Band structures of lossy photonic time crystals

Photonic time crystals (PTCs) are characterized by temporally periodic modulation of electromagnetic parameters while maintaining spatial homogeneity, which have unique momentum bandgaps distinct from conventional energy bandgaps in photonic crystals. Within the non-Hermitian framework, the momentum bandgap boundaries can be regarded as exceptional points. In this letter, we study the band properties of the lossy PTCs by introducing the loss mechanisms to the systems. We find the loss eliminates the exceptional points (EPs) and induces the splitting of the imaginary parts in the complex frequency spectra. The temporal modulation provides an effective degree of freedom for manipulating the band characteristics in binary PTCs. Furthermore, we study the band properties of the truncated continuous PTCs, and find the loss enables the emergence of the energy bandgaps. This work established a theoretical framework for band engineering in open PTCs systems and offers fundamental insights for emerging applications.