  Gas-filled hollow core fibers allow the generation of single-cycle pulses at
megahertz repetition rates. When coupled with difference frequency generation,
they can be an ideal driver for the generation of carrier-envelope phase
stable, octave-spanning pulses in the short-wavelength infrared. In this work,
we investigate the dependence of the polarization state in gas-filled
hollow-core fibers on the subsequent difference frequency generation stage. We
show that by adjusting the input polarization state of light in geometrically
symmetric systems, such as hollow-core fibers, one can achieve precise control
over the polarization state of the output pulses. Importantly, this
manipulation preserves the temporal characteristics of the ultrashort pulses
generated, especially when operating near the single-cycle regime. We leverage
this property to boost the down-conversion efficiency of these pulses in a type
I difference frequency generation stage. Our technique overcomes the bandwidth
and dispersion constraints of the previous methods that rely on broadband
waveplates or adjustment of crystal axes relative to the laboratory frame. This
advancement is crucial for experiments demanding pure polarization states in
the eigenmodes of the laboratory frame.
