Polarization- and Frequency-Selective Light Amplification in Magneto-Optic Photonic Time Crystals.

Light amplification in photonic time crystals (PTCs), enabled by their momentum bandgap, is a well-established phenomenon. However, prior research has predominantly focused on achieving a substantial gap, whereas the controlled manipulation of light properties remains largely unexplored. Here, we exploit spatially finite magneto-optic photonic time crystals (MO-PTCs) to achieve polarization- and frequency-selective light amplification. By magnetizing the MO-PTC, we dynamically tune the effective permittivity of extraordinary light (e-light), thereby controlling its amplification threshold. Applying periodic modulation to the diagonal elements of the dielectric tensor enables selective amplification of either ordinary light (o-light) or extraordinary light, depending on which has the lower threshold. Furthermore, modulating the off-diagonal elements induces an effective modulation comprising both the fundamental frequency and its second harmonic in the extraordinary light. Adjusting the extraordinary light's permittivity allows preferential amplification of either the fundamental or second-harmonic component based on their respective thresholds. This work advances the understanding of spatially finite PTCs and introduces a novel approach to light manipulation in time-varying media.