Skip to main content
SpringerLink
Log in

Nonlinear Optical Fibre Resonators with Applications in Electrical Engineering and Computing

  • Chapter
  • First Online:
Applications of Chaos and Nonlinear Dynamics in Engineering - Vol. 1

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

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].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Agrawal, G.P.: Nonlinear Fiber Optics, 4th edn. Academic (2006)

    Google Scholar 

  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. Borresen, J., Lynch, S.: Binary Half Adder and other Logic Circuits. UK patent pending application number 1011110.2 (2010)

    Google Scholar 

  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)

    Article  Google Scholar 

  5. Brambilla, G.: Optical fibre nanowires and microwires: a review. J. Optic. 12, 043001 (2010)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  7. Desurvire, E.: Erbium-doped fiber amplifiers: principles and applications. Wiley, New York (1994)

    Google Scholar 

  8. Doran, N.J., and Wood, D.: Nonlinear-optical loop mirror. Optics Lett. 13, 56–58 (1988)

    Google Scholar 

  9. Duling, I.N. III: All-fiber ring soliton laser mode locked with a nonlinear mirror. Optics Lett. 16, 539–541 (1991)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  13. Gibbs, H.M.: Optical Bistability: Controlling Light with Light. Academic (1985)

    Google Scholar 

  14. Hwang, J., Pototschnig, M., Lettow, R., et al.: A single-molecule optical transistor. Nature 460, 76–80 (2009)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  20. Lynch, S.: Dynamical Systems with Applications using Maple, 2nd edn. Springer, Birkhäuser (2010)

    Book  MATH  Google Scholar 

  21. Lynch, S.: Dynamical Systems with Applications using Mathematica. Springer, Birkhäuser (2007)

    MATH  Google Scholar 

  22. Lynch, S.: Dynamical Systems with Applications using MATLAB., Springer, Birkhäuser (2004)

    Google Scholar 

  23. Marburger, J.H., Felber, F.S.: Theory of a lossless nonlinear Fabry-Perot interferometer. Phy. Rev. A 17, 335–342 (1978)

    Article  Google Scholar 

  24. Matsumoto, M., Hasegawa, A.: Adiabatic amplification of solitons by means of nonlinear amplifying loop mirrors. Optics Lett. 19, 1019–1021 (1994)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  26. Ogusu, K.: Dynamic behavior of reflection optical bistability in a nonlinear fiber ring resonator. IEEE J. Quant. Electron. 32, 1537–1543 (1996)

    Article  Google Scholar 

  27. Pal, P., Knox W.H.: Fabrication and characterization of fused microfiber resonators. IEEE Photonics Tech. Lett. 21, 766–768 (2009)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  29. Seidel, H.: Bistable optical circuit using saturable absorber within a resonant cavity. U.S. Patent 3610731 October (1971)

    Google Scholar 

  30. Shi, C.-X.: Nonlinear fiber loop mirror with optical feedback. Optics Comm. 107, 276–280 (1994)

    Article  Google Scholar 

  31. Simova, E., Golub, I., Picard, M.J.: Ring resonator in a Sagnac loop. J. Opt. Soc. Am. B 22, 1723–1730 (2005)

    Article  Google Scholar 

  32. Smith, S.D.: Towards the optical computer. Nature 307, 315–316 (1984)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Sumetsky, M., Dulashko, Y., Fini, J.M., et al.: The microfiber loop resonator: theory, experiment, and application. J. Lightwave Tech. 24, 242–250 (2006)

    Article  Google Scholar 

  37. Sumetsky, M.: Optical micro- and nanofibers for sensing applications. Proc. SPIE 6556, 65560J (2007)

    Article  Google Scholar 

  38. Sumetsky, M.: Recent progress in the theory and applications of optical microfibers. Proc. SPIE 6593, 659302 (2007)

    Article  Google Scholar 

  39. Szöke, A., Daneu, V., Goldhar, J., et al.: Bistable optical element and its applications. Appl. Phys. Lett. 15, 376–379 (1969)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  43. Vienne, G., Yuhang, Li, Limin, Tong, et al.: Observation of a nonlinear microfiber resonator. Optics Lett. 33, 1500–1502 (2008)

    Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. School of Computing, Mathematics and Digital Technology, Manchester Metropolitan University, Manchester, M1 5GD, UK

    S. Lynch

  2. Department of Electronics, Carleton University, Ottawa, Ontario, K1S 5B6, Canada

    A. L. Steele

Authors
  1. S. Lynch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. L. Steele
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Lynch .

Editor information

Editors and Affiliations

  1. Politechnico di Torino, Department of Mathematics, Corso Duca degli Abruzzi 24, Torino, 10129, Italy

    Santo Banerjee

  2. and Technology, Department of Physics, Camellia School of Engineering, Nadibag PO Kajipara Barasat, Kolkata, 700124, India

    Mala Mitra

  3. , Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, Torino, 10129, Italy

    Lamberto Rondoni

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Lynch, S., Steele, A.L. (2011). Nonlinear Optical Fibre Resonators with Applications in Electrical Engineering and Computing. In: Banerjee, S., Mitra, M., Rondoni, L. (eds) Applications of Chaos and Nonlinear Dynamics in Engineering - Vol. 1. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21922-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21922-1_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21921-4

  • Online ISBN: 978-3-642-21922-1

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation