Resonant diffraction gratings for differentiation of optical signals in reflection and transmission
N.V. Golovastikov, D.A. Bykov, L.L. Doskolovich, V.A. Soifer

PDF, 654 kB

Full text of article: Russian language.

DOI: 10.18287/0134-2452-2013-37-2-138-145

Pages: 138-145.

Abstract:
The propagation of an optical pulse through a diffraction grating with a resonance at the pulse’s central frequency is considered. It is demonstrated that afore-mentioned gratings can perform time-domain differentiation of optical pulses in reflection and transmission. The correlation between the amplitude of the transformed pulse and the differentiation quality is investigated. A resonant grating intended for differentiation of picosecond pulses in reflection and transmission is computed.

Key words:
diffraction gratings, optical differentiation, differentiation in reflection, differentiation in transmission.

References:

  1. Kulishov, M. Design of high-order all-optical temporal differentiators based on multiple-phase-shifted fiber Bragg gratings / M. Kulishov, J. Azana // Opt. exp. - 2007. - Vol. 15. - P. 6152-6166.
  2. Slavík, R. Ultrafast all-optical differentiators / R. Slavík, Y. Park, M. Kulishov, R. Morandotti, J. Azana // Opt. exp. - 2006. - Vol. 14. - P. 10699-10707.
  3. Kulishov, M. Long-period fiber gratings as ultrafast optical differentiators / M. Kulishov, J. Azana // 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. Azana // 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. Azana // 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. Azana // Opt. exp. - 2007. - Vol. 15. - P. 371-381.
  7. 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.
  8. 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.
  9. Bykov, D.A. Temporal differentiation of optical signals using resonant gratings / D.A. Bykov, L.L. Doskolovich, V.A. Soifer // Opt. Lett. - 2011. - Vol. 36. - P. 3509-3511.
  10. Bykov, D. On ability of resonant diffraction gratings to dif­ferentiate a pulsed optical signal / D.A. Bykov, L.L. Do­skolovich and V.A. Soifer // J. exp. Theor. Phys. - 2012. - Vol. 114. - P. 724–730.
  11. Golovastikov, N. Temporal differentiation of optical signzls in reflection using resonant gratings / N.V. Golovastikov, D.A. Bykov, L.L. Doskolovich, V.A. Soifer // Computer Op­tics. - 2012. - Vol. 36(2). - P. 151-157.
  12. Popov, e. Theoretical study of the anomalies of coated dielectric gratings / e. Popov, L. Mashev // Optica Acta. - 1986. - Vol. 33. - P. 607-619.
  13. 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.
  14. 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.
  15. 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. Kazanskiy // J. exp. Theor. Phys. - 2010. - Vol. 111, N 6. - P. 967-974.
  16. Bykov, D.A. Single-resonance diffraction gratings for time-domain pulse transformations: integration of optical signals / D.A. Bykov, L.L. Doskolovich, V.A. Soifer // J. Opt. Soc. Am. A. - 2012. - Vol. 29, N 8. - P. 1734-1740.
  17. Bykov, D.A. Numerical methods for calculating poles of the scattering matrix with applications in grating theory / D.A. Bykov, L.L. Doskolovich // Journal of Lightwave Technology. - 2013. - Vol. 31, N 5. - P. 793-801.
  18. Shestopalov, V.P. Resonant wave scattering. Vol. 1. Diffraction gratings / V.P. Shestopalov, A.A. Kirilenko, S.A. Masalov, Y.K. Sirenko. - Kiev: “Naukova Dumka” Publisher, 1986. - 232 p. - (In Russian).
  19. Bonnans, J.-F. Numerical optimization, theoretical and numerical aspects / J.-F. Bonnans, J.-C. Gilbert, C. Lema­re?chal [et al.]. - N.Y.: Springer, 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, N 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, N 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, N 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.

© 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