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Nonlinear dispersive waves in nonlinear optics


Small, Robert Donald (1973) Nonlinear dispersive waves in nonlinear optics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KKBY-7364.


A study is made of solutions of the macroscopic Maxwell equations in nonlinear media. Both nonlinear and dispersive terms are responsible for effects that are not taken into account in the geometrical optics approximation. The nonlinear terms can, depending on the nature of the nonlinearity, cause plane waves to focus when the amplitude varies across the wavefront. The dispersive terms prevent the singularities that nonlinearity alone would produce. Solutions are found which de scribe periodic plane waves in fully nonlinear media. Equations describing the evolution of the amplitude, frequency and wave number are generated by means of averaged Lagrangian techniques. The equations are solved for near linear media to produce the form of focusing waves which develop a singularity at the focal point. When higher dispersion is included nonlinear and dispersive effects can balance and one finds amplitude profiles that propagate with straight rays.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Physics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Whitham, Gerald Beresford
Thesis Committee:
  • Unknown, Unknown
Defense Date:27 June 1972
Record Number:CaltechTHESIS:03292013-143344675
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7566
Deposited By: Dan Anguka
Deposited On:29 Mar 2013 22:01
Last Modified:09 Nov 2022 19:20

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