  We consider the polarization properties of photospheric emission originating
in jets consisting of a highly relativistic core of opening angle theta_j and
Lorentz factor Gamma_0, and a surrounding shear layer where the Lorentz factor
is decreasing as a power law of index p with angle from the jet axis. We find
significant degrees of linear polarization for observers located at viewing
angles theta_v \gtrsim theta_j. In particular, the polarization degree of
emission from narrow jets (theta_j \approx 1/Gamma_0) with steep Lorentz factor
gradients (p \gtrsim 4) reaches \sim 40%. The angle of polarization may shift
by pi/2 for time-variable jets. The spectrum below the thermal peak of the
polarized emission appears non-thermal due to aberration of light, without the
need for additional radiative processes or energy dissipation. Furthermore,
above the thermal peak a power law of photons forms due to Comptonization of
photons that repeatedly scatter between regions of different Lorentz factor
before escaping. We show that polarization degrees of a few tens of percent and
broken power law spectra are natural in the context of photospheric emission
from structured jets. Applying the model to gamma-ray bursts, we discuss
expected correlations between the spectral shape and the polarization degree of
the prompt emission.
