Use of photonic crystal resonators for differentiation of optical impulses in time
N.L. Kazanskiy, P.G. Serafimovich, S.N. Khonina

Full text of article: Russian language.

Abstract:
The ability of general optical resonators to perform differentiation of optical signals in time. Analytical dependencies for such resonators are obtained with temporal coupled wave theory. A compact nanocavity-aided differentiator based on ridged photonic-crystal waveguide is designed.

Key words:
optical nanoresonator; photonic crystal waveguide; resonance mode; optical differentiation.

References:

  1. Gavrilov, A.V. Perspectives of development of analogous computers / A.V. Gavrilov, V.  Soifer. // Computer Optics. – 2012. – V. 36, N 2. – P. 140-150. – (In Russian).
  2. Kulishov, M. Design of terahertz-bandwidth arbitrary-order temporal differentiators based on long-period fiber gratings / M. Kulishov, D. Krcmarík and R. Slavík // Opt. Lett. – 2007. – Vol. 32, N 20. – P. 2978-2980.
  3. Park, Y. Ultrafast all-optical first- and higher-order differentiators based on interferometers / Y. Park, J. Azaña and R. Slavík // Opt. Lett. – 2007. – Vol. 32, N 6. – P. 710-712.
  4. Liu, F. Compact optical temporal differentiator based on silicon microring resonator / F. Liu, T. Wang, L. Qiang, T. Ye, Z. Zhang, M.  Qiu and Y. Su // Opt. Express – 2008. – Vol. 16, N 20. – P. 15880-15886.
  5. Bykov, D. Temporal differentiation of optical signals using resonant gratings / D. Bykov, L. Doskolovich, V. Soifer // Opt. Lett. – 2011. – Vol. 36. – P. 3509-3511.
  6. Golovastikov, N.V. Resonance diffractive gratings for differentiation of optical impulses in reflection / N.V. Golovastikov, D. Bykov, L. Doskolovich, V. Soifer // Computer Optics. – 2012. – V. 36, N 2. – P. 151-157. – (In Russian).
  7. Joannopoulos, J. Photonic Crystals - Molding the Flow of Light / J. Joannopoulos [et al.]. – 2nd ed. – Princeton, 2008.
  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 and V. Pruneri // Opt. Express – 2009. – Vol. 17, N 22. – P. 19798-19807.
  9. Fan, S. Guided and defect modes in periodic dielectric waveguides / S. Fan, J.N. Winn, A. Devenyi, J.C. Chen, R.D. Meade and J.D. Joannopoulos // J. Opt. Soc. Am. B. – 1995. – Vol. 12(7). – P. 1267-1272.
  10. Sauvan, M. Modal-reflectivity enhancement by gemetry tuning in photonic crystal microcavities / C. Sauvan, G. Lecamp, P. Lalanne, J. Hugonin // Opt. Express. – 2005. – Vol. 13. – P. 245-255.
  11. Quan, Q. Deterministic design of high Q, small mode volume photonic crystal nanobeam cavities / Q. Quan and M. Loncar // Opt. Express – 2011. – Vol. 19, N 5. – P. 18529-18542.
  12. Taflove, A. Computational Electrodynamics: The Finite-Dif­ference Time-Domain Method / A. Taflove and S.C. Hagness. – 3rd ed. – Norwood, MA: Artech House, 2005.
  13. Ashrafi, R. Figure of merit for photonic differentiators / R. Ashrafi and J. Azaña // Optics Express. – 2012. – Vol. 20, N 3. – P. 2626-2639.
  14. Ashrafi, R. Ultrafast optical arbitrary-order differentiators based on apodized long period gratings / R. Ashrafi, M.H. Asghari and J. Azaña // IEEE Photon. J. – 2011. – Vol. 3, N 3. – P. 353-364.
  15. Slavík, R. Terahertz-bandwidth high-order temporal differentiators based on phase-shifted long-period fiber gratings / R. Slavík, Y. Park, M. Kulishov and J. Azaña // Opt. Lett. – 2009. – Vol. 34, N 20. – P. 3116-3118.
  16. Rivas, L.M. Experimental demonstrationof ultrafast all-fiber high-order photonic temporal differentiators / Luis M. Rivas, Sylvian Boudreau, Yongwoo Park, Radan Slavik, Sophie LaRochelle, Alejandro Carballar, José Azaña // Opt. Letters. – 2009. – Vol. 34(12). – P. 1792-1794.
© 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