AN ABSTRACT REPRESENTATION OF THE SCALAR WAVE-EQUATION OF OPTICS .3.

The abstract representation of the scalar wave equation of optics is extended from the time-dependent wave equation to the stationary wave equation via the fundamental action integral. It is demonstrated that the stationary wave equation together with general initial conditions is not equivalent with the corresponding time-dependent equation, because with the transition one has lost physical information. The consequences thereof are discussed. Subsequently the modes of the stationary wave equation are defined and their attributes, which follow from missing losses of the physical system, are given. Finally the mode coupling method for the stationary wave equation is derived by geometrical reflections. Two examples illustrate the considerations.