The normalized phase-amplitude representation and the Darboux figure are first defined. Then as an example, we establish the quantum optics description for the field in photonic crystal fibers in the defined representation. The field is evolved from one Darboux state to another state in the Darboux figure. By the continuous inputting (pump) of light, the waves induced by nonlinear effects become stronger (the wave frequency number remains constant at the same distance, and their intensities accumulate). The blueshifted waves induced by the third-order resonant susceptibility are not strong enough to cover other nonlinear effect and turn weak along the length (pump turns weak).