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

Spyridon G. Kosionis, Emmanuel Paspalakis

Published Jan 30, 2023• 3 citations
Publisher

Abstract

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.

DOI
10.1016/j.cartre.2023.100249

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In this paper, a new model is proposed for manipulating the Kerr nonlinearity of right-hand circular probe light in a monolayer of graphene nanostructure. By using the density matrix equations and quantum optical approach, the third-order susceptibility of probe light is explored numerically. It is realized that the enhanced Kerr nonlinearity with zero linear absorption can be provided by selecting the appropriate quantities of controllable parameters, such as Rabi frequency and elliptical parameter of elliptical polarized coupling field. Our results may be useful applications in future all-optical system devices in nanostructures.
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Hybrid nanocomposites can provide a promising platform for integrated optics. Optical nonlinearity can significantly widen the range of applications of such structures. In the present paper, a theoretical investigation is carried out by solving the density matrix equations derived for a metal nanoparticles-graphene nanodisks-quantum dots hybrid system interacting with weak probe and strong control fields, in the steady state. We derive analytical expressions for linear and third-order nonlinear susceptibilities of the probe field. A giant self-Kerr nonlinear index of refraction is obtained in the optical region with relatively low light intensity. The optical absorption spectrum of the system demonstrates electromagnetically induced transparency and amplification without population inversion in the linear optical response arising from the negative real part of the polarizabilities for the plasmonic components at the energy of the localized surface plasmon resonance of the graphene nanodisks induced by the probe field. We find that the self-Kerr nonlinear optical properties of the system can be controlled by the geometrical features of the system, the size of metal nanoparticles and the strength of the control field. The controllable self-Kerr nonlinearities of hybrid nanocomposites can be employed in many interesting applications of modern integrated optics devices allowing for high nonlinearity with relatively low light intensity.
We study theoretically the time evolution of nonlinear optical phenomena of a probe electromagnetic field pulse in intersubband transitions of a semiconductor quantum well structure under the influence of a pump electromagnetic field. More specifically, we take into consideration the effects of electron-electron interactions and consider the interaction of a two-subband system with rectangular electromagnetic fields. The spectral form of the linear absorption, dispersion, and nonlinear optical Kerr effect is described, from the time that the external field is applied up until the dynamics of the system has reached a steady state. In order to describe the dynamics of the system, the effective nonlinear Bloch equations are used, in which renormalized terms for the transition energy and the applied field have been added, due to the effects of electron-electron interactions. These equations are properly combined, and the differential equations of the density matrix elements for the several optical phenomena up to third order are derived. These are solved numerically in the whole time range up to the steady state for a GaAs/AlGaAs quantum well structure. We show that the form of the several optical spectra studied here has a significantly altered evolution over time, according to the value of the frequency of the pump field and of electron sheet density. Even in the case in which the spectral form in the steady state case is almost identical for two different sets of parameters, their evolution can be quite different, according to the precise value of these parameters.
A microscopic semi-classical theory for the self-consistent calculation of the nonlinear response field is applied to the exciton–microcavity coupled systems. Our results show that the respective spectral features of the degenerated four wave mixing (DFWM) signal in both the weak (Ω ≤ Γ) and the strong coupling (Ω ≫ Γ) regimes, where Ω is the Rabi splitting and Γ is the width of the modes, can be clearly described with a single framework. In the weak coupling regime, the nonlinear signal is strongest at the bare excitonic resonance, and its enhancement due to cavity effect is remarkable. In the strong coupling regime, our framework very well reproduces the polarization dependent DFWM spectra in a recent experiment.
We investigate theoretically the optical response of a zinc-phthalocyanine molecular quantum system near a gold spherical nanoparticle with a radius of 80 nm. The quantum system is irradiated by a strong pump and a weak probe coherent electromagnetic field. Using the density matrix methodology, we obtain analytical expressions for the absorption, dispersion, and the four-wave-mixing coefficients. The influence of the nanoparticle on the spontaneous decay rate of the quantum system, as well as on the external fields, are obtained by an electromagnetic Green's tensor method. The spectroscopic parameters of the molecule are also obtained by ab initio methods. For the studied optical spectra, we find that, below a critical distance between the molecule and the plasmonic nanoparticle, determined by the minimal value of the effective Rabi frequency, single-peaked spectra are observed. Above this critical distance, the spectra exhibit the characteristic Mollow-shaped profiles. The enhancement of the pump field detuning induces the shift of the sideband resonances away from the origin. Lastly, and most importantly, regardless of the value of the detuning, the optical response of the system is maximized for an intermediate value of the interparticle distance.