Gate tunable third-order nonlinear optical response of massless Dirac fermions in graphene (1710.04758v1)

Abstract: Materials with massless Dirac fermions can possess exceptionally strong and widely tunable optical nonlinearities. Experiments on graphene monolayer have indeed found very large third-order nonlinear responses, but the reported variation of the nonlinear optical coefficient by orders of magnitude is not yet understood. A large part of the difficulty is the lack of information on how doping or chemical potential affects the different nonlinear optical processes. Here we report the first experimental study, in corroboration with theory, on third harmonic generation (THG) and four-wave mixing (FWM) in graphene that has its chemical potential tuned by ion-gel gating. THG was seen to have enhanced by ~30 times when pristine graphene was heavily doped, while difference-frequency FWM appeared just the opposite. The latter was found to have a strong divergence toward degenerate FWM in undoped graphene, leading to a giant third-order nonlinearity. These truly amazing characteristics of graphene come from the possibility to gate-control the chemical potential, which selectively switches on and off one- and multi-photon resonant transitions that coherently contribute to the optical nonlinearity, and therefore can be utilized to develop graphene-based nonlinear optoelectronic devices.

• The paper demonstrates that ion-gel gating enables up to a 30-fold enhancement in graphene's third-harmonic generation, revealing strong tunability of its nonlinear optical response.
• The experiments highlight a marked contrast in nonlinear responses between third-harmonic generation and four-wave mixing, with doping significantly altering the optical coefficients.
• The use of ion-gel gating to modulate chemical potential facilitates selective activation of multi-photon resonances, paving the way for advanced graphene-based optoelectronic devices.

Analysis of the Third-Order Nonlinear Optical Response in Graphene

The paper "Gate tunable third-order nonlinear optical response of massless Dirac fermions in graphene" presents an extensive paper on the third-order nonlinear optical responses of graphene using a novel ion-gel gating technique. The researchers primarily investigated the phenomena of third harmonic generation (THG) and four-wave mixing (FWM) in graphene, while modulating its chemical potential. The results elucidated significant enhancements and tunability of nonlinear optical responses, offering potential advancements in optoelectronic applications.

This research notably addresses the variation of third-order nonlinear optical responses in graphene. Previous reports demonstrated nonlinear optical coefficients differing by several orders of magnitude, underscoring an unresolved issue in the optical properties' variability based on chemical potential tuning. Graphene, a material characterized by massless Dirac fermions and exhibiting a linear, gapless two-dimensional band structure, serves as an excellent medium with significant nonlinear optical responses. Despite its strong linear response, detailed information about third-order nonlinear processes, particularly influenced by chemical potential, remained sparse.

Key Experimental Findings

1. Third Harmonic Generation (THG): Through ion-gel gating, the researchers demonstrated that THG in heavily doped graphene could be enhanced nearly 30-fold compared to undoped graphene. This enhancement is pivotal for potential applications, as it indicates remarkable control over the nonlinear optical response by adjusting the chemical potential.
2. Four-Wave Mixing (FWM): Contrarily, the experiments showed that difference-frequency FWM (DFM) exhibited a divergent nonlinearity in undoped graphene, presenting a scenario where the nonlinear response vastly differs from that in doped conditions. The selective switching on and off of resonant transitions plays a crucial role in these observations, validating the theoretical predictions.
3. Gate Tuning of Chemical Potential: The experiment utilized an ion-gel gating technique, which allowed a substantial shift of chemical potential, facilitating selective activation of one-, two-, and three-photon resonances. Such a technique empowers the control of carrier density and optical properties without compromising material structure integrity.

Theoretical Insights

The theoretical framework was based on the work by Cheng et al., capturing the resonant terms and the alterations of nonlinear susceptibilities in response to changes in the chemical potential. The research affirmed that the third-order nonlinear susceptibility, predominantly influenced by interband transitions, exhibited distinct responses as resonances switched off. This mechanism was mathematically interpreted via specific frequency combinations and photon resonance transitions that contribute to the venturing nonlinearity.

Practical and Theoretical Implications

The implications of this research are multifaceted:

• Photonic Devices: The ability to finely tune optical properties suggests the development of advanced graphene-based optoelectronic devices. Devices capable of handling large ranges of chemical potential modulation could potentially integrate into adaptive and flexible photonic systems, furthering advancements in communication technologies.
• Material Science Approaches: The findings elevate the significance of studying massless Dirac fermions in materials such as topological insulators and Weyl semimetals, where similar nonlinear phenomena might further elucidate electronic interactions in high-symmetry lattice structures.
• Unified Nonlinear Optical Theory: The outcomes contribute towards a comprehensive model of graphene's nonlinear optical response, aiding in predictive capabilities for future research, and enhancing the design frameworks of nonlinear optical systems.

Prospective Research Directions

Future investigations could move towards the deeper exploration of frequency tunability and scaling to other third-order processes, as well as extended studies on high-order harmonics generation in related materials. Bridging experimental data with refined theoretical models will likely remain a focal point for achieving consensus on the governing dynamics across varying conditions in Dirac materials. Additionally, exploring the integration of graphene with heterogeneous materials might reveal synergies for novel hybrid devices harnessing unprecedented optical properties.

In conclusion, this paper provides substantial contributions to the understanding and exploitation of graphene's third-order nonlinear optical properties, illustrating how ion-gel gating significantly modifies these responses. The encapsulated theoretical and experimental findings lay foundational work for further explorations into the fascinating optical characteristics of graphene and similar materials.