Plasma and light: Shaping High Harmonic Generation in Time-Varying Media

High harmonic generation in solids is typically described under the assumption of a stationary medium. This assumption is rarely questioned because the electronic properties of most media evolve on timescales much slower than the harmonic emission process itself. However, in strongly driven time-varying transparent conductive oxides the plasma frequency, carrier density, and effective mass can evolve on the same femtosecond timescale as harmonic generation. Under these conditions, harmonic generation and material evolution are no longer independent processes. Within this context, we consider a two-field pumping scheme in which a strong field generates a comb of high-order harmonics across a broad spectral window, while a weaker field simultaneously reshapes its own individual spectral lines. Distinct from geometry-dependent wave-mixing processes, the evolving electron plasma reshapes multiple collinear harmonic channels simultaneously. A fully self-consistent hydrodynamic-Maxwell framework reveals that even- and odd-order harmonics naturally emerge from free- and bound-electron dynamics without the typical need to invoke phenomenological nonlinearities. Our model captures the full spectral evolution on an ultra-broad bandwidth, while experiments performed on ITO confirm the distinct behavior of bulk-driven odd harmonics and interface-driven even harmonics under strong pumping. These results establish time-dependent plasma dynamics as a powerful new tool for broadband hyperspectral shaping of multiple harmonic channels beyond the framework of four-wave-mixing processes. Our findings are of particular relevance to ultrafast science, with potential applications in ultrafast pulse manipulation and the generation and control of tailored multi harmonic waveforms.