Nonlinear optics in carbon nanotube, graphene, and related 2D materials

One- and two-dimensional forms of carbon, carbon nanotube, and graphene, and related 2D materials, have attracted great attention of researchers in many fields for their interesting and useful electrical, optical, chemical, and mechanical properties. In this tutorial, we will introduce the basic physics and the linear optical properties of these 1D/2D materials. We then focus on their nonlinear optical properties, saturable absorption, electro-optic effect, and nonlinear Kerr effect. We will also review and discuss a few key applications using the ultrafast nonlinear phenomena possessed by these 1D/2D materials: (1) short-pulse fiber lasers using saturable absorption, (2) electro-optic modulators, and (3) all-optical signal processing devices.