Modulational instability

In the fields of nonlinear optics and fluid dynamics, modulational instability or sideband instability is a phenomenon whereby deviations from a periodic waveform are reinforced by nonlinearity, leading to the generation of spectral-sidebands and the eventual breakup of the waveform into a train of pulses.[1][2][3]

It is widely believed that the phenomenon was first discovered − and modeled − for periodic surface gravity waves (Stokes waves) on deep water by T. Brooke Benjamin and Jim E. Feir, in 1967.[4] Therefore, it is also known as the Benjamin−Feir instability. However, spatial modulation instability of high-power lasers in organic solvents was observed by Russian scientists N. F. Piliptetskii and A. R. Rustamov in 1965,[5] and the mathematical derivation of modulation instability was published by V. I. Bespalov and V. I. Talanov in 1966.[6] Modulation instability is a possible mechanism for the generation of rogue waves.[7][8]

  1. ^ Benjamin, T. Brooke; Feir, J.E. (1967). "The disintegration of wave trains on deep water. Part 1. Theory". Journal of Fluid Mechanics. 27 (3): 417–430. Bibcode:1967JFM....27..417B. doi:10.1017/S002211206700045X. S2CID 121996479.
  2. ^ Benjamin, T.B. (1967). "Instability of Periodic Wavetrains in Nonlinear Dispersive Systems". Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 299 (1456): 59–76. Bibcode:1967RSPSA.299...59B. doi:10.1098/rspa.1967.0123. S2CID 121661209. Concluded with a discussion by Klaus Hasselmann.
  3. ^ Agrawal, Govind P. (1995). Nonlinear fiber optics (2nd ed.). San Diego (California): Academic Press. ISBN 978-0-12-045142-5.
  4. ^ Yuen, H.C.; Lake, B.M. (1980). "Instabilities of waves on deep water". Annual Review of Fluid Mechanics. 12: 303–334. Bibcode:1980AnRFM..12..303Y. doi:10.1146/annurev.fl.12.010180.001511.
  5. ^ Piliptetskii, N. F.; Rustamov, A. R. (31 May 1965). "Observation of Self-focusing of Light in Liquids". JETP Letters. 2 (2): 55–56.
  6. ^ Bespalov, V. I.; Talanov, V. I. (15 June 1966). "Filamentary Structure of Light Beams in Nonlinear Liquids". ZhETF Pisma Redaktsiiu. 3 (11): 471–476. Bibcode:1966ZhPmR...3..471B. Archived from the original on 31 July 2020. Retrieved 17 February 2021.
  7. ^ Janssen, Peter A.E.M. (2003). "Nonlinear four-wave interactions and freak waves". Journal of Physical Oceanography. 33 (4): 863–884. Bibcode:2003JPO....33..863J. doi:10.1175/1520-0485(2003)33<863:NFIAFW>2.0.CO;2.
  8. ^ Dysthe, Kristian; Krogstad, Harald E.; Müller, Peter (2008). "Oceanic rogue waves". Annual Review of Fluid Mechanics. 40 (1): 287–310. Bibcode:2008AnRFM..40..287D. doi:10.1146/annurev.fluid.40.111406.102203.