Electrically tuned nonlinearity

The demonstration of broadband, electrically tunable third-order nonlinear optical responses in graphene is promising for a host of nonlinear optical applications.

Nonlinear optics is the branch of photonics dedicated to the nonlinear interaction between light and matter, more specifically when the induced dielectric polarization in a material responds nonlinearly to the electric field of light. In 1961, almost one year after the invention of the first laser, Peter Franken and co-workers observed the nonlinear effect of second-harmonic generation (SHG) for the first time with a pulsed ruby laser, where two photons with the same frequency are converted into a new photon having twice the frequency of the incident photons1. This demonstration marked the birth of nonlinear optics. Currently, various devices enabled by nonlinear optics are extensively used throughout our daily lives2,3: for example, ultrafast lasers for micromachining and microsurgery; various forms of nonlinear optical spectroscopies for medical diagnostics, biosensing and imaging; and systems for optical telecommunications and security.

Now, writing in Nature Photonics, Shiwei Wu and co-workers report that a nonlinear optical process called third-harmonic generation (THG) can be widely tuned in graphene using an electric gate voltage4. Electrically tunable SHG has already been reported in other 2D materials, namely, monolayer WSe2 (a well-studied semiconductor in the family of 2D transition metal dichalcogenides) with excitons, but the spectral bandwidth was limited5.

Graphene, a monolayer of carbon atoms packed into a 2D honeycomb lattice, exhibits a strong ultra-wideband light–matter interaction, which has been utilized for a broad range of photonic and optoelectronic devices including photon sources, modulators and photodetectors6. For nonlinear optics, second-order optical nonlinearity in graphene is forbidden due to inversion symmetry, but third-order optical nonlinearity in graphene is extremely large7. The doping-dependent third-order nonlinear optical responses in graphene have been previously reported7,8. For example, saturable absorption, where the material absorption reduces at high incident light intensity, is a widely used third-order nonlinear optical response for ultrafast pulse generation. It has been shown that saturable absorption in graphene is doping dependent and electrically tunable for high-performance ultrafast lasers7,8.

The latest results from Wu and co-workers originate from the ability to adjust the chemical potential (Ef) of graphene to selectively switch on or off single-photon and multiphoton resonant transitions (Fig. 1). A maximum tuning strength of up to ~30 times is achieved with a change of ~0.74 eV in chemical potential at an excitation wavelength of 1,566 nm. Similar results have also been demonstrated in ref. 9, indicating that gated (or doped) graphene is more suitable than chemically pristine graphene samples for THG applications if no wavelength tuning is needed. The benefits are enhanced third-order nonlinear optical susceptibility |χ(3)| and reduced linear optical absorption that is necessary for devices with a low insertion loss.

Fig. 1: Multiphoton resonance effects in graphene.

The increase of |Ef| can successively switch off one-photon (|Ef| > 1/2ħω0), two-photon (|Ef| > ħω0) and three-photon (|Ef| > 3/2ħω0) interband transitions by Pauli blocking. Note that two-photon interband transitions contribute to χ(3) positively and one- and three-photon interband transitions contribute to χ(3) negatively4. The red arrows indicate the input photons at ω0 frequency and the blue arrows indicate the generated third-harmonic photons at 3ω0 frequency. ħ, reduced Planck constant.

Wu and colleagues also demonstrate electrical manipulation of various four-wave mixing (FWM) processes, a third-order nonlinear optical process where two or three photons are mixed to generate one or two photons at new frequencies. The team found that difference-frequency FWM behaves differently from THG and sum-frequency FWM due to phase differences of one-photon or multiphoton resonant transitions. Note that such gate-tunable nonlinear optical responses with multiphoton resonance selection should exist for other nonlinear optical processes with graphene, such as high-order harmonic generation.

