  By analyzing the optical tomogram of a linear superposition of coherent
states, we show that distinctive signatures of the macroscopic superposition
states are displayed directly in the optical tomograms of the states. We also
study the effect of decoherence on the optical tomograms of the macroscopic
superposition states. Since the wave packet fractional revivals are associated
with the generation of macroscopic superposition states, these signatures help
in visualizing the revivals and fractional revivals occurring in a nonlinear
medium directly in the optical tomogram of the time-evolved state. We found
that the optical tomogram of the time-evolved state at the instants of
fractional revivals show structures with sinusoidal strands. Using a class of
initial superposed wave packets evolving in the Kerr-like medium, we further
show that the condition for the occurrence of fractional revival phenomenon
depends on the number of wave packets composing the initial superposition
state. In the case of a two-mode electromagnetic field, we investigate the
entanglement of the state directly using the optical tomogram. We have shown
that the signatures of entanglement can be observed directly in the single-mode
optical tomogram of the state without reconstructing the density matrix of the
system. We also analyze the effect of decoherence on the optical tomograms of
the entangled states. Further, we examine the optical tomograms of the
entangled states generated using a beam splitter with a Kerr medium placed into
one of its input modes. We have found the signatures of entanglement in the
optical tomogram for the entangled states generated at the instants of two- and
three-subpacket fractional revival times.
