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Conservation law for multimoded nonlinear optical waveguide interactions and its physical interpretation.

D R Rowland1

  • 1School of Mathematics and Statistics, University College, The University of New South Wales, Australian Defence Force Academy, Canberra, Australian Capital Territory 2600, Australia.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
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Power exchange in nonlinear optical waveguides conserves total power and a Hamiltonian. This Hamiltonian is a weak guidance limit of a general conservation law, linked to wave momentum, providing physical interpretation.

Area of Science:

  • Nonlinear Optics
  • Waveguide Theory
  • Mathematical Physics

Background:

  • Nonlinear optical waveguides exhibit power exchange between modes.
  • Two conserved quantities are known: total power and a Hamiltonian.
  • The physical interpretation of the conserved Hamiltonian is not fully understood.

Purpose of the Study:

  • To generalize the conserved Hamiltonian in nonlinear optical waveguides.
  • To link the Hamiltonian to a more fundamental conservation law.
  • To provide a physical interpretation of the conserved Hamiltonian.

Main Methods:

  • Analysis of continuous wave (cw) waves in lossless nonlinear optical waveguides.
  • Formulation of a general conservation law.
  • Weak guidance approximation for cw waves.

Related Experiment Videos

  • Connecting conservation laws to wave momentum (real momentum and pseudomomentum).

    • Main Results:

    • A general formulation of the conserved Hamiltonian was derived.
    • This Hamiltonian is shown to be the weak guidance limit of a more general conservation law.
    • A direct link was established between this general conservation law and the conservation of wave momentum.

    Conclusions:

    • The conserved Hamiltonian in nonlinear optical waveguides can be physically interpreted.
    • Wave momentum, a combination of real momentum and pseudomomentum, is key to this interpretation.
    • This work provides a deeper understanding of conserved quantities in nonlinear optics.