Temporal differentiation of optical signals in reflection using resonant gratings
N.V. Golovastikov, D.A .Bykov, L.L. Doskolovich, V.A. Soifer

Full text of article: Russian language.

Abstract:
The possibility of performing time-domain differentiation of optical pulse by the use of resonant gratings is considered. It is demonstrated that the subwavelength resonant gratings with a horizontal mirror plane are well suited for time-domain differentiation in reflection regime. A method for computing the grating parameters is proposed and the resonant gratings intended for differentiation of picosecond pulses are computed. The gratings computed provide various ratios between the differentiation accuracy and the reflected pulse energy.

Key words:
diffraction grating, resonance, optical differentiation.

References:

  1. Kulishov, M. Design of high-order all-optical temporal differentiators based on multiple-phase-shifted fiber Bragg gratings / M. Kulishov, J. Azaña // Opt. Exp. - 2007. - Vol. 15. - P. 6152-6166.
  2. Slavík, R. Ultrafast all-optical differentiators / R. Slavík, Y. Park, M. Kulishov, R. Morandotti, J. Azaña // Opt. Exp. - 2006. - Vol. 14. - P. 10699-10707.
  3. Kulishov, M. Long-period fiber gratings as ultrafast optical differentiators / M. Kulishov, J. Azaña // Opt. Lett. - 2005. - Vol. 30. - P. 2700-2702.
  4. Slavík, R. Terahertz-bandwidth high-order temporal differentiators based on phase-shifted long-period fiber gratings / R. Slavík, Y. Park, M. Kulishov, J. Azaña // Opt. Lett. - 2009. - Vol. 34. - P. 3116-3118.
  5. Rivas, L.M. Experimental demonstration of ultrafast all-fiber high-order photonic temporal differentiators / L. M. Rivas, S. Boudreau, Y. Park, R. Slavík, S. LaRochelle, A. Carballar, J. Azaña // Opt. Lett. - 2009. - Vol. 34. - P. 1792-1794.
  6. Berger, N.K. Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating / N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, J. Azaña // Opt. Exp. - 2007. - Vol. 15. - P. 371-381.
  7. Kulishov, M. Design of high-order all-optical temporal differentiators based on multiple-phase-shifted fiber Bragg gratings / M. Kulishov, J. Azaña // Opt. Exp. - 2007. - Vol. 15. - P. 6152-6166.
  8. Li, M. Arbitrary-order all-fiber temporal differentiator based on a fiber Bragg grating: design and experimental demonstration / M. Li, D. Janner, J. Yao, V. Pruneri // Opt. Exp. - 2009. - Vol. 17. - P. 19798-19807.
  9. Preciado, M.A. Design of an ultrafast all-optical differentiator based on a fiber Bragg grating in transmission / M. A. Preciado, M. A. Muriel // Opt. Lett. - 2008. - Vol 33. - P. 2458-2460.
  10. Bykov, D. Temporal differentiation of optical signals using resonant gratings / D. Bykov, L. Doskolovich, V. Soifer // Opt. Lett. - 2011. - Vol. 36. - P. 3509-3511.
  11. Bykov, D. On ability of resonant diffraction gratings to differentiate impulse optical signal / D. A. Bykov, L. L. Doskolovich, and V. A. Soifer // J. Exp. Theor. Phys. - 2012-Vol.141, no 5 - P. 832-839.
  12. Tikhodeev, S.G. Quasiguided modes and optical properties of photonic crystal slabs / S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, T. Ishihara // Phys. Rev. B - 2002. - Vol. 66. - P. 045102-045118.
  13. Gippius, N.A. Optical properties of photonic crystal slabs with an asymmetrical unit cell / N. A. Gippius, S. G. Tikhodeev, T. Ishihara // Phys. Rev. B - 2005. - Vol. 72. - P. 045138-045144.
  14. Bykov D.A. Extraordinary Magneto-Optical Effect of a Change in the Phase of Diffraction Orders in Dielectric Diffraction Gratings / D. A. Bykov, L. L. Doskolovich, V. A. Soifer, N. L. Kazansky // J. Exp. Theor. Phys. - 2010. - Vol. 111, no. 6. - P. 967--974.
  15. Sarrazin, M. Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes / M. Sarrazin, J.-P. Vigneron, J.-M. Vigoureux // Phys. Rev. B - 2003. - Vol. 67. - P. 085415-085422.
  16. Gippius, N.A. Resonant mode coupling of optical resonances in stacked nanostructures / N.A. Gippius, T. Weiss, S. G. Tikhodeev, H. Giessen // Opt. Exp. - 2010. - Vol. 18. - P. 7569-7574.
  17. Popov, E. Theoretical study of the anomalies of coated dielectric gratings / E. Popov, L. Mashev // Optica Acta - 1986. - Vol. 33. - P. 607-619.
  18. Park, Y. Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings / Y. Park, M. Kulishov, R. Slavík, J. Azaña. // Opt. Exp. - 2006. - Vol. 14(26). - P. 12670-12678.
  19. Bonnans J.-F. Numerical optimization, theoretical and numerical aspects / J.-F. Bonnans, J.-C. Gilbert, C. Lemare?chal et al. // Springer, N.Y., 2003. - 437 p.
  20. Moharam, M.G. Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings / M. G. Moharam, E. B. Grann, D. A. Pommet [et al.] // J. Opt. Soc. Am. A - 1995. - Vol. 12, No. 5. - P.  1068-1076.
  21. Moharam, M.G. Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach/ M. G. Moharam, D. A. Pommet, E. B. Grann [et al.] // J. Opt. Soc. Am. A - 1995. - Vol. 12, No. 5. - P. 1077-1086.
  22. Li, L. Use of Fourier series in the analysis of discontinuous periodic structures/ L. Li // J. Opt. Soc. Am. A - 1996. - Vol. 13, No. 9. - P. 1870-1876.
  23. Nakagawa, W. Ultrashort pulse propagation in near-field periodic diffractive structures by use of rigorous coupled-wave analysis / W. Nakagawa, R.-C. Tyan, P.-C. Sun [et al.[ // J. Opt. Soc. Am. A - 2001. -Vol.18. - P. 1072-1081.
  24. Smirnov, N.V. The course in probability theory and mathematical statistics for engineering applications / N.V. Smirnov, I.V. Dunin-Barkovskiy -Moscow: “Nauka” Publisher, 1965. - 512 p. - (in Russian).

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20