Nonlinear Optical Response Of Graphene Research Articles

Ultrafast Opto-Electronic and Thermal Tuning of Third-Harmonic Generation in a Graphene Field Effect Transistor.

Graphene is a unique platform for tunable opto-electronic applications thanks to its linear band dispersion, which allows electrical control of resonant light-matter interactions. Tuning the nonlinear optical response of graphene is possible both electrically and in an all-optical fashion, but each approach involves a trade-off between speed and modulation depth. Here, lattice temperature, electron doping, and all-optical tuning of third-harmonic generation are combined in a hexagonal boron nitride-encapsulated graphene opto-electronic device and demonstrate up to 85% modulation depth along with gate-tunable ultrafast dynamics. These results arise from the dynamic changes in the transient electronic temperature combined with Pauli blocking induced by the out-of-equilibrium chemical potential. The work provides a detailed description of the transient nonlinear optical and electronic response of graphene, which is crucial for the design of nanoscale and ultrafast optical modulators, detectors, and frequency converters.

Pulsed Four-Wave Mixing at Telecom Wavelengths in Si3N4 Waveguides Locally Covered by Graphene.

Recently, the nonlinear optical response of graphene has been widely investigated, as has the integration of this 2D material onto dielectric waveguides so as to enhance the various nonlinear phenomena that underpin all-optical signal processing applications at telecom wavelengths. However, a great disparity continues to exist from these experimental reports, depending on the used conditions or the hybrid devices under test. Most importantly, hybrid graphene-based waveguides were tested under relatively low powers, and/or combined with waveguide materials that already exhibited a nonnegligible nonlinear contribution, thereby limiting the practical use of graphene for nonlinear applications. Here, we experimentally investigate the nonlinear response of Si3N4 waveguides that are locally covered by submillimeter-long graphene patches by means of pulsed degenerate four-wave mixing at telecom wavelength under 7 W peak powers. Our measurements and comparison with simulations allow us to estimate a local change of the nonlinearity sign as well as a moderate increase of the nonlinear waveguide parameter (γ∼-10 m-1W-1) provided by graphene. Our analysis also clarifies the tradeoff associated with the loss penalty and nonlinear benefit afforded by graphene patches integrated onto passive photonic circuits, thereby providing some guidelines for the design of hybrid integrated nonlinear devices, coated with graphene, or, more generally, any other 2D material.

Second-order nonlinear optical response of graphene irradiated by two-color lights: ellipticity and phase modulation

We investigate the second-order optical response of graphene irradiated by two-color lights with frequencies ω and 3 ω , focusing on the modulation by ellipticity and phase of the incident fields. Based on the analytical perturbation theory, it is found that the interplay between the second harmonic generation (SHG) ( ω + ω ) and difference frequency generation (DFG) ( 3 ω − ω ) processes leads to nontrivial nonlinear optical properties. The interference between the two processes (SHG and DFG) results in different dependencies of the second-order response intensity I ( 2 ω ) on ellipticity, including monotonic, nonmonotonic change of I ( 2 ω ) with ellipticity, or even nearly independent of ellipticity under suitable conditions. The optimal incident angles for the highest I ( 2 ω ) are found, which can be tuned by changing the ellipticity, relative phase, or field strength of the incident light. In particular, a large output enhancement with respect to a small increment of the incident field can be achieved. We have found effective methods of modulating nonlinear optical processes, which may have applications in optical devices based on two-dimensional materials.

Linear and Nonlinear Optical Properties of Graphene: A Review

This article gives a brief overview of the linear and nonlinear optical response of graphene and its applications. Graphene exhibits unique physical properties. The charge carriers in graphene follow the relativistic massless Dirac equation; thus, they are known as the Dirac fermions. These Dirac fermions in graphene exhibit peculiar linear band structure at the Dirac point in the first Brillouin zone. These carriers exhibit novel linear and nonlinear optical properties in the presence of an intense electromagnetic field. The unique optical properties (linear and nonlinear) are a consequence of the unusual low-energy electronic band structure of graphene. The linear and nonlinear optical response of graphene can be tuned in the terahertz regime by the application of magnetic field. The uniqueness of graphene is shown by different findings in nonlinear optics such as four-wave mixing, saturation and reverse saturation absorption, two-photon absorption and optical limiting, among others. Therefore, the present review article describes the recent development in the field of linear and nonlinear optics of graphene. The different applications of graphene in the context of optics have been highlighted.

