Parametric Amplification of Optical Pulses through Synthetic Motion in a Time-Varying Medium

Parametric amplification of optical waves conventionally requires phase matching and frequency offsets between interacting beams. Here, we demonstrate a fundamentally different amplification mechanism in epsilon-near-zero (ENZ) materials, where intense optical pumping creates a time-varying medium. We show, both theoretically and experimentally, that large spatiotemporal index modulations enable parametric amplification of frequency-degenerate pulses without requiring chirp or frequency offsets. The gain scales quadratically rather than linearly with the product of the pump intensity and the nonlinear refractive index coefficient n₂I, transitioning from conventional two-beam coupling to a regime dominated by time refraction. In a subwavelength-thick indium tin oxide film, we demonstrate significant probe amplification that overcomes the material's strong absorption. Our findings reveal that strong optical nonlinearities enable qualitatively new parametric processes, opening pathways for ultrashort-pulse amplification via dynamic metasurfaces and optical nanoswitches that exploit large gain modulation.