where β β 2 = GVD parameter, z is propagation distance, E o ( z , t ) is the reshaped output pulse at distance z and time t. The response of this dispersive element in the time-stretch system can be approximated as a phase propagator as presented in H ( ω ω ) = e i φ φ ( ω ω ) = e i ∑ ∑ m = 0 ∞ ∞ φ φ m ( ω ω ) = ∏ ∏ m = 0 ∞ ∞ H m ( ω ω ) (2)