ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology , Castelldefels, 08860 Barcelona, Spain.
ICREA-Institució Catalana de Recerca i Estudis Avançats , Passeig Lluís Companys 23, 08010 Barcelona, Spain.
ACS Nano. 2016 Feb 23;10(2):1995-2003. doi: 10.1021/acsnano.5b06110. Epub 2016 Jan 19.
The ability of graphene to support long-lived, electrically tunable plasmons that interact strongly with light, combined with its highly nonlinear optical response, has generated great expectations for application of the atomically thin material to nanophotonic devices. These expectations are mainly reinforced by classical analyses performed using the response derived from extended graphene, neglecting finite-size and nonlocal effects that become important when the carbon layer is structured on the nanometer scale in actual device designs. Here we show that finite-size effects produce large contributions that increase the nonlinear response of nanostructured graphene to significantly higher levels than those predicted by classical theories. We base our analysis on a quantum-mechanical description of graphene using tight-binding electronic states combined with the random-phase approximation. While classical and quantum descriptions agree well for the linear response when either the plasmon energy is below the Fermi energy or the size of the structure exceeds a few tens of nanometers, this is not always the case for the nonlinear response, and in particular, third-order Kerr-type nonlinearities are generally underestimated by the classical theory. Our results reveal the complex quantum nature of the optical response in nanostructured graphene, while further supporting the exceptional potential of this material for nonlinear nanophotonic devices.
石墨烯具有支持长寿命、电可调等离子体的能力，这些等离子体与光强烈相互作用，加上其高度非线性的光学响应，为将这种原子级薄材料应用于纳米光子器件产生了巨大的期望。这些期望主要通过使用扩展石墨烯得出的响应进行经典分析得到加强，而忽略了有限尺寸和非局域效应，这些效应在实际器件设计中当碳层在纳米尺度上结构化时变得很重要。在这里，我们表明，有限尺寸效应会产生很大的贡献，从而使纳米结构石墨烯的非线性响应显著提高，远远超过经典理论的预测。我们的分析基于使用紧束缚电子态结合随机相位近似的石墨烯的量子力学描述。虽然在线性响应方面，无论是等离子体能量低于费米能还是结构尺寸超过几十纳米，经典和量子描述都非常吻合，但对于非线性响应情况并非总是如此，特别是三阶克尔型非线性通常被经典理论低估。我们的结果揭示了纳米结构石墨烯中光学响应的复杂量子性质，同时进一步支持了这种材料在非线性纳米光子器件中的特殊潜力。
