Nonlinear Optical Fibre Resonators with Applications in Electrical Engineering and Computing

  • S. LynchEmail author
  • A. L. Steele
Part of the Understanding Complex Systems book series (UCS)


In 1969, Szöke et al. reported their first experiments on optical bistability [39] and Seidel filed his patent [29] on a bistable optical circuit. Both reported optical hysteresis and suggested applications. The two essential ingredients for bistability are nonlinearity and feedback. Bistability is a phenomenon where a given optical device can have two possible output powers for a given input power. In 1976, Gibbs [10] demonstrated bistability using a sodium-filled Fabry-Perot interferometer. Bistability is a hysteresis effect that is dependent upon the history of the system. There are two stable steady-states within a bistable region and the path followed is dependent upon whether the input power is increasing or decreasing. Consider Fig. 3.1 , the power is increased from zero and the output power follows the route A, B, C. The input power is then decreased back down to zero and the output power follows the route C, D, A, giving a counterclockwise bistable region. For an input power, x, say, there are two possible outputs depending on whether the input power is increasing or decreasing. This bistable behavior can be introduced through an absorption process or a dispersion process. With the first process a saturable absorber could be contained within a cavity [29].


Input Power Bifurcation Diagram Linear Stability Analysis Ring Resonator Nonlinear Refractive Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1].
    Agrawal, G.P.: Nonlinear Fiber Optics, 4th edn. Academic (2006)Google Scholar
  2. [2].
    Babkina, T.K., Bass, F.G., Bulgakov, S.A., Grigor’yants, V.V., Konotop, V.V.: On multistability on nonlinear fiber interferometer with recirculating delay line. Optics Comm. 78, 398–402 (1990)Google Scholar
  3. [3].
    Borresen, J., Lynch, S.: Binary Half Adder and other Logic Circuits. UK patent pending application number 1011110.2 (2010)Google Scholar
  4. [4].
    Boscolo, S., Turitsyn, S.K., Blow, K.J.: Nonlinear loop mirror-based all-optical signal processing in fiber-optic communications. Opt. Fiber Tech. 14, 299–316 (2008)CrossRefGoogle Scholar
  5. [5].
    Brambilla, G.: Optical fibre nanowires and microwires: a review. J. Optic. 12, 043001 (2010)CrossRefGoogle Scholar
  6. [6].
    Cao, W., Wai, P.K.A.: Comparison of fiber-based Sagnac interferometers for self-switching of optical pulses. Opt. Comm. 245, 177–186 (2005)CrossRefGoogle Scholar
  7. [7].
    Desurvire, E.: Erbium-doped fiber amplifiers: principles and applications. Wiley, New York (1994)Google Scholar
  8. [8].
    Doran, N.J., and Wood, D.: Nonlinear-optical loop mirror. Optics Lett. 13, 56–58 (1988)Google Scholar
  9. [9].
    Duling, I.N. III: All-fiber ring soliton laser mode locked with a nonlinear mirror. Optics Lett. 16, 539–541 (1991)CrossRefGoogle Scholar
  10. [10].
    Gibbs, H.M., McCall, S.L., Venkatesan, T.N.C.: Differential gain and bistability using a sodium-filled Fabry-Perot interferometer. Phys. Rev. Lett. 36, 1135–1138 (1976)CrossRefGoogle Scholar
  11. [11].
    Fraile-Pelaez, F.J., Capmany, J., Muriel, M.A.: Transmission bistability in a double-coupler fiber ring resonator, Optics Lett. 16, 907–909 (1991)CrossRefGoogle Scholar
  12. [12].
    Gibbs, H.M., Hopf, F.A., Kaplan D.L., et al.: Observation of chaos in optical bistability. Phys. Rev. Lett. 46, 474–477 (1981)CrossRefGoogle Scholar
  13. [13].
    Gibbs, H.M.: Optical Bistability: Controlling Light with Light. Academic (1985)Google Scholar
  14. [14].
    Hwang, J., Pototschnig, M., Lettow, R., et al.: A single-molecule optical transistor. Nature 460, 76–80 (2009)Google Scholar
  15. [15].
    Ibrahim, T.A., Amarnath, K., Kuo, L.C., et al.: Photonic logic NOR gate based on two symmetric microring resonators. Optics Lett. 29, 2779–2781 (2004)CrossRefGoogle Scholar
  16. [16].
    Ikeda, K.: Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Optics Comm. 30, 257–261 (1979)CrossRefGoogle Scholar
  17. [17].
    Ja, Y.H.: Multiple bistability in an optical-fiber double-ring resonator utilizing the Kerr effect. IEEE J. Quant. Electron. 30, 329–333 (1994)CrossRefGoogle Scholar
  18. [18].
    Lee, J.H., Kogure, T., Richardson, D.J.: Wavelength tunable 10-GHz 3-ps pulse source using a dispersion decreasing fiber-based nonlinear optical loop mirror. IEEE J. Quant. Electron. 10, 181–185 (2004)CrossRefGoogle Scholar
  19. [19].
