Advertisement

Ultrashort Pulse Propagation in Nonlinear Dispersive Fibers

  • Govind P. Agrawal
Chapter

Abstract

Ultrashort optical pulses are often propagated through optical waveguides for a variety of applications including telecommunications and supercontinuum generation [1]. Typically the waveguide is in the form of an optical fiber but it can also be a planar waveguide. The material used to make the waveguide is often silica glass, but other materials such as silicon or chalcogenides have also been used in recent years. What is common to all such materials is they exhibit chromatic dispersion as well as the Kerr nonlinearity. The former makes the refractive index frequency dependent, whereas the latter makes it to depend on the intensity of light propagating through the medium [2]. Both of these effects become more important as optical pulses become shorter and more intense. For pulses not too short (pulse widths > 1 ns) and not too intense (peak powers < 10 mW), the waveguide plays a passive role (except for small optical losses) and acts as a transporter of optical pulses from one place to another, without significantly affecting their shape or spectrum. However, as pulses become shorter and more intense, both the dispersion and the Kerr nonlinearity start to affect the shape and spectrum of an optical pulse during its propagation inside the waveguide. This chapter focuses on silica fibers but similar results are expected for other waveguides made of different materials

Keywords

Optical Pulse Input Pulse Dispersive Wave Gaussian Pulse Supercontinuum Generation 
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.