Ellipticity dependence of the third-order nonlinear optical response of graphene irradiated by two-color lights

We theoretically investigate the third-order optical response of graphene irradiated by two-color lights, paying special attention to the quantum interference. Our studies reveal that the interplay between harmonic generation and four-wave mixing leads to unusual nonlinear optical properties with nontrivial ellipticity dependence. It is shown that, unlike the case of monochromatic light with frequency ω0 (where the intensity of the third order response (I(3ω0)) decreases monotonically with the ellipticity and becomes zero for circularly polarized light), I(3ω0) may increase monotonically with the ellipticity, or be nearly independent on the ellipticity. In particular, under suitable condition, there exists an optimal nonzero ellipticity for the highest I(3ω0). Moreover, circularly polarized third-order optical response can be generated. We have found effective methods of modulating the nonlinear optical processes, which may have various applications in optical devices based on two dimensional materials.

Ultrafast all-optical switching in the presence of Bloch surface waves

It is commonly known that Bloch surface waves (BSW) can be excited at the photonic crystal/dielectric boundary that leads to many features attractive for application these states as the basis of sensors and nanophotonic devices. The narrow spectral-angular resonance of BSW is very sensitive to properties of top layer and surrounding medium. There are few ways to enhance nonlinear optical response of a top layer without violation of BSW excitation conditions. In this work we choose graphene monolayer as a source of strong nonlinearity with tiny thickness. We study temporal nonlinear optical response of graphene in the case of Bloch surface waves excitation revealing subpicosecond switching time of probe dynamics.

Nonlinear optical absorption and asymmetric charge carrier conduction in chemical vapor deposited single-layer graphene

In this work, we report the nonlinear optical absorption and asymmetric charge carrier conduction in single layer graphene films deposited by chemical vapor deposition (CVD) technique on copper foils with pretreated surface. XRD texture and pole figure analysis of the substrate are utilized for the visualization of the effect of the pretreatment on the substrate. The synthesised graphene is employed as a channel layer in a back gated field-effect transistor and the asymmetric behavior of charge carriers is analyzed. Nonlinear optical response of graphene is recorded after transferring it onto a quartz substrate. Open aperture Z-scan technique yields a nonlinear absorption coefficient of 5.34 × 106 cm GW−1. The film exhibits saturable absorption in the visible range with a saturation intensity as low as 0.134 GW cm−2.

Band Tuning of a Phosphorene Semiconductor via Floquet Theory

Graphene and phosphorene are monolayer of graphite and phosphorous, respectively. Graphene is completely relativistic (Dirac) fermionic system, but phosphorene is pseudorelativistic fermionic system. In phosphorene, electronic spectrum of phosphorene has a Dirac like (linear) band in one direction and Schrodinger like (parabolic) band in other direction. Conventional Rabi oscillations are studied by using rotating wave approximation in resonance case. The Floquet theory is an alternative way of study Rabi oscillations in off-resonance case and dominating in case of low energy physics. In this article, the nonlinear optical response of graphene and phosphorene studied under intense applied quantized electromagnetic field via Floquet theory. The Bloch-Siegert shift is observed for graphene and phosphorene. A numerical model is applied for justifying the role of anisotropy in phosphorene. Therefore, the Floquet theory can be utilized to characterize the different fermionic systems.

