Amplified transmission in full-<i>k</i> space empowered by photonic temporal quasicrystal

Photonic time crystals can induce amplified radiation associated through momentum-gap modes, leading to various optical applications. However, the size of momentum is finite because of the finite relative change of the refraction index, while the amplification of the gaps is needed in the entire momentum space. Here, we introduce the concept of the photonic temporal Fibonacci quasicrystal. We impose periodic boundary conditions on a series of temporal Fibonacci sequences constructed using the recursive method as the approximation of the quasicrystal. We show that the momentum gap could cover almost full momentum space in the quasicrystal limit, leading to the amplified transmission of light in almost the full-<i>k</i> space. The different gaps of the same sequence show different abilities in amplifying transmission. Our work extends the functionalities of temporal media, offering a new way of controlling the light.