  Although Gamma Ray Bursts (GRBs) have been detected for many decades, the
lack of knowledge regarding the radiation mechanism that produces the energetic
flash of radiation, or prompt emission, from these events has prevented the
full use of GRBs as probes of high energy astrophysical processes. While there
are multiple models that attempt to describe the prompt emission, each model
can be tuned to account for observed GRB characteristics in the gamma and X-ray
energy bands. One energy range that has not been fully explored for the purpose
of prompt emission model comparison is that of the optical band, especially
with regards to polarization. Here, we use an improved MCRaT code to calculate
the expected photospheric optical and gamma-ray polarization signatures
($\Pi_\mathrm{opt}$ and $\Pi_\gamma$, respectively) from a set of two
relativistic hydrodynamic long GRB simulations, which emulate a constant and
variable jet. We find that time resolved $\Pi_\mathrm{opt}$ can be large ($\sim
75\%$) while time-integrated $\Pi_\mathrm{opt}$ can be smaller due to
integration over the asymmetries in the GRB jet where optical photons
originate; $\Pi_\gamma$ follows a similar evolution as $\Pi_\mathrm{opt}$ with
smaller polarization degrees. We also show that $\Pi_\mathrm{opt}$ and
$\Pi_\gamma$ agree well with observations in each energy range. Additionally,
we make predictions for the expected polarization of GRBs based on their
location within the Yonetoku relationship. While improvements can be made to
our analyses and predictions, they exhibit the insight that global radiative
transfer simulations of GRB jets can provide with respect to current and future
observations.
