  Artificial defects embedded in periodic structures are important foundation
for creating localized states with vast range of applications in condensed
matter physics, photonics and acoustics. In photonics, localized states are
extensively used to confine and manipulate photons. Up to now, all the proposed
localized states are reciprocal and restricted by time reversal symmetry.
Consequently, localization is bidirectional and photons at the allowed passband
in the otherwise forbidden stop band are confined irrespective of the direction
of incident beam. In this report, by embedding a single defect in a
one-dimensional spatiotemporally modulated photonic lattice, we demonstrate
that it is possible to have localization of photon only in one direction. In a
spatiotemporally modulated photonics lattice, a time dependent potential
generates an effective magnetic biasing, which breaks the reciprocity.
Moreover, in such moving lattices the dispersion relation obtains a shift
depending on the direction of effective magnetic biasing. A static defect
synthesized in a temporally modulated lattice will generate a spatial
localization of light in the bandgap. However, due to the shift of the bandgap
the localization occurs in different frequencies depending on the direction of
incident field. We envisage that this phenomenon might has impact not only in
photonics but also other areas of physics and engineering such as condensed
matter and acoustics, opens the doors for designing new types of devices such
as non-reciprocal traps, sensors, unidirectional tunable filters, and might
result in unconventional transports such as unidirectional lasing. Despite its
applications, our proposal, namely a defect sate in a driven system, can be
considered as a pedagogical example of Floquet problem with analytical
solution.
