The optical properties of a solid-state material not only often lend themselves to optical or device applications (such as in solid-state lasers), but also can serve as probes of the material’s electronic structure. Graphene is such material, whether in atomic monolayer or multilayer form. Most previous work that has used optics as a probe of the graphene electronic structure has typically involved the measurement of parameters such as optical dispersion and absorption coefficients of graphene over a wide range of optical frequencies. In this paper, which combines theoretical modeling with experimental demonstration, we report a different approach to exploring the nonlinear optical properties of graphene thin films: the generation of light at the third harmonic (TH)— times the frequency—of the input light and the use of TH generation (THG) as a probe of the electronic as well as physical structure of graphene. This approach to imaging will have certain advantages over the current imaging methods.

The TH nonlinear optical response we have investigated is closely connected to the electronic excitation of a particular momentum (the so-called M point). Our goal for this research is twofold: to characterize the physics of the TH response of graphene near its M point and to examine the potential of THG as an optical probe and imaging approach for graphene. Theoretical understanding suggests the dominance of the in-plane nonlinear optical response over the out-of-plane response. By varying the polarization of the input light and detecting the TH at various polarizations, we are able to infer experimentally this tensorial nature of the nonlinear optical response. One fundamental result of particular practical importance is the observation of in-plane isotropy of the nonlinear response in other words, the optical signal observed at any local spot of a sample does not change under sample rotation. This immediately implies that the possibility of using THG for topographical imaging of graphene should be explored. Moreover, by taking advantage of the strength of the TH signals by virtue of three-photon resonance, we have succeeded in carrying out microscopic imaging of isolated graphene crystals. The coherent nature of the THG signals has also allowed us to infer the number of atomic monolayers in a multilayer film.

We anticipate a number of practical applications grow out of our study that answer needs for graphene-based materials and device engineering. These include probing the physical structure of graphene without crystallographic orientation dependence, characterization of graphene structures grown on arbitrary substrates, and topographical imaging. We also anticipate that our study will stimulate theoretical examination, using full band-structure calculations, of the nonlinear optical response in the presence of many-body effects.