  Dilatons ($\phi(x)$) are a class of bosonic scalar particles associated with
scaling symmetry and its compensation (under the violations of the same). Due
to two photon coupling, they can produce optical signatures in a magnetic
field. In vacuum or plain matter they couple to one of the transversely
polarized state of the photon. But in a magnetized matter, they couple to both
the transversely polarized state of photon (due to emergence of a parity
violating part of photon self energy contribution from a magnetized matter). A
part of this work is directed towards understanding the issue of mixing of
scalar with various polarizations states of photon in a medium ( magnetized or
unmagnetized ) due to the constraints from different discrete (CPT) symmetries
associated with the interaction. Based on these symmetry aided arguments, the
structure of the mixing matrix is found to be $3 \times 3$. Thus there exists
non-zero finite probabilities of oscillation between different polarization
states of photon to dilaton. Our analytical and numerical analysis show no
existence of periodic oscillation length either in temporal or spatial
direction for most general values of the parameters in the theory. Possible
astrophysical consequences of these results, those can be detected through
observations are discussed.
