The influence of driving field phase fluctuation on lasing without population inversion in a three-level cascade system was studied. In the rotating wave and slowly varying envelope approximations

the density-matrix motion equations for the three-level cascade system

considered the influence of driving-field phase diffusion is solved

and the exact linear analytical solutions of the three-level cascade system with the driving field having the phase fluctuation in the steady state are obtained. The dependence of LWI gain

dispersion and the populations on the probe field detuning and the strengths of coherent pumping

respectively

are examined and simulated numerically. It was shown from the results of numerical calculation about the steady-state solutions of three-level cascade system that the gain of lasing without population inversion will be decreased due to driving-field phase-fluctuation. The effect can be compensated by increased driving-field intensities. However

the effect that LWI gain is decreased due to driving-field phase-fluctuation can not be always compensated by increased driving field Rabi frequency. Lasing without population inversion is still obtained even if the linewidth due to driving-field phase-fluctuation is large enough. The pre-sence of the linewidth prevents the cascade system from obtaining a high refractive index along with zero absorption. The cascade system can still exhibit a larger refractive index and zero absorption at the lesser linewidth. The linewidth tends to destroy lasing without population inversion and refractive index enhancement. There is no population inversion for the lasing transition and for the driving transition under the given condition. And the condition without population inversion has nothing to do with the variety of linewidth in the steady-state analytical solutions. That is to say

there is not possibility for the cascade system that a change from lasing with population inversion to lasing without population inversion can occur with the linewidth increasing or with the Rabi frequency of driving-field increasing. The conclusion is very different from that obtained in other inversionless lasing system.