ABSTRACT
This chapter outlines a way of constructing nonlinear constitutive equations, beginning with Maxwell’s equations, the causality principle and the concept of non-locality of response. It demonstrates the procedure of elimination of the magnetic induction of the light wave from the constitutive equations and derives the constitutive equations in the spectral representation. Maxwell’s equations form the basis of the mathematical apparatus which allows one to find the relation of the electromagnetic action on the medium and the medium’s response and also to describe the feedback of the response to the action. An additional constraint necessary at the microscopic level for closing the set of Maxwell’s equations is to be obtained from the equation of motion of charge carriers in the presence of the electric and magnetic fields.
