  Originally emerged within the context of string and quantum field theory, and
later fruitfully extrapolated to photonics, the algebraic transformations of
quantum-mechanical supersymmetry were conceived in the space realm. Here, we
introduce a paradigm shift, demonstrating that Maxwell's equations also possess
an underlying supersymmetry in the time domain. As a result, we obtain a simple
analytic relation between the scattering coefficients of a large variety of
time-varying optical systems and uncover a wide new class of reflectionless,
three dimensional, all-dielectric, isotropic, omnidirectional,
polarization-independent, non-complex media. Temporal supersymmetry is also
shown to arise in dispersive media supporting temporal bound states, which
allows engineering their momentum spectra and dispersive properties. These
unprecedented features define a promising design platform for free-space and
integrated photonics, enabling the creation of a number of novel reconfigurable
reflectionless devices, such as frequency-selective, polarization-independent
and omnidirectional invisible materials, compact frequency-independent phase
shifters, broadband isolators, and versatile pulse-shape transformers.
