A spectrum-, temporal- and spatial-resolved physical model of LD pumping dynamics is set up, which includes the wavelength chirping and transient behavior of the power output of LD arrays. Based on this model, we investigate in detail the spectrum selective absorption characteristics from LD output by laser materials with different absorption bandwidths. Also the pumping excitation performances for typical three kinds of laser crystals, Yb:YAG, Yb:S-FAP, and Nd:YAG, are investigated specifically for the pulsed-energy-storage operation mode. Finally, we have optimized the initial central wavelength of LD arrays for the above three crystals and compared their sensitivity to the wavelength chirping of LD arrays.