Abstract: A model for an open four-level atomic system driven by two fields is presented. Density matrix equations of motion are obtained by electric dipole and rotating wave approximations. Physical mechanism of lasing without inversion (LWI) is discussed. Effects of detuning on gain without inversion and population difference are studied. Dispersion equals to zero as two driving and probe fields are resonant. As one driving field (probe field) is resonant, the gain and the population difference versus detuning of driving field (probe field)show even symmetry, and the dispersion shows central symmetry. As two or three of driving and probe fields are off-resonance, the symmetries disappear. LWI gain is obtained when the dispersion equals to zero. When beth driving and probe fields are off-resonance, the gain, the dispersion and the population difference change greatly. High dispersion without absorption is obtained by adjusting suitable parameters of the system.

Key words: lasing without inversion (LWI), four-level system, detuning, gain, population difference