Excitation Dependent Saturation Intensity in Ultrathin Epsilon-Near-Zero Films

Studies in epsilon near zero (ENZ) thin films have shown extreme nonlinear light-matter interactions leading to giant ultrafast nonlinearities. This corresponds to the excitation of ENZ modes and the associated electric field intensity enhancement (FIE) inside the material. Recent progress in the field mainly focuses on ENZ nonlinearity caused by electron absorption within the conduction band only, thus lacking an understanding of optical transition absorption near the ENZ regime. Therefore, an in-depth study of the nonlinearity, especially the nonlinear absorption behavior of the ENZ materials in the presence of optical transition, is crucial. With three-photon absorption, the intensity-dependent absorption coefficient can be written as: α = α_ns + α₀/ (1 + I/I_sat) + γI², where the 1^st and the 2^nd term are related to the saturable absorption caused by conduction band free electrons, and the 3^rd term is related to the 3-photon absorption. α = total absorption coefficient, γ = 3-photon absorption coefficient, α_ns = nonsaturable absorption, α₀= linear absorption coefficient, and I_sat= saturation intensity is defined as the intensity when nonlinear absorption becomes α₀/2.<br/>In this work, we demonstrated that at ENZ wavelength (1190 nm for a 300 nm thick ITO sample), where 3-photon absorption is absent, saturable absorption decreases as intensity and angle of incident of light increase. These are because of the increased absorption and enhancement field intensity caused by ENZ mode excitation at a larger angle of incidence. We also observed that near the ENZ regime (1090nm), where 3-photon absorption is possible, saturable and 3-photon absorption compete with each other. In contrast to the saturable absorption, 3-photon absorption increases with increasing intensity but decreases at larger angles of incidence. The decrease of 3-photon absorption at a large incident angle can result from increased absorption by the free electrons in the conduction band. Since ENZ mode excitation causes the free electrons to absorb more photons at larger incident angles, there are fewer photons available to contribute to multiple-photon absorption. These competing nonlinear absorption mechanisms can provide a new and significant optical-nonlinearity tuning mechanism to implement in optics/optomechanical devices (i.e., ultrafast all-optical switches/modulators).