Theory of Self-Phase Modulation and Spectral Broadening

  • Y. R. Shen
  • Guo-Zhen Yang


Self-phase modulation refers to the phenomenon in which a laser beam propagating in a medium interacts with the medium and imposes a phase modulation on itself. It is one of those very fascinating effects discovered in the early days of nonlinear optics (Bloembergen and Lallemand, 1966; Brewer, 1967; Cheung et al., 1968; Lallemand, 1966; Jones and Stoicheff, 1964; Shimizu, 1967; Stoicheff, 1963). The physical origin of the phenomenon lies in the fact that the strong field of a laser beam is capable of inducing an appreciable intensity-dependent refractive index change in the medium. The medium then reacts back and inflicts a phase change on the incoming wave, resulting in self-phase modulation (SPM). Since a laser beam has a finite cross section, and hence a transverse intensity profile, SPM on the beam should have a transverse spatial dependence, equivalent to a distortion of the wave front. Consequently, the beam will appear to have self-diffracted. Such a self-diffraction action, resulting from SPM in space, is responsible for the well-known nonlinear optical phenomena of self-focusing and self-defocusing (Marburger, 1975; Shen, 1975). It can give rise to a multiple ring structure in the diffracted beam if the SPM is sufficiently strong (Durbin et al., 1981; Santamato and Shen, 1984). In the case of a pulsed laser input, the temporal variation of the laser intensity leads to an SPM in time. Since the time derivative of the phase of a wave is simply the angular frequency of the wave, SPM also appears as a frequency modulation. Thus, the output beam appears with a self-induced spectral broadening (Cheung et al., 1968; Gustafson et al., 1969; Shimizu, 1967).


Laser Pulse Ultrashort Pulse Refractive Index Change Molecular Reorientation Molecular Redistribution 
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.



This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098.


