Non-uniform wave momentum bandgap in biaxial anisotropic photonic time crystals

Photonic time crystals (PTCs) host momentum bandgaps enabling intriguing non-resonant light amplification in propagating waves, but opening substantial bandgaps demands refractive index changes too extreme for conventional nonlinear optics. Here, we introduce momentum bandgaps for non-uniform waves, including evanescent and ghost types, by extending PTCs to biaxial anisotropic photonic time crystals that periodically alternate between uniform biaxial anisotropy and isotropic media over time. We show that ghost waves, unlike evanescent waves, sustain only momentum bandgaps, opening wide bandgaps at even the smallest modulation depths. Moreover, we demonstrate momentum bandgap effects on non-uniform waves that can be amplified, or through decaying modes, selectively attenuated. We find that ghost wave momentum bandgaps uniquely boost refracted over reflected waves under one-way incidence, in stark contrast to balanced amplification seen in both propagating and evanescent waves. Our approach expands time-varying metamaterials by integrating wave characteristics, bridging the gap between conventional nonlinear optics and PTC momentum bandgaps, and shedding new light on extreme manipulation of surface polaritons.