Hydrodynamic and optical waves: A common approach for unidimensional propagation

Abstract

The aim of this chapter is to build a bridge between water and optical waves. After a brief introduction on the role played by the so-called normal variable in the D’Alembert equation and a short description of the Hamiltonian formulation of water waves, we introduce a similar formalism for describing optical waves. We restrict our analysis to one-dimensional propagation. Under a number of assumptions, we rewrite the Maxwell equations in a very general form that account for three- and four-wave interactions. Those equations are very similar to the one describing water waves. Analogies and differences between hydrodynamic and optical waves are also discussed.