Two-Dimensional Materials Photonics
Two-dimensional materials represent a revolutionary class of substances where matter is confined to a single atomic layer or a few layers, creating unique optical and electronic properties impossible in their bulk counterparts. Since the isolation of graphene in 2004, an entire family of atomically thin materials has emerged, each offering distinct advantages for photonic applications. These materials interact strongly with light despite their extreme thinness, supporting novel excitations that enable compact, fast, and tunable optical devices.
The photonic properties of two-dimensional materials arise from their modified electronic band structure under quantum confinement. Graphene, with its linear dispersion and zero band gap, absorbs light uniformly across an extraordinarily broad spectrum. Transition metal dichalcogenides develop direct band gaps when thinned to monolayers, becoming efficient light emitters and absorbers. Black phosphorus provides a tunable band gap bridging the technologically important mid-infrared region. Together, these materials cover wavelengths from ultraviolet through visible to far-infrared.
Beyond their intrinsic optical properties, two-dimensional materials can be stacked into van der Waals heterostructures that combine different functionalities in designer architectures. The ability to assemble these structures layer by layer creates opportunities for engineering optical responses unavailable in any single material. This article provides comprehensive coverage of two-dimensional materials photonics, from fundamental physics through device applications and emerging research directions.
Graphene Photonics
Optical Properties of Graphene
Graphene exhibits remarkable optical properties stemming from its unique electronic structure where conduction and valence bands meet at Dirac points with linear dispersion. This band structure produces a universal optical conductance that absorbs exactly 2.3% of incident light per layer across a vast wavelength range from ultraviolet to terahertz. The absorption is determined solely by fundamental constants: the fine structure constant and pi, making graphene a natural optical standard.
The linear dispersion means that optical transitions can occur at any photon energy, limited only by Pauli blocking when the photon energy falls below twice the Fermi level. This broadband absorption contrasts with semiconductors where absorption onset occurs at the band gap energy. For undoped graphene at room temperature, interband transitions dominate in the visible and near-infrared, while intraband transitions become important in the mid-infrared and terahertz as doping increases.
Carrier dynamics in graphene following optical excitation proceed through distinct stages. Initial photoexcitation creates a non-thermal distribution that thermalizes within tens of femtoseconds through carrier-carrier scattering. The resulting hot carrier distribution cools over picosecond timescales through optical phonon emission, followed by slower acoustic phonon cooling. These ultrafast dynamics enable graphene optoelectronic devices operating at speeds exceeding 100 GHz.
Graphene Plasmonics
Graphene supports surface plasmons at infrared and terahertz frequencies where they are strongly confined to the atomic sheet. Unlike noble metal plasmons that operate in the visible spectrum, graphene plasmons can be tuned across a wide frequency range by adjusting the carrier concentration through electrostatic gating. This electrical tunability provides dynamic control over plasmonic resonances impossible with conventional metals.
The confinement of graphene plasmons exceeds that of metal surface plasmons by orders of magnitude, with plasmonic wavelengths compressed by factors of 100 or more compared to free-space light. This extreme confinement produces correspondingly large field enhancement, valuable for sensing and nonlinear optics. Structured graphene nanoribbons and nanodisks exhibit localized plasmonic resonances at frequencies determined by their dimensions, analogous to metallic nanoparticle resonances but with electrical tunability.
Losses in graphene plasmons arise from both intrinsic carrier scattering and extrinsic factors including substrate phonons and charged impurities. Hexagonal boron nitride substrates provide atomically smooth surfaces with reduced scattering, enabling propagation lengths of several plasmonic wavelengths. Encapsulating graphene between boron nitride layers further improves quality by screening charged impurities in the environment.
Graphene Photodetectors
Graphene photodetectors leverage the material's broadband absorption and ultrafast carrier dynamics for detection spanning ultraviolet through terahertz frequencies. The gapless band structure enables photocurrent generation at any wavelength, though the weak absorption per layer limits responsivity. Various device architectures enhance performance by exploiting photothermoelectric effects, photovoltaic effects at junctions, or gain mechanisms.
Metal-graphene-metal photodetectors generate photocurrent through the photovoltaic effect at asymmetric metal contacts that create built-in fields. The internal responsivity can reach tens of milliamps per watt with bandwidth exceeding 40 GHz, suitable for high-speed optical communications. Integrating graphene with waveguides increases the interaction length and absorption, improving responsivity while maintaining the large bandwidth inherent to graphene.
Bolometric detection exploits the temperature-dependent resistance of graphene, where absorbed photons heat the electron gas and change conductivity. Hot-electron bolometers operating at cryogenic temperatures achieve noise-equivalent powers approaching fundamental limits for terahertz detection. The weak electron-phonon coupling in graphene at low temperatures maintains electron temperature elevation, enhancing sensitivity.
Graphene Modulators
Electro-optic modulators based on graphene control light transmission through voltage-induced changes in optical absorption. Shifting the Fermi level through electrostatic gating blocks interband