  Telescopes are now able to resolve dust polarization across circumstellar
disks at multiple wavelengths, allowing the study of the polarization spectrum.
Most disks show clear evidence of dust scattering through their unidirectional
polarization pattern typically at the shorter wavelength of $\sim 870 \mu$m.
However, certain disks show an elliptical pattern at $\sim 3$mm, which is
likely due to aligned grains. With HL Tau, its polarization pattern at $\sim
1.3$mm shows a transition between the two patterns making it the first example
to reveal such transition. We use the T-matrix method to model elongated dust
grains and properly treat scattering of aligned non-spherical grains with a
plane-parallel slab model. We demonstrate that a change in optical depth can
naturally explain the polarization transition of HL Tau. At low optical depths,
the thermal polarization dominates, while at high optical depths, dichroic
extinction effectively takes out the thermal polarization and scattering
polarization dominates. Motivated by results from the plane-parallel slab, we
develop a simple technique to disentangle thermal polarization of the aligned
grains $T_{0}$ and polarization due to scattering $S$ using the azimuthal
variation of the polarization fraction. We find that, with increasing
wavelength, the fractional polarization spectrum of the scattering component
$S$ decreases, while the thermal component $T_{0}$ increases, which is expected
since the optical depth decreases. We find several other sources similar to HL
Tau that can be explained by azimuthally aligned scattering prolate grains when
including optical depth effects. In addition, we explore how spirally aligned
grains with scattering can appear in polarization images.
