(a) Gaussian pump propagating through the chirped QPM PPLN crystal and splitting into signal and idler pulses during SPDC; (b) Schematic diagram of the down conversion for the pump, signal and idler pulses; (c) The real and imaginary parts for the response function of chirped QPM PPLN crystal; (d) The kernel of the biphoton state amplitude(BSA) function can be viewed as the product of pump function and phase matching function of the crystal.