Difference Frequency Generation-based ultralow threshold Optical Bistability in graphene at visible frequencies, an experimental realization

We experimentally show that Difference Frequency Generation (DFG) can efficiently occur in a graphene ink for a visible pump-probe radiation in consequence of the second order nonlinear optical response of graphene. DFG induces the local field enhancement over the graphene sheets and subsequently motivates Surface Plasmons (SPs). We then show that SPs can appear as internal feedback entities to realize Optical Bistability (OB) if a large nonlinear response is guaranteed. However, the figure of merit is the experimental demonstration of ultralow rise/fall threshold OB process, not only by using no external feedback procedure but also caused by a single visible guide beam (in contrast to the double pump-probe radiation). The reason is inferred as the presence of strong Raman scattering which in turn triggers a probe radiation interacting with the guide beam as the pump radiation. We repeat the experiment for different wavelengths/nonlinear medium lengths. We deduce that the smaller lengths as well as the larger wavelengths demonstrate better OB features. We previously bring a simple theory, yet mathematically rigorous to interpret the effects. Then, conforming to the Ishikawa's theory of the graphene nonlinear optical response as the interplay of both interband and intraband transitions, we indicate the agreement between the experimental observations and simulation results. Our experimental results can delineate a plain route for Raman scattering and the other elastic scattering mechanisms within the complex medium of graphene ink, breeding thus the connected theory development. On the other hand, since the low threshold OB can be used to sense SPs' formation elaborately, our proposed approach to control SPs via a single visible beam can be extended to the potential applications like the optical switching, plasmonic wave generation, sensing, etc. with the purpose of energy saving.

Enhanced nonlinear optical response of core–shell graphene-wrapped spherical nanoparticles

We study the nonlinear optical response of graphene in nanostructures. The spherical nanoparticle coated with a monolayer of graphene displays enhanced optical Kerr nonlinearity and, consequently, optical bistability and multistability in a broad range of incident optical intensity. This optical bistability significantly appertains on the geometry of the shell-coated nanoparticle, the fractional volume of the metallic core, as well as the core genre and Fermi energy of graphene. In particular, Fermi energy could also affect the optical bistability and induce switching from optical bistability to optical multistability. Due to the importance of core–shell nanoparticles, this model may find potential applications in optical bistable devices such as all-optical switches, optical transistors, and memories.

Enhanced nonlinear optical response of graphene by silver-based nanoparticle modification for pulsed lasing

In this work, we report on the synthesis and characterization of a functionalized graphene modified by Ag based nanoparticles (Ag2S@Ag) and the applications as an optical modulator for pulsed laser generation at 1μm in the compact waveguide platform written by a femtosecond laser. The nonlinear optical response of the Ag2S@Ag nanoparticle modified graphene has been explored by the Z-scan technique, which exhibits an enhanced ultrafast saturable absorption response with higher modulation depth and lower saturation intensity. The Q-switching and Q-switched mode locking have been realized in a waveguide laser system by using Ag nanoparticle modified graphene as a saturable absorber (SA) mirror. Fundamental Q-switched mode-locked waveguide lasers with a repetition rate of 6.44 GHz have been achieved, reaching shorter pulse duration (33 ps) in comparison to that (52 ps) through unmodified graphene SA. This work suggests potential applications of functionalized graphene in ultrafast photonics.

Impact of electron-electron Coulomb interaction on the high harmonic generation process in graphene

Generation of high harmonics in a monolayer graphene initiated by strong coherent radiation field, taking into account electron-electron Coulomb interaction is investigated. A microscopic theory describing the nonlinear optical response of graphene is developed. The Coulomb interaction of electrons is treated in the scope of dynamic Hartree-Fock approximation. The closed set of integrodifferential equations for the single-particle density matrix of a graphene quantum structure is solved numerically. The obtained solutions show the significance of many-body Coulomb interaction on the high harmonic generation process in graphene.

Surface oxygen-containing defects of graphene nanosheets with tunable nonlinear optical absorption and refraction.

