Pump-probe response, four-wave mixing and self-Kerr effect in a suspended monolayer Z-shaped graphene nanoribbon nanoresonator

We study the pump-probe optical response and the third-order self-Kerr nonlinearity of a localized exciton coupled to a suspended monolayer Z-shaped graphene nanoribbon nanoresonator, while it is strongly pumped by a near-resonant electromagnetic field. We derive the quantum Langevin equations that govern the dynamics of the electron population and after expanding the physical quantities involved in a third-order series with respect to the probe field Rabi frequency, we obtain a set of density matrix differential equations. Analytical expressions for the effective linear optical susceptibility and the four-wave mixing coefficient are derived, while the third-order optical susceptibility is calculated numerically. We investigate the modification of the characteristics of the spectra related to these effects for different values of the pump field Rabi frequency, within and outside the bistability region. In the low pump field intensity regime, we detect on the spectra two doublets of resonances with quite different widths, while, in the high pump field intensity regime, the spectral profiles come as a consequence of superimposing a doublet of sharp resonances on the corresponding optical response exhibited by an uncoupled two-level system. This work may find applications in the creation of nonlinear nanophotonic devices for ultrafast optical switching and ultra-sensitive optical sensing.

Automated summary

We study the pump-probe optical response and the third-order self-Kerr nonlinearity of a localized exciton coupled to a suspended monolayer Z-shaped graphene nanoribbon nanoresonator. The quantum Langevin equations governing the dynamics of the electron population are derived. Analytical expressions for the linear optical susceptibility and four-wave mixing coefficient are obtained, while the third-order optical susceptibility is calculated numerically. The findings demonstrate the impact of the pump field Rabi frequency on the spectral characteristics and suggest potential applications in nonlinear nanophotonic devices.