    Lim, H.C., Futami, F., Kikuchi, K.: Polarization independent wavelength-shift-free optical phase conjugator using a nonlinear fiber Sagnac interferometer. IEEE Photo. Technol. Lett. 11, 578–580 (1999)CrossRefGoogle Scholar
  20. [20].
    Lynch, S.: Dynamical Systems with Applications using Maple, 2nd edn. Springer, Birkhäuser (2010)zbMATHCrossRefGoogle Scholar
  21. [21].
    Lynch, S.: Dynamical Systems with Applications using Mathematica. Springer, Birkhäuser (2007)zbMATHGoogle Scholar
  22. [22].
    Lynch, S.: Dynamical Systems with Applications using MATLAB., Springer, Birkhäuser (2004)Google Scholar
  23. [23].
    Marburger, J.H., Felber, F.S.: Theory of a lossless nonlinear Fabry-Perot interferometer. Phy. Rev. A 17, 335–342 (1978)CrossRefGoogle Scholar
  24. [24].
    Matsumoto, M., Hasegawa, A.: Adiabatic amplification of solitons by means of nonlinear amplifying loop mirrors. Optics Lett. 19, 1019–1021 (1994)CrossRefGoogle Scholar
  25. [25].
    Nakatsuka, H., Asaka, S., Itoh, H., et al.: Observation of bifurcation to chaos in an all-optical bistable system. Phys. Rev. Lett. 50, 109–112 (1983)CrossRefGoogle Scholar
  26. [26].
    Ogusu, K.: Dynamic behavior of reflection optical bistability in a nonlinear fiber ring resonator. IEEE J. Quant. Electron. 32, 1537–1543 (1996)CrossRefGoogle Scholar
  27. [27].
    Pal, P., Knox W.H.: Fabrication and characterization of fused microfiber resonators. IEEE Photonics Tech. Lett. 21, 766–768 (2009)CrossRefGoogle Scholar
  28. [28].
    Schwelb, O.: Transmission, group delay, and dispersion in single-ring optical resonators and add/drop filters – a tutorial overview. J. Lightwave Tech. 22, 1380–1394 (2004)CrossRefGoogle Scholar
  29. [29].
    Seidel, H.: Bistable optical circuit using saturable absorber within a resonant cavity. U.S. Patent 3610731 October (1971)Google Scholar
  30. [30].
    Shi, C.-X.: Nonlinear fiber loop mirror with optical feedback. Optics Comm. 107, 276–280 (1994)CrossRefGoogle Scholar
  31. [31].
    Simova, E., Golub, I., Picard, M.J.: Ring resonator in a Sagnac loop. J. Opt. Soc. Am. B 22, 1723–1730 (2005)CrossRefGoogle Scholar
  32. [32].
    Smith, S.D.: Towards the optical computer. Nature 307, 315–316 (1984)Google Scholar
  33. [33].
    Sotobayashi, H., Sawaguchi, C., Koyamada, Y., et al.: Ultrafast walk-off-free nonlinear optical loop mirror by a simplified configuration for 320-Gbit/s time-division multiplexing signal demultiplexing. Optics Lett. 27, 1555–1557 (2002)CrossRefGoogle Scholar
  34. [34].
    Steele, A.L., Lynch, S., Hoad, J.E.: Analysis of optical instabilities and bistability in a nonlinear optical fibre loop mirror with feedback. Optics Comm. 137, 136–142 (1997)CrossRefGoogle Scholar
  35. [35].
    Sumetsky, M., Dulashko, Y., Fini, J.M., et al.: Optical microfiber loop resonator. Appl. Phys. Lett. 86, 161108-1-3 (2005)Google Scholar
  36. [36].
    Sumetsky, M., Dulashko, Y., Fini, J.M., et al.: The microfiber loop resonator: theory, experiment, and application. J. Lightwave Tech. 24, 242–250 (2006)CrossRefGoogle Scholar
  37. [37].
    Sumetsky, M.: Optical micro- and nanofibers for sensing applications. Proc. SPIE 6556, 65560J (2007)CrossRefGoogle Scholar
  38. [38].
    Sumetsky, M.: Recent progress in the theory and applications of optical microfibers. Proc. SPIE 6593, 659302 (2007)CrossRefGoogle Scholar
  39. [39].
    Szöke, A., Daneu, V., Goldhar, J., et al.: Bistable optical element and its applications. Appl. Phys. Lett. 15, 376–379 (1969)CrossRefGoogle Scholar
  40. [40].
    Tong, L., Gattass, R.R., Ashcom, J.B., et al.: Subwavelength-diameter silica wires for low-loss optical wave guiding. Nature 426, 816–819 (2003)CrossRefGoogle Scholar
  41. [41].
    Tong, L., Lou, J., Mazur E.: Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides. Optic. Express 12, 1025–1035 (2004)CrossRefGoogle Scholar
  42. [42].
    Vienne, G., Grelu, P., Pan, X., et al.: Theoretical study of microfiber resonator devices exploiting a phase shift. J. Optics A: Pure Appl. Optics 10, 025303 (2008)CrossRefGoogle Scholar
  43. [43].
    Vienne, G., Yuhang, Li, Limin, Tong, et al.: Observation of a nonlinear microfiber resonator. Optics Lett. 33, 1500–1502 (2008)Google Scholar
  44. [44].
    Linjie, Zhou, Djordjevic, S.S., Fontaine N.K., et al.: Silicon microring resonator-based reconfigurable optical lattice filter for on-chip optical signal processing. LEOS Annual Meeting Conference Proc., 2009. LEOS ’09. IEEE, pp. 501–502 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Computing, Mathematics and Digital TechnologyManchester Metropolitan UniversityManchesterUK
  2. 2.Department of ElectronicsCarleton UniversityOttawaCanada

Personalised recommendations