The reported operation bandwidth of gate-tunable THG is from ~1,300 nm to 1,650 nm, covering the most common spectral range for optical fibre telecommunications at 1,550 nm. Such a broad operation bandwidth comes from the linear energy dispersion of the graphene Dirac fermions (Fig. 1). This is fundamentally different from the previous demonstration of the electrically tunable SHG with excitons in monolayer WSe2, which has a limited operation bandwidth (around few tens of millielectronvolts at low operating temperature) because of the narrow band of the exciton transition energy5. In theory, broader bandwidth operation of gate-tunable nonlinear optics in Dirac materials should be possible because a longer operation wavelength (for example the mid-infrared spectral region) is naturally covered with smaller doping, while a shorter operation wavelength (for example the visible spectral region) is feasible with higher doping. Other interesting Dirac materials such as topological insulators and Weyl semimetals that have been studied less with nonlinear optics are also worth further investigation for basic science and potential applications. Nevertheless, the broadband gate-tunable optical nonlinearities in graphene offer a new approach to build electrically tunable nonlinear optical devices.

In the past decade, studies of nonlinear optics with 2D materials (including graphene and other 2D layered materials) and their mixed-dimensional heterostructures have witnessed significant progress. However, there is a huge variation in their measured nonlinear optical responses, with results from the same material differing by a few orders of magnitude: in the case of the |χ(3)| of graphene and the second-order nonlinear optical susceptibility |χ(2)| of MoS2 (the most studied semiconductor in the family of 2D transition metal dichalcogenides)7. Wu and colleagues’ results indicate that the large variation in |χ(3)| of graphene at different doping levels needs to be considered to obtain a fair comparison of nonlinear optical responses.

The nonlinear interaction between light and a nanomaterial typically builds up coherently along the interaction length. Graphene and other 2D materials contain only one or few atomic layers, which thus have a very limited interaction length. Therefore, the frequency conversion efficiency of 2D materials is typically low (for example, ~3 × 10–10 % in the experiment reported by Wu and co-workers) despite having a large |χ(3)|. Future research efforts are likely to be dedicated to finding ways to enhance the nonlinear optical interaction in 2D materials using various approaches, including heterostructures, phase-matching methods, waveguide/fibre integration, and optical resonators (Fig. 2a–c). Furthermore, various polaritons (for example, plasmon, phonon and exciton polaritions; Fig. 2d) and photonic metamaterials can provide localized enhancement and manipulation of the optical nonlinearities in 2D materials and their mixed-dimensional heterostructures.

Fig. 2: Enhancement and manipulation of nonlinear optical responses in 2D materials with various methods.

a, Photonic crystal cavity. b, Microdisk resonator. c, Electrically tunable microring resonator. d, Plasmonic structure. The red arrows indicate the input photons, and the blue and green arrows indicate the generated photons at different frequencies.

The development of electrically tunable nonlinear optical materials is likely to play an increasingly important role in every aspect of photonics. It has already enabled diverse and widely used photonic devices (for example, pulsed lasers, switches, modulators and memories), underscoring the unparalleled advantages of photonic techniques over their electronic counterparts. In recent years, exciting nonlinear nanophotonic applications including on-chip photonics, quantum nanophotonics, nonlinear plasmonics and strong-field nanophysics have also attracted attention. However, the present solutions to these applications using traditional bulk crystals have hit a technical limit imposed by their characteristics, such as a relatively small nonlinear optical susceptibility and their complex and expensive fabrication and integration methods.

Graphene and other 2D materials with large nonlinear optical responses offer the benefit of being compatible with chip-integration and thus are promising for tackling the upcoming challenges of nonlinear nanophotonics and nanophysics. The gate-tunable nonlinear optics mechanisms of graphene and graphene-like materials can, in principle, offer various technical advantages, such as devices with a compact footprint, extremely fast speed (more than a few tens of GHz) and compatibility with complementary metal-oxide–semiconductor (CMOS) technology, all of which are desirable for future on-chip photonic and optoelectronic applications. If nonlinear optical interaction enhancement in 2D materials and the production of large-scale and high-quality 2D materials are successful, it is anticipated that 2D materials have the great potential to enable completely different approaches to construct electrically tunable nonlinear optical nanodevices (for example, frequency combs, ultrafast lasers, terahertz components, quantum sources, optical parametric sources) for new and emerging applications in metrology, sensing and imaging, quantum technology, and telecommunications.


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Sun, Z. Electrically tuned nonlinearity. Nature Photon 12, 383–385 (2018). https://doi.org/10.1038/s41566-018-0201-9

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