Conservation law for multimoded nonlinear optical waveguide interactions and its physical interpretation.
The swapping of power between the modes of cw waves in lossless nonlinear optical waveguides always admit two conserved quantities, the total power and one other, which is sometimes identified as a Hamiltonian. We show that a general formulation of this Hamiltonian is in fact the weak guidance limit for cw waves of a more general conservation law. We make the link between this more general conservation law and the conservation of "wave" momentum, where wave momentum is a combination of both real momentum and so-called pseudomomentum. This allows us to interpret the conserved Hamiltonian in physical terms.
Rowland
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School of Mathematics and Statistics, University College, The University of New South Wales, Australian Defence Force Academy, Canberra, Australian Capital Territory 2600, Australia.