Based on the theory of optical signal transmitting in discrete medium, the two- frequency mutual coherence function and impulse response are derived for laser pulse delay and broadening problem in sand and dust weather, respectively. The relationship of laser pulse delay and broadening to atmospheric visibility in sand and dust weather is presented. In particular, the time delay and broadening is analyzed when the laser pulse wavelength is 3.8, 7.6 and 10.6 μm. Simulation results show that when using a specific laser wavelength, the laser pulse delay and broadening will decrease in a negative exponent form with the increase of atmospheric visibility and eventually converged to a definite value. Moreover, the laser pulse delay and broadening will increase with the laser wavelength increasement under a certain atmospheric visibility.