Surface oxygen-containing defects of graphene nanosheets (G NSs) are important for the nonlinear optical (NLO) properties in optoelectric devices. G NSs with different surface oxygen-containing defects are successfully tuned by a chemical reduction process, and are characterized by several experimental measurements of morphology and structure and by spectroscopy. Their NLO properties are measured with the Z-scan technique and the NLO transmission method using a 30 picosecond single-pulse laser source at 532 nm wavelength. Their NLO susceptibility is enhanced 11.8 times (from 0.38 × 10-12 esu to 4.5 × 10-12 esu) with the decrease in the density of surface oxygen-containing groups, while it is reduced 7.2 times (2.7 × 10-12 esu) with a further decrease in oxygen. Accordingly, the nonlinear absorption coefficient of graphene is increased from 0.51 cm GW-1 to 5.90 cm GW-1, and then decreased to 3.41 cm GW-1, indicating that the NLO response of graphene NSs should be weakened whether the component of surface oxygen-containing groups is too large or too small. The local field effect arising from surface oxygen-containing groups and isolated sp2 clusters is the dominant mechanism for the NLO improvement, while the connection of small sp2 clusters depresses the optical nonlinearity. An evolution from two-photon absorption to saturable absorption with the decrease of surface oxygen concentration is obtained. The intensity-related NLO absorption and refraction in NSs are also discussed. Tuning the surface oxygen-containing defects of graphene is a useful way to enhance the optical nonlinearity for potential applications in devices.

Intensity dependences of the nonlinear optical excitation of plasmons in graphene.

Recently, we demonstrated an all-optical coupling scheme for plasmons, which takes advantage of the intrinsic nonlinear optical response of graphene. Frequency mixing using free-space, visible light pulses generates surface plasmons in a planar graphene sample, where the phase matching condition can define both the wavevector and energy of surface waves and intraband transitions. Here, we also show that the plasmon generation process is strongly intensity-dependent, with resonance features washed out for absorbed pulse fluences greater than 0.1 J m-2 This implies a subtle interplay between the nonlinear generation process and sample heating. We discuss these effects in terms of a non-equilibrium charge distribution using a two-temperature model.This article is part of the themed issue 'New horizons for nanophotonics'.

Second-order nonlinear optical response of graphene

Although massless Dirac fermions in graphene constitute a centrosymmetric medium for in-plane excitations, their second-order nonlinear optical response is nonzero if the effects of spatial dispersion are taken into account. Here we present a rigorous quantum-mechanical theory of the second-order nonlinear response of graphene beyond the electric dipole approximation, which includes both intraband and interband transitions. The resulting nonlinear susceptibility tensor satisfies all symmetry and permutation properties, and can be applied to all three-wave mixing processes. We obtain useful analytic expressions in the limit of a degenerate electron distribution, which reveal quite strong second-order nonlinearity at long wavelengths, Fermi-edge resonances, and unusual polarization properties.

Coherent nonlinear optical response of graphene in the quantum Hall regime

We study nonlinear optical response of graphene in the quantum Hall regime to an intense laser pulse. In particular, we consider harmonic generation process. We demonstrate that the generalized magneto-optical conductivity of graphene on the harmonics of a strong pump laser radiation has a characteristic Hall plateaus feature. The plateaus heights depend on the laser intensity and broadening of Landau levels, so that are not quantized exactly. This nonlinear effect remains robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and nonlinear Faraday effect, which are within the experimental feasibility.

Nonlinear quantum optical properties of graphene

We present a semiclassical theory of the linear and nonlinear optical response of graphene. The emphasis is placed on the nonlinear optical response of graphene from the standpoint of the underlying chiral symmetry. The Bloch quasiparticles in the low-energy limit around the degeneracy points are dominantly chiral. It is shown that this chiral behavior in conjunction with scale invariance in graphene around the Dirac points results in the strong nonlinear optical response. Explicit expressions for the linear and nonlinear conductivity tensors are derived based on semiconductor Bloch equations (SBEs). The linear terms agree with the result of Kubo formulation. The three main additive mechanisms contribute in the nonlinear optical response of graphene: pure intraband, pure interband and the interplay between them. For each contribution, an explicit response function is derived. The Kerr-type nonlinearity of graphene is then numerically studied and it is demonstrated that the nonlinear refractive index of graphene can be tuned and enhanced by applying a gate voltage. It is also discussed that a strong Kerr nonlinearity can be achieved in a gated graphene monolayer. However, this nonlinearity is accompanied with a significant amount of absorption loss.

