The four-color three-step selective photoionization process of atom is very important in laser isotope separation technology. The population trapping phenomena and their influences are studied theoretically in monochromatic and non-monochromatic laser fields based on the density matrix theory in this work. Time evolutions of the photoionization properties of the four-color, three-step process are given. The population trapping effects occur intensely in monochromatic excitation, while it gradually turns weak as the laser bandwidth increases. The effects of bandwidth, Rabi frequency, time delay, and frequency detuning on the population trapping effect are investigated in monochromatic and non-monochromatic laser fields. The effects of laser process parameters and atomic parameters on the effective selective photoionization are also discussed. The ionization probability and selectivity factors, as evaluation indexes, are difficult to improve synchronously by adjusting systematic parameters. Besides, the existence of metastable state may play a negative role when its population is low enough.
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