  We demonstrate universal polarization transformers based on an engineered
diffractive volume, which can synthesize a large set of arbitrarily-selected,
complex-valued polarization scattering matrices between the polarization states
at different positions within its input and output field-of-views (FOVs). This
framework comprises 2D arrays of linear polarizers with diverse angles, which
are positioned between isotropic diffractive layers, each containing tens of
thousands of diffractive features with optimizable transmission coefficients.
We demonstrate that, after its deep learning-based training, this diffractive
polarization transformer could successfully implement N_i x N_o = 10,000
different spatially-encoded polarization scattering matrices with negligible
error within a single diffractive volume, where N_i and N_o represent the
number of pixels in the input and output FOVs, respectively. We experimentally
validated this universal polarization transformation framework in the terahertz
part of the spectrum by fabricating wire-grid polarizers and integrating them
with 3D-printed diffractive layers to form a physical polarization transformer
operating at 0.75 mm wavelength. Through this set-up, we demonstrated an
all-optical polarization permutation operation of spatially-varying
polarization fields, and simultaneously implemented distinct spatially-encoded
polarization scattering matrices between the input and output FOVs of a compact
diffractive processor that axially spans 200 wavelengths. This framework opens
up new avenues for developing novel optical devices for universal polarization
control, and may find various applications in, e.g., remote sensing, medical
imaging, security, material inspection and machine vision.