All-optical generation of surface plasmons in graphene

Here we present an all-optical plasmon coupling scheme, utilising the intrinsic nonlinear optical response of graphene. We demonstrate coupling of free-space, visible light pulses to the surface plasmons in a planar, un-patterned graphene sheet by using nonlinear wave mixing to match both the wavevector and energy of the surface wave. By carefully controlling the phase-matching conditions, we show that one can excite surface plasmons with a defined wavevector and direction across a large frequency range, with an estimated photon efficiency in our experiments approaching $10^{-5}$.

Preface to the second special issue on Terahertz Wave Science, Technology, and Application

Terahertz (THz) frequency region has attracted considerable interest, due to its unique nature and promising applications. A number of breakthroughs were achieved by the worldwide research groups in this field, including high-performed sources, detectors, functional devices, interaction with materials as well as applications. Previously, the first special issue on “Terahertz Wave Science, Technology, and Application” was presented (June 2014). This is the second special Issue with 3 review articles and 8 research articles, which introduce and discuss recent developments of relevant subjects. These papers can be divided into such categories: nonlinear optical response of grapheme, semiconductor activated metamaterials, superconducting metamaterials, THz generation with air and GaAs photoconductive antenna, double-probe-pulse THz detection, applications in sensing, imaging and spectroscopy, and so on. Prof. Chao Zhang and coworkers of University of Wollongong reviewed the recent developments of nonlinear optical response of graphene in THz and near-infrared frequency regime. Prof. Hou-Tong Chen of Los Alamos National Laboratory reviewed the recent progresses on semiconductor activated THz metamaterials. Prof. Weili Zhang and coworkers of Tianjin University reviewed the recent results on tailoring electromagnetic responses in THz superconducting metamaterials. In the research articles, Prof. Kun Zhao’s group of China University of Petroleum reported the detection of nheptane, n-octane and nitrate solutions with THz time-domain spectroscopy. Prof. Zhi Hong and coworkers of China Jiliang University investigated a high Q THz asymmetrically coupled resonator and its sensing performance. Prof. Alexander Shkurinov’s group of Lomonosov Moscow State University demonstrated the simultaneous generation of nonlinear optical harmonics and THz radiation in air: polarization discrimination of various nonlinear contributions. Prof. J. Bianca Jackson and coworkers of Ecole Polytechnique applied THz pulse imaging in archaeology. Dr. Haiwei Du of RIKEN investigated optical ionization evolution effect on photocurrent produced from two-color femtosecond laser pulses. Prof. Jinsong Liu’s group presented the studies on the behavior of GaAs photoconductive antenna. The articles in this special issue have certain significance for promoting the development of THz technology. It is hoped that the second special issue will benefit THz applications. On behalf of the editorial committee, we express our sincere thanks to all the authors and reviewers for their great contribution to this special issue. Also, we thank the editorial committee members for their excellent assistance. Finally, we are grateful to the editorial staff for their help, also thanks for my research assistants Dr. Pengxiang Liu, Dr. Lanju Liang and Yating Zhang. Without all of the contributions of these hard-working, dedicated people, it would have been impossible to produce this second special issue.

Nonlinear optical response of graphene in terahertz and near-infrared frequency regime

In this review, we discuss our recent theoretical work on the nonlinear optical response of graphene and its sister structure in terahertz (THz) and near-infrared frequency regime. Due to Dirac-like linear energy-momentum dispersion, the third-order nonlinear current in graphene is much stronger than that in conventional semiconductors. The nonlinear current grows rapidly with increasing temperature and decreasing frequency. The third-order nonlinear current can be as strong as the linear current under moderate electric field strength of 104 V/cm. In bilayer graphene (BLG) with low energy trigonal warping effect, not only the optical response is strongly nonlinear, the optical nonlinearity is well-preserved at elevated temperature. In the presence of a bandgap (such as semihydrogenated graphene (SHG)), there exists two well separated linear response and nonlinear response peaks. This suggests that SHG can have a unique potential as a two-color nonlinear material in the THz frequency regime where the relative intensity of the two colors can be tuned with the electric field. In a graphene superlattice structure of Kronig-Penney type periodic potential, the Dirac cone is elliptically deformed. We found that not only the optical nonlinearity is preserved in such a system, the total optical response is further enhanced by a factor proportional to the band anisotropy. This suggests that graphene superlattice is another potential candidate in THz device application.