Ultrafast changes in effective permittivity of hyperbolic metamaterials and related multi-resonance-induced ultrafast process excited by femtosecond pulses

Hyperbolic metamaterials (HMMs) exhibit rich optical nonlinear responses for the epsilon-near-zero (ENZ) and anisotropy. In this study, we extract the time-dependent change in the effective permittivity of an Ag nanorod array under femtosecond pulses pumping around its ENZ wavelength. The transmittance and transient absorption spectra measured by s- and p-polarizations are used in the extraction process. We experimentally confirm the existence of an ultrafast recovery process with a relaxation time of 0.24 ps in the transient absorption spectra. The calculation based on the extracted nonlinear effective permittivity indicates that the ultrafast signal originates from the superposition of two slower recovery processes, with relaxation times of 0.74 ps and 1.19 ps, respectively. The results indicate that when the responses of two nonlinear processes have different signs and recovery speeds, their superposition may cause faster signal recovery in the combined process than in the two individual processes.