  A density matrix based analytical model is developed to study the coherent
probe field propagation through a four-level V type system in presence of a
coherent control field. The model allows coupling of the probe field from the
upper ground level to both of the excited levels keeping the control field
locked to a particular transition. The addition of an extra ground level to a
conventional three-level V type system creates extra decay paths to the ground
levels for the upper level population. A set of sixteen density matrix based
equations are formed and then solved analytically under rotating wave
approximation to study the probe response under steady state condition. The
simulated probe absorption spectra shows absorption dip at the centre of a
transparency window only under Doppler broadened condition although the
conventional EIT window appears under Doppler free condition. The dependence of
the field induced absorption signal on the Rabi frequency of the control field,
population transfer rate among the ground levels and temperature of the vapour
medium has been studied in details.
