Effects of spontaneous decay on absorptive lineshape in closely spaced transitions of an open four level system

A semi classical treatment of atom field interaction is adopted under Doppler free condition, for an open four level system with three closely spaced upper levels. The field induced polarization in closed analytical form is used in order to examine the absorption lineshape. Through the off-diagonal density matrix elements, the introduction of phase angles between the levels participating in dipole allowed / forbidden transitions are automatic. By the proper control of ground level decay and field independent coherence, we obtain inversionless gain.