  The control of polarization, an essential property of light, is of wide
scientific and technological interest. The general problem of generating
arbitrary time-varying states of polarization (SOP) has always been
mathematically formulated by a series of linear transformations, i.e. a product
of matrices, imposing a serial architecture. Here we show a parallel
architecture described by a sum of matrices. The theory is experimentally
demonstrated by modulating spatially-separated polarization components of a
laser using a digital micromirror device that are subsequently beam combined.
This method greatly expands the parameter space for engineering devices that
control polarization. Consequently, performance characteristics, such as speed,
stability, and spectral range, are entirely dictated by the technologies of
optical intensity modulation, including absorption, reflection, emission, and
scattering. This opens up important prospects for polarization state generation
(PSG) with unique performance characteristics and applications in spectroscopic
ellipsometry, spectropolarimetry, communications, imaging, and security.
