Modern Physics Letters B, Vol. 9, No. 23 (1995) 1479-1506.
World Scientific Publishing Company

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UNIFICATION OF LINEAR AND NONLINEAR WAVE OPTICS ALLAN W. SNYDER, D. JOHN MITCHELL, and YURI S. KIVSHAR Institute of Advanced Studies, Australian National University Canberra ACT 0200, Australia Received 6 October 1995

A new conceptual approach unifies the seemingly disparate fields of linear and nonlinear waves. Linear physics is shown to be the natural way to approach nonlinear wave optics. It generates the fundamental equations, allows for unforeseen generalizations and, through physical insight, motivates novel phenomena.

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• Introduction
• Conceptual Foundations of the Linear Perspective
• Beams whose Intensity is Axial Uniform
  • Beams that are one mode of their induced waveguides
  • Beams that are two orthogonal modes of their induced waveguides
  • Discoveries motivated by the linear perspective
  • Example 1. Optical vortex soliton
  • Example 2. Rotating vector solitons
  • Example 3. Parallel solitons
  • Example 4. Light guiding light
• Solitons by Inverting Linear Waves
  • Example 1. Bright solitons
  • Example 2. Dark solitons
  • Example 3. Bistable solitons
  • Example 4. Dynamic solitons
  • Example 5. Dark-like, bright solitons
  • Example 6. Surface waves and nonlinear modes
• Variational Approximation - the Linear Perspective
• Universal Stability Criteria
• Beams whose Intensity Changes with Propagation
  • Example 1. Self tapering --- beams in a medium with loss or gain
  • Example 2. Nonlinear couplers and soliton switching
  • Example 3. Beams that attract, repel and spiral
  • Example 4. Beams with periodic changes
  • Example 5. Colliding beams
• Weakly Guiding Nonlinear Waves
  • Schrödinger Equation from Maxwell's Equations
  • Limitations of the Scalar Approximation
• Spatial Solitons in a Medium Exhibiting Harmonic Generation
• Conclusions
• Appendix
• References
• About this document ...