Exceptional points, lasing, and coherent perfect absorption in Floquet scattering systems.

Periodically time-varying media, known as photonic time crystals (PTCs), provide a promising platform for observing unconventional wave phenomena. We analyze the scattering of electromagnetic waves from spatially finite PTCs using the multispectral Floquet scattering matrix, which naturally incorporates the frequency-mixing processes intrinsic to such systems. For dispersionless, real, and time-periodic permittivities, this matrix is pseudounitary. Here, we demonstrate that this property leads to multiple symmetry-breaking transitions: for increasing driving strength, scattering matrix eigenvalues lying on the unit circle (unbroken symmetry regime) meet at exceptional points (EPs), where they break up into inverse complex conjugate pairs (broken symmetry regime). We identify the symmetry operator associated with these transitions and show that, in time-symmetric systems, it corresponds to the time-reversal operator. Remarkably, at the parametric resonance condition, one eigenvalue vanishes while its partner diverges, signifying simultaneous coherent perfect absorption (CPA) and lasing. Since our approach relies solely on the Floquet scattering matrix, it is not restricted to a specific geometry but instead applies to any periodically time-varying scattering system. To illustrate this universality, we apply our method to a variety of periodically time-modulated structures, including slabs, spheres, and metasurfaces. In particular, we show that using quasi-bound states in the continuum resonances sustained by a metasurface, the CPA and lasing conditions can be attained for a minimal modulation strength of the permittivity. Our results pave the way for engineering time-modulated photonic systems with tailored scattering properties, opening new avenues for dynamic control of light in next-generation optical devices.