  Exponential localization of wavefunctions in lattices, whether in real or
synthetic dimensions, is a fundamental wave interference phenomenon.
Localization of Bloch-type functions in space-periodic lattice, triggered by
spatial disorder, is known as Anderson localization and arrests diffusion of
classical particles in disordered potentials. In time-periodic Floquet
lattices, exponential localization in a periodically driven quantum system
similarly arrests diffusion of its classically chaotic counterpart in the
action-angle space. Here we demonstrate that nonlinear optical response allows
for clear detection of the disorder-induced phase transition between
delocalized and localized states. The optical signature of the transition is
the emergence of symmetry-forbidden even-order harmonics: these harmonics are
enabled by Anderson-type localization and arise for sufficiently strong
disorder even when the overall charge distribution in the field-free system
spatially symmetric. The ratio of even to odd harmonic intensities as a
function of disorder maps out the phase transition even when the associated
changes in the band structure are negligibly small.
