  The nematic twist-bend ($\mathrm{N_{TB}}$) phase, exhibited by certain
thermotropic liquid crystalline (LC) dimers, represents a new orientationally
ordered mesophase -- the first distinct nematic variant discovered in many
years. The $\mathrm{N_{TB}}$ phase is distinguished by a heliconical winding of
the average molecular long axis (director) with a remarkably short (nanoscale)
pitch and, in systems of achiral dimers, with an equal probability to form
right- and left-handed domains. The $\mathrm{N_{TB}}$ structure thus provides
another fascinating example of spontaneous chiral symmetry breaking in nature.
The order parameter driving the formation of the heliconical state has been
theoretically conjectured to be a polarization field, deriving from the bent
conformation of the dimers, that rotates helically with the same nanoscale
pitch as the director field. It therefore presents a significant challenge for
experimental detection. Here we report a second harmonic light scattering
(SHLS) study on two achiral, $\mathrm{N_{TB}}$-forming LCs, which is sensitive
to the polarization field due to micron-scale distortion of the helical
structure associated with naturally-occurring textural defects. These defects
are parabolic focal conics of smectic-like "pseudo-layers", defined by planes
of equivalent phase in a coarse-grained description of the $\mathrm{N_{TB}}$
state. Our SHLS data are explained by a coarse-grained free energy density that
combines a Landau-deGennes expansion of the polarization field, the elastic
energy of a nematic, and a linear coupling between the two.
