Transient phase conjunction in a two-level system

An analytical expression for conjugate signals is developed for a case where three rectangular pulses with the same center frequency are injected into a two-level system. The Maxwell's equation is solved with the slowly varying envelope approximation and with the perturbative third-order nonlinear polarization expression of a two-level system. Numerical examples are discussed in such a way that the input pulsewidth is changed relative to the energy relaxation and dephasing times. As the optical pulsewidth becomes short, ripples appear in the signal pulse due to the beat between the optical field and the resonant oscillation of the atomic system