  1. Alfano, R.R. and S.L. Shapiro (1970) Emission in the region 4000–7000 A via four-photon coupling in glass; Observation of self-phase modulation and small scale filaments in crystals and glasses; Direct distortion of electronic clouds of rare-gas atoms in intense electric fields. Phys. Rev. Lett. 24, 584, 592, 1219.CrossRefADSGoogle Scholar
  2. Alfano, R.R. and S.L. Shapiro (1971) Picosecond spectroscopy using the inverse Raman effect. Chem. Phys. Lett. 8, 631.CrossRefADSGoogle Scholar
  3. Alfano, R.R., Q. Li, T. Jimbo, J.T. Manassah, and P.P. Ho (1986) Induced spectral broadening of a weak picosecond pulse in glass produced by an intense picosecond pulse. Opt. Lett. 11, 626.CrossRefADSGoogle Scholar
  4. Alfano, R.R., Q. Wang, T. Jimbo, and P.P. Ho (1987) Induced spectral broadening about a second harmonic generated by an intense primary ultrashort laser pulse in ZuSe. Phys. Rev. A 35, 459.CrossRefADSGoogle Scholar
  5. Bloembergen N. and P. Lallemand (1966) Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman lines, and stimulated Rayleigh scattering. Phys. Rev. Lett. 16, 81.CrossRefADSGoogle Scholar
  6. Brewer, R.G. (1967) Frequency shifts in self-focusing light. Phys. Rev. Lett. 19, 8.CrossRefADSGoogle Scholar
  7. Busch, G.E., R.P. Jones, and P.M. Rentzepis (1973) Picosecond spectroscopy using a picosecond continuum. Chem. Phys. Lett. 18, 178.CrossRefADSGoogle Scholar
  8. Cheung, A.C., D.M. Rank, R.Y. Chiao, and C.H. Townes (1968) Phase modulation of Q-switched laser beams in small-scale filaments. Phys. Rev. Lett. 20, 786.CrossRefADSGoogle Scholar
  9. Corkum, P.B., P.P. Ho, R.R. Alfano, and J.T. Manassah (1985) Generation of infrared supercontinuum covering 3–14 μm in dielectrics and semiconductors. Opt. Lett. 10, 624.CrossRefADSGoogle Scholar
  10. Corkum, P.B., C. Rolland, and T. Rao (1986) Supercontinuum generation in gases. Phys. Rev. Lett. 57, 2268.CrossRefADSGoogle Scholar
  11. Cubbedu, R. and F. Zagara (1971) Nonlinear refractive index of CS2 in small-scale filaments. Opt. Commun. 3, 310.CrossRefADSGoogle Scholar
  12. Cubbedu, R., R. Polloni, C.A. Sacchi, O. Svelto, and F. Zagara (1971) Study of small-scale filaments of light in CS2 under picosecond excitation. Phys. Rev. Lett. 26, 1009.CrossRefADSGoogle Scholar
  13. DeMartini, F., C.H. Townes, T.K. Gustafson, and P.L. Kelley (1967) Self-steepening of light pulses. Phys. Rev. 164, 312.CrossRefADSGoogle Scholar
  14. Durbin, S.D., S.M. Arakelian, and Y.R. Shen (1981) Laser-induced diffraction rings from a nematic liquid crystal film. Opt. Lett. 6, 411.CrossRefADSGoogle Scholar
  15. Fabellinski, I.L. (1967) Molecular Scattering of Light. Plenum, New York, Chapter VIII.Google Scholar
  16. Fisher, R.A. and W. Bischel (1975) Numerical studies of the interplay between self-phase modulation and dispersion for intense plane-wave light pulses. J. App. Phys. 46, 4921.CrossRefADSGoogle Scholar
  17. Fisher, R.A., B. Suydam, and D. Yevich (1983) Optical phase conjugation for time domain undoing of dispersive self-phase modulation effects. Opt. Lett. 8, 611.CrossRefADSGoogle Scholar
  18. Fork, R.L., C.V. Shank, C. Hirliman, and R. Yen (1983) Femtosecond white-light continuum pulses. Opt. Lett. 8, 1.CrossRefADSGoogle Scholar
  19. Fork, R.L., C.H. Brito Cruz, P.C. Becker, and C.V. Shank (1987). Compression of optical pulses to six femtoseconds by using cubic phase compensation. Opt. Lett. 12, 483.CrossRefADSGoogle Scholar
  20. Glownia, J., G. Arjavalingam, P. Sorokin, and J. Rothenberg (1986) Amplification of 350-fs pulses in XeCl excimer gain modules. Opt. Lett. 11, 79.CrossRefADSGoogle Scholar
  21. Gustafson, T.K., J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley (1969) Self-phase modulation, self steepening, and spectral development of light in small-scale trapped filaments. Phys. Rev. 177, 306.CrossRefADSGoogle Scholar
  22. Hellwarth, R.W. (1970) Theory of molecular light scattering spectra using the linear-dipole approximation. J. Chem. Phys. 52, 2128.CrossRefADSGoogle Scholar
  23. Hellwarth, R.W. (1977) Third-order optical susceptibilities of liquids and solids. Prog. Quantum Electron. 5, 1.CrossRefADSGoogle Scholar
  24. Ho, P.P., Q.X. Li, T. Jimbo, Y.L. Ku, and R.R. Alfano (1987) Supercontinuum pulse generation and propagation in a liquid CCl4. Appl. Opt. 26, 2700.CrossRefADSGoogle Scholar
  25. Ippen, E.P. and C.V. Shank (1975) Dynamic spectroscopy and subpicosecond pulse compression. Appl. Phys. Lett. 27, 488.CrossRefADSGoogle Scholar
