Experimental Characterization of the Ultrafast, Tunable and Broadband Optical Kerr Nonlinearity in Graphene

Abstract

Graphene’s giant nonlinear optical response along with its integrability has made it a vaunted material for on-chip photonics. Despite a multitude of studies confirming its strong nonlinearity, there is a lack of reports examining the fundamental processes that govern the response. Addressing this gap in knowledge we analyse the role of experimental parameters by systematically measuring the near-infrared spectral dependence, the sub-picosecond temporal evolution and pulse-width dependence of the effective Kerr coefficient ( n 2 , eff ) of graphene in hundreds of femtosecond regime. The spectral dependence measured using the Z-scan technique is corroborated by a density matrix quantum theory formulation to extract a n 2 , eff ∝ λ 2 dependence. The temporal evolution obtained using the time-resolved Z-scan measurement shows the nonlinearity peaking at zero delay time and relaxing on a time-scale of carrier relaxation. The dependence of the n 2 , eff on pulse duration is obtained by expanding the input pulse using a prism-pair set-up. Our results provide an avenue for controllable tunability of the nonlinear response in graphene, which is limited in silicon photonics.

Predicting Graphene's Nonlinear‐Optical Refractive Response for Propagating Pulses

“…Equation () also recovers the scaling of n 2, gr with pulse duration in the sub‐ps excitation regime as experimentally observed in refs. [8, 9]. Furthermore, as discussed in the Supporting Information, according to our theory, the nonlinear response is mainly introduced by the dynamical behavior of the temperature rather than chemical potential and its switching in sign is mainly produced by changes in the interband contribution.…”

“…The research results reported since then seem to point in different directions, and have made it a major challenge to fully understand graphene's nonlinear‐optical behavior. The experimental data include both positive‐ [ 4,9 ] and negative‐valued [ 6–8,12 ] effective nonlinearities with a magnitude compatible with that of Hendry's experiments, [ 3 ] as well as much smaller nonlinearities. [ 10 ] From the theory point of view, calculations for the perturbative nonlinearity [ 1,2 ] give rise to nonlinearities that are two orders of magnitude smaller than measured in the aforementioned experiments.…”

“…It should be noted that the quantity often measured in nonlinear experiments is the temporal average of the refractive index change where represents the instantaneous light intensity, and subsequently, the nonlinear index defined via . Modeling graphene as a thin layer of 3D material as done in many experiments, [ 3–5,7–10 ] we derive the following expression to determine the magnitude and sign of graphene's n 2 (see Supporting Information): where denotes the fine‐structure constant, nm is the effective graphene thickness, n sat is the saturation value of n , and T FWHM indicates the full‐width‐at‐half‐maximum of the pulse du...…”

“…Over the past decade there has been a rapidly growing interest in the theoretical [ 1,2 ] and experimental [ 3–13 ] investigation of nonlinear‐optical refraction in graphene using free‐space and waveguided excitation configurations. This new research field was pioneered by the experiments of Hendry et al.…”

Fast Gating for Raman Spectroscopy

“…We should also mention systems based on commercial fs lasers [ 22 , 33 , 34 , 35 ] allowing one to achieve time resolution of ≈100 fs, but with limitations due to the spectral broadening (i.e., spectral resolution is too low for Raman detection) and experimental setups designed for ultrafast, or more generally, pump-probe, spectroscopy [ 36 , 37 ]. The latter represent valuable possibilities to be considered, but they involve high costs and complex optical setups.…”