References

  1. 1.
    G.P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic Press, 2013).Google Scholar
  2. 2.
    P.D. Maker, R.W. Terhune, and C. M Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507-509 (1964).CrossRefADSGoogle Scholar
  3. 3.
    R.L. Fork, C.H. Brito Cruz, P.C. Becker, and C.V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12,483-485 (1987).CrossRefADSGoogle Scholar
  4. 4.
    A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers: I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142-144 (1973).CrossRefADSGoogle Scholar
  5. 5.
    L.F. Mollenauer, R.H. Stolen, and J.P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095-1098 (1980).CrossRefADSGoogle Scholar
  6. 6.
    L.F. Mollenauer and R.H. Stolen, “The soliton laser,” Opt. Lett. 9, 13-15 (1984).CrossRefADSGoogle Scholar
  7. 7.
    R.H. Stolen, “The early years of fiber nonlinear optics,” J. Lightwave Technol. 26, 1021-1031 (2008).CrossRefADSGoogle Scholar
  8. 8.
    J.K. Ranka, R.S. Windeler, and A.J. Stentz, “Visible continuum generation in air–silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25-27 (2000).CrossRefADSGoogle Scholar
  9. 9.
    J.M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135-1184 (2006).CrossRefADSGoogle Scholar
  10. 10.
    G. Genty, S. Coen, and J.M. Dudley, “Fiber supercontinuum sources,” J. Opt. Soc. Am. B 24, 1771-1785 (2007).CrossRefADSGoogle Scholar
  11. 11.
    J.M. Dudley and J.R. Taylor, Eds., Supercontinuum Generation in Optical Fibers (Cambridge University Press, 2010).Google Scholar
  12. 12.
    R.R. Alfano and S.L. Shapiro, “Emission in the region 4000 to 7000 Åvia four-photon coupling in glass,” Phys. Rev. Lett. 24, 584-587 (1970).CrossRefADSGoogle Scholar
  13. 13.
    R.R. Alfano and S.L. Shapiro, “Observation of self-phase modulation and small scale filaments in crystals and glasses,” Phys. Rev. Lett. 24, 592-594 (1970).CrossRefADSGoogle Scholar
  14. 14.
    R.R. Alfano and S.L. Shapiro, “Direct distortion of electronic clouds of rare gas atoms in intense electric fields,” Phys. Rev. Lett. 24, 1217-1220 (1970).CrossRefADSGoogle Scholar
  15. 15.
    R.R. Alfano and S.L. Shapiro, “Picosecond spectroscopy using the inverse Raman effect,” Chem. Phys. Lett. 8, 631-633 (1971).CrossRefADSGoogle Scholar
  16. 16.
    R.H. Stolen, J.P. Gordon, W.J. Tomlinson, and H.A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159-1166 (1989).CrossRefADSGoogle Scholar
  17. 17.
    R.H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448-1453 (1978).CrossRefADSGoogle Scholar
  18. 18.
    G.P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed., (Academic Press, 2008).Google Scholar
  19. 19.
    W.J. Tomlinson, R.H. Stolen, and A.M. Johnson, “Optical wave breaking in nonlinear optical fibers,” Opt. Lett. 10, 457459 (1985).CrossRefGoogle Scholar
  20. 20.
    P.K.A. Wai, C.R. Menyuk, Y.C. Lee, and H.H. Chen, “Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers,” Opt. Lett. 11, 464-488 (1986).CrossRefADSGoogle Scholar
  21. 21.
    N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602-2607 (1995).CrossRefADSGoogle Scholar
  22. 22.
    Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510-524 (1987).CrossRefADSGoogle Scholar
  23. 23.
    P.K.A. Wai, H.H. Chen, and Y.C. Lee, “Radiations by solitons at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426-439 (1990).CrossRefADSGoogle Scholar
  24. 24.
    J.P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 91-97 (1992).CrossRefADSGoogle Scholar
  25. 25.
    S. Roy, S.K. Bhadra, and G.P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A 79, 023824 (2009).CrossRefADSGoogle Scholar
  26. 26.
    F.M. Mitschke and L.F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11,659-661 (1986).CrossRefADSGoogle Scholar
  27. 27.
    J.P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662-664 (1986).CrossRefADSGoogle Scholar
  28. 28.
    J. Santhanam and G.P. Agrawal, “Raman-induced spectral shifts in optical fibers: general theory based on the moment method,” Opt. Commun. 222, 413-420 (2003).CrossRefADSGoogle Scholar
  29. 29.
    X. Liu, C. Xu, W.H. Knox, J.K. Chandalia, B.J. Eggleton, S.G. Kosinski, and R.S. Windeler, “Soliton self-frequency shift in a short tapered air–silica microstructure fiber,” Opt. Lett. 26, 358-360 (2001).CrossRefADSGoogle Scholar
  30. 30.
    P. Beaud, W. Hodel, B. Zysset, and H.P. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938-1946 (1987).CrossRefADSGoogle Scholar
  31. 31.
    C. Lin and R.H. Stolen, “New nanosecond continuum for excited-state spectroscopy,” Appl. Phys. Lett. 28, 216-28 (1976).CrossRefADSGoogle Scholar
  32. 32.
    G. Qin, X. Yan, C. Kito, M. Liao, C. Chaudhari, T. Suzuki, and Y. Ohishi, “Ultrabroadband supercontinuum generation from ultraviolet to 6.28 μm in a fluoride fiber,” Appl. Phys. Lett. 95, 161103 (2009).CrossRefADSGoogle Scholar
