Analytical model for nonlinear response of carbon nanotubes enhanced by a plasmonic metamaterial

TL;DR

This paper develops an analytical model for the nonlinear optical response of a hybrid system combining carbon nanotubes and plasmonic metamaterials, highlighting the nonlinear enhancement due to resonant field effects.

Contribution

The paper introduces a coupled quantum-classical model for CNT-metamaterial systems, accounting for nonlinearity enhancement and inhomogeneity effects, which advances understanding of their complex dynamics.

Findings

CNT nonlinearity is significantly enhanced by metamaterial resonance.

Inhomogeneity in CNT layers affects the degree of nonlinearity enhancement.

Purcell effect is effectively equivalent to field enhancement in this system.

Abstract

We present an analytical model describing complex dynamics of a hybrid nonlinear system consisting of interacting carbon nanotubes (CNT) and a plasmonic metamaterial. Our model is based on the set of coupled equations, which incorporates well-established density matrix formalism appropriate for quantum systems (CNT are described as a two level system) and harmonic-oscillator approach ideal for modelling sub-wavelength plasmonic and optical resonators. We show that the saturation nonlinearity of CNT increases multifold in the resonantly enhanced near field of a metamaterial. In the framework of our model, we discuss the effect of inhomogeneity of the CNT layer (band gap value distribution) on the nonlinearity enhancement. It is shown, that the Purcell effect is indistinguishable from the field enhancement and is described by the same phenomenological constant.