A comprehensive theoretical model for analyzing both static and dynamic properties of arbitrary composition In1-xGaxAsyP1-y quantum-well (QW) electro-absorption modulator (EAM) is proposed. Optical absorption spectra of the QW-EAM considering both excitonic transitions and continuum conduction-band to valence-band transitions are included to evaluate the QW-EAM static performance. The dynamic absorption recovery of EAM is calculated as a function of electric field and pump power. Then, based on the theory of the carrier and absorption dynamics, a 40 Gb/s pump-probe configuration for optical signal processing using In0.53Ga0.47 As/InP QW-EAM as nonlinear element is thoroughly investigated. Influence of various parameters including pulse width, optical wavelength, optical power, and QW structure on the intensity and phase variation of the output probe signal through nonlinear interactions between pump and probe signals are investigated. The presented model and investigation are suitable for optimizing the device design and describing the properties of In1-xGaxAsyP1-y QW-EAM used in ultrafast optical signal processing applications.