  The temporal degree of freedom in photonics has been a recent research
hotspot due to its analogy with spatial axes, causality, and open-system
characteristics. In particular, the temporal analogues of photonic crystals
have stimulated the design of momentum gaps and their extension to topological
and non-Hermitian photonics. Although recent studies have also revealed the
effect of broken discrete time-translational symmetry in view of the temporal
analogy of spatial Anderson localization, the broad intermediate regime between
time order and time uncorrelated disorder has not been examined. Here we
investigate the inverse design of photonic time disorder to achieve optical
functionalities in spatially homogeneous platforms. By developing the structure
factor and order metric using causal Green's functions for the domain of time
disorder, we demonstrate engineered time scatterer, which provides
unidirectional scattering with controlled scattering amplitudes. We also reveal
that the order-to-disorder transition in the time domain allows for the
manipulation of scattering bandwidths, which inspires resonance-free temporal
colour filtering. Our work will pave the way for advancing optical
functionalities without spatial patterning.
