Floquet modeling of surface-wave amplification in two-dimensional photonic time crystals

Photonic time crystals (PTCs) are spatially homogeneous materials with a dielectric parameter that is modulated periodically in time, paving a new way in electromagnetic wave manipulation and field enhancement. Modeling of time-varying media requires the involvement of a dispersion effect, which is widely present in materials capable of dynamic modulation. Surface waves are another important phenomenon in strongly dispersive systems, appearing at the material interface. Their intrinsic characteristics of subwavelength resolution and local-field enhancement are desirable in constructing PTCs in finite-size structures. In this work, by introducing a nonlocal dispersive PTC-air interface model, we analyze the dispersion relationship of the time-modulated bulk plasma and the surface-wave amplification at the PTC-air interface. It is found that a momentum gap appears under slight modulation, which is due to the low group velocity of surface-plasmon polaritons (SPPs) at the interface. In addition, we also consider the magnetic bias as a degree of freedom in the model, which allows for shifting frequency corresponding to the momentum gap. Finally, we investigate the spatiotemporal evolution of the surface wave at the PTC-air interface excited by a point source and observe a narrow-wave-vector amplification in the momentum gap. The research on the surface wave of the PTC-air interface model not only enables systematic investigation of tunable nonresonant wave amplification in the subwavelength structure, but also offers a platform for studying plenty of novel electromagnetic phenomena in time-varying and spatially finite systems.