laborde, A. Carrascosa, A. Díez, J. L. Cruz, and M. V. Andres, "Photonic fractional Fourier transformer with a single dispersive device," Opt. Express 21, 8558-8563 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8558


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. Cuadrado-Laborde and M. V. Andrés, “In-fiber all-optical fractional differentiator,” Opt. Lett.34(6), 833–835 (2009). [CrossRef] [PubMed]
  2. C. Cuadrado-Laborde and M. V. Andrés, “Proposal and design of an all-optical in-fiber fractional integrator,” Opt. Commun.283(24), 5012–5015 (2010). [CrossRef]
  3. C. Cuadrado-Laborde, “Proposal and design of a photonic in-fiber fractional Hilbert transformer,” IEEE Photon. Technol. Lett.22(1), 33–35 (2010). [CrossRef]
  4. C. Cuadrado-Laborde, M. V. Andrés, and J. Lancis, “Self-referenced phase reconstruction proposal of GHz-bandwidth non-periodical optical pulses by in-fiber semi-differintegration,” Opt. Commun.284(24), 5636–5640 (2011). [CrossRef]
  5. T. Alieva, M. J. Bastiaans, and M. L. Calvo, “Fractional transforms in optical information processing,” EURASIP J. Appl. Sig. P.10, 1498–1519 (2005).
  6. M. A. Muriel, J. Azaña, and A. Carballar, “Real-time Fourier transformer based on fiber gratings,” Opt. Lett.24(1), 1–3 (1999). [CrossRef] [PubMed]
  7. J. Azaña, L. R. Chen, M. A. Muriel, and P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett.35(25), 2223–2224 (1999). [CrossRef]
  8. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, New York, 2001).
  9. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A10(10), 2181–2186 (1993). [CrossRef]
  10. W. Lohmann, Z. Zalevsky, R. G. Dorsch, and D. Mendlovic, “Experimental considerations and scaling property of the fractional Fourier transform,” Opt. Commun.146(1-6), 55–61 (1998). [CrossRef]
  11. J. Hua, L. Liu, and G. Li, “Observing the fractional Fourier transform by free-space Fresnel diffraction,” Appl. Opt.36(2), 512–513 (1997). [CrossRef] [PubMed]
  12. H. M. Ozaktas, S. Ö. Arık, and T. Coşkun, “Fundamental structure of Fresnel diffraction: natural sampling grid and the fractional Fourier transform,” Opt. Lett.36(13), 2524–2526 (2011). [CrossRef] [PubMed]
  13. C. Cuadrado-Laborde, R. Duchowicz, R. Torroba, and E. E. Sicre, “Fractional Fourier transform dual random phase encoding of time-varying signals,” Opt. Commun.281(17), 4321–4328 (2008). [CrossRef]
  14. A. W. Lohmann and D. Mendlovic, “Fractional Fourier transform: photonic implementation,” Appl. Opt.33(32), 7661–7664 (1994). [CrossRef] [PubMed]
  15. C. Cuadrado-Laborde, P. Costanzo-Caso, R. Duchowicz, and E. E. Sicre, “Periodic pulse train conformation based on the temporal Radon-Wigner transform,” Opt. Commun.275(1), 94–103 (2007). [CrossRef]
  16. K. Ennser, M. N. Zervas, and R. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron.34(5), 770–778 (1998). [CrossRef]
  17. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron.30(8), 1951–1963 (1994). [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.

Figures

Fig. 1 Fig. 2 Fig. 3
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited