Negative Optical Phase Accumulation in Ultrathin Conductive Films

We report on the first direct observation of negative optical-phase accumulation in an ultrathin carbon-nanotube (CNT) film and show that it leads to an apparent superluminal advance of a picosecond electric field pulse. The time traces measured with a terahertz time-domain spectrometer, reproduced quantitatively with a single-parameter Drude model, reveal that the pulse peak emerges 40 fs earlier than through an empty aperture, confirming the validity of the model for ultrafast propagation in conductors. As the observed effect depends solely on the ratio of the carrier-momentum relaxation rate to the radiation frequency, any conductive layer with comparable scattering dynamics should exhibit the same negative phase shift, due to negative group velocity without violating causality. The phase shift spans a broad spectral range and is actively tunable: illuminating the film with a 500 mW laser reduces its magnitude by a few decibels, providing an optical control knob. These findings establish negative phase engineering in nanoscale conductors as a versatile route to ultra-high-speed phase and intensity modulators for next-generation photonic and optoelectronic systems.