  26. Jones, W.J. and B.P. Stoicheff (1964) Induced absorption at optical frequencies. Phys. Rev. Lett. 13, 657.CrossRefADSGoogle Scholar
  27. Lallemand, P. (1996) Temperature variation of the width of stimulated Raman lines in liquids. Appl. Phys. Lett. 8, 276.CrossRefADSGoogle Scholar
  28. Loy, M.M.T. and Y.R. Shen (1973) Study of self-focusing and small-scale filaments of light in nonlinear media. IEEE J. Quantum Electron. QE-9, 409.CrossRefADSGoogle Scholar
  29. Manassah, J.T., R.R. Shapiro, and M. Mustafa (1985) Spectral distribution of an ultrashort supercontinuum laser source. Phys. Lett. A107, 305.CrossRefADSGoogle Scholar
  30. Manassah, J.T., M.A. Mustafa, R.R. Alfano, and P.P. Ho (1986) Spectral extent and pulse shape of the supercontinuum for ultrashort laser pulse. IEEE J. Quantum Electron. QE-22, 197.CrossRefADSGoogle Scholar
  31. Marburger, J.H. (1975) Self-focusing: theory. Prog. Quantum Electron. 4, 35.CrossRefADSGoogle Scholar
  32. Nakatsuka, H. and D. Grischkowsky (1981) Recompression of optical pulses broadened by passage through optical fibers. Opt. Lett. 6, 13.CrossRefADSGoogle Scholar
  33. Nakatsuka, H., D. Grischkowsky, and A.C. Balant (1981) Nonlinear picosecond pulse propagation through optical fibers with positive group velocity dispersion. Phys. Rev. Lett. 47, 910.CrossRefADSGoogle Scholar
  34. Nikolaus, B. and D. Grischkowsky (1983a) 12× pulse compression using optical fibers. Appl. Phys. Lett. 42, 1.Google Scholar
  35. Nikolaus, B. and D. Grischkowsky (1983b) 90-fs tunable optical pulses obtained by two-state pulse compression. Appl. Phys. Lett. 43, 228.Google Scholar
  36. Penzkofer, A. (1974) Parametrically generated spectra and optical breakdown in H2O and NaCl. Opt. Commun. 11, 265.CrossRefADSGoogle Scholar
  37. Penzkofer, A., A. Laubereau, and W. Kaiser (1973) Stimulated short-wave radiation due to single-frequency resonances of χ (3). Phys. Rev. Lett. 31, 863.CrossRefADSGoogle Scholar
  38. Penzkofer, A., A. Seilmeier, and W. Kaiser (1975) Parametric four-photon generation of picosecond light at high conversion efficiency. Opt. Commun. 14, 363.CrossRefADSGoogle Scholar
  39. Santamato, E. and Y.R. Shen (1984) Field curvature effect on the diffraction ring pattern of a laser beam dressed by spatial self-phase modulation in a nematic film. Opt. Lett. 9, 564.CrossRefADSGoogle Scholar
  40. Shen, Y.R. (1966) Electrostriction, optical Kerr effect, and self-focusing of laser beams. Phys. Lett., 20, 378.CrossRefADSGoogle Scholar
  41. Shen, Y.R. (1975) Self-focusing: experimental. Prog. Quantum Electron. 4, 1.CrossRefADSGoogle Scholar
  42. Shen, Y.R. (1984) The Principles of Nonlinear Optics. Wiley, New York, Chapters 1 and 16.Google Scholar
  43. Shen, Y.R. and M.M.T. Loy (1971) Theoretical investigation of small-scale filaments of light originating from moving focal spots. Phys. Rev. A 3, 2099.CrossRefADSGoogle Scholar
  44. Shimizu, F. (1967) Frequency broadening in liquids by a short light pulse. Phys. Rev. Lett. 19, 1097.CrossRefADSGoogle Scholar
  45. Shimizu, F. and E. Courtens (1973) Recent results on self-focusing and trapping. In Fundamental and Applied Laser Physics, M.S. Feld, A. Javan, and N.A. Kurnit, eds. Wiley, New York, p. 67.Google Scholar
  46. Stoicheff, B.P. (1963) Characteristics of stimulated Raman radiation generated by coherent light. Phys. Lett. 7, 186.CrossRefADSGoogle Scholar
  47. Stolen, R. and C. Lin (1978) Self-phase modulation in silica optical fibers. Phys. Rev. A 17, 1448.CrossRefADSGoogle Scholar
  48. Topp, M.R. and P.M. Rentzepis (1971) Time-resolved absorption spectroscopy in the 10−12-sec range. J. Appl. Phys. 42, 3415.CrossRefADSGoogle Scholar
  49. Treacy, E.P. (1968) Compression of picosecond light pulses. Phys. Lett. 28A, 34.CrossRefADSGoogle Scholar
  50. Treacy, E.P. (1969a) Measurements of picosecond pulse substructure using compression techniques. Appl. Phys. Lett. 14, 112.Google Scholar
  51. Treacy, E.P. (1969b) Optical pulse compression with diffraction gratings. IEEE J. Quantum Electron. 5, 454.Google Scholar
  52. Wong, G.K.L. and Y.R. Shen (1972) Study of spectral broadening in a filament of light. Appl. Phys. Lett. 21, 163.CrossRefADSGoogle Scholar
  53. Yang, G. and Y.R. Shen (1984) Spectral broadening of ultrashort pulses in a nonlinear medium. Opt. Lett. 9, 510.CrossRefADSGoogle Scholar

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© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Y. R. Shen
    • 1
  • Guo-Zhen Yang
    • 1
  1. 1.Department of PhysicsUniversity of CaliforniaBerkeleyUSA

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