  33. 33.
    Q. Lin and G.P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31, 3086–3088 (2006).CrossRefADSGoogle Scholar
  34. 34.
    N. Nishizawa and T. Goto, “Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlation frequency resolved optical gating,” Opt. Express 8, 328-334 (2001).CrossRefADSGoogle Scholar
  35. 35.
    R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, 2002).Google Scholar
  36. 36.
    G.E. Town, T. Funaba, T. Ryan, and K. Lyytikainen, “Optical supercontinuum generation from nanosecond pump pulses in an irregularly microstructured air-silica optical fiber,” Appl. Phys. B 77, 235-238 (2003).CrossRefADSGoogle Scholar
  37. 37.
    A.V. Avdokhin, S.V. Popov, and J.R. Taylor, “Continuous-wave, high-power, Raman continuum generation in holey fibers,” Opt. Lett. 28, 1353-1355 (2003).CrossRefADSGoogle Scholar
  38. 38.
    J.W. Nicholson, A.K. Abeeluck, C. Headley, M.F. Yan, and C.G. Jørgensen, “Pulsed and continuous-wave supercontinuum generation in highly nonlinear, dispersion-shifted fibers,” Appl. Phys. B 77, 211-218 (2003).CrossRefADSGoogle Scholar
  39. 39.
    A.K. Abeeluck, C. Headley, and C.G. Jørgensen, “High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser,” Opt. Lett. 29, 2163-2164 (2004).CrossRefADSGoogle Scholar
  40. 40.
    J.C. Travers, “Continuous wave supercontinuum generation,” Chap. 8 in Supercontinuum Generation in Optical Fibers, J.M. Dudley and J.R. Taylor, Eds. (Cambridge University Press, 2010).Google Scholar
  41. 41.
    A. Mussot, E. Lantz, H. Maillotte, R. Sylvestre, C. Finot, and S. Pitois, “Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers,” Opt. Express 12, 2838–2843 (2004).CrossRefADSGoogle Scholar
  42. 42.
    F. Vanholsbeeck, S. Martin-Lopez, M. Gonzlez-Herrez, and S. Coen, “The role of pump incoherence in continuous-wave supercontinuum generation,” Opt. Express 13, 6615 (2005).CrossRefADSGoogle Scholar
  43. 43.
    S.M. Kobtsev and S.V. Smirnov, “Modelling of high-power supercontinuum generation in highly nonlinear, dispersion shifted fibers at CW pump,” Opt. Express 13, 6912-8918 (2005).CrossRefADSGoogle Scholar
  44. 44.
    B.A. Cumberland, J.C. Travers, S.V. Popov, and J.R. Taylor, “29 W High power CW supercontinuum source,” Opt. Express 16, 5954-5962 (2008).CrossRefADSGoogle Scholar
  45. 45.
    B.A. Cumberland, J.C. Travers, S.V. Popov, and J.R. Taylor, Opt. Lett. 33, 2122 (2008).CrossRefADSGoogle Scholar
  46. 46.
    A. Kudlinski, G. Bouwmans, O. Vanvincq, Y. Quiquempois, A. Le Rouge, L. Bigot, G. Melin, and A. Mussot, “White-light cw-pumped supercontinuum generation in highly GeO2-doped-core photonic crystal fibers Opt. Lett. 34, 3631-3634 (2009).CrossRefADSGoogle Scholar
  47. 47.
    A. Kudlinski, B. Barviau, A. Leray, C. Spriet, L. Héliot, and A. Mussot, “Control of pulse-to-pulse ?uctuations in visible supercontinuum,” Opt. Express 18, 27445-27454 (2010).CrossRefADSGoogle Scholar
  48. 48.
    S.M. Kobtsev and S.V. Smirnov, “Coherent properties of supercontinuum containing clearly defined solitons,” Opt. Express 14, 3968-3980 (2006).CrossRefADSGoogle Scholar
  49. 49.
    D. Türke, S. Pricking, A. Husakou, J. Teipel, J. Herrmann, and H. Giessen, “Coherence of subsequent supercontinuum pulses generated in tapered fibers in the femtosecond regime,” Opt. Express 15, 2732-2741 (2007).CrossRefADSGoogle Scholar
  50. 50.
    G. Genty, M. Surakka, J. Turunen, and A.T. Friberg, “Second-order coherence of supercontinuum light,” Opt. Lett. 35, 3057-3059 (2010).CrossRefADSGoogle Scholar
  51. 51.
    P. Falk, M.H. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express 13, 7535-7540 (2005).CrossRefADSGoogle Scholar
  52. 52.
    A.M. Heidt, A. Hartung, G.W. Bosman, P. Krok, E.G. Rohwer, H. Schwoerer, and H. Bartelt, “Coherent octave spanning near-infrared and visible supercontinuum generation in all-normal dispersion photonic crystal fibers,” Opt. Express 19, 3775-3787 (2011).CrossRefADSGoogle Scholar
  53. 53.
    L.E. Hooper, P.J. Mosley, A.C. Muir, W.J. Wadsworth, and J.C. Knight, “Coherent supercontinuum generation in photonic crystal fiber with all-normal group velocity dispersion,” Opt. Express 19, 4902-4907 (2011).CrossRefADSGoogle Scholar
  54. 54.
    A.M. Heidt, J. Rothhardt, A. Hartung, H. Bartelt, E.G. Rohwer, J. Limpert, and A. Tnnermann, High quality sub-two cycle pulses from compression of supercontinuum generated in all-normal dispersion photonic crystal fiber, Opt. Express 19, 1387313879 (2011).ADSGoogle Scholar
  55. 55.
    A. Hartung, A.M. Heidt, and H. Bartelt, “Nanoscale all-normal dispersion optical fibers for coherent supercontinuum generation atultraviolet wavelengths,” Opt. Express 20, 13777-13788 (2012).CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Govind P. Agrawal
    • 1
  1. 1.Institute of OpticsUniversity of RochesterRochesterUSA

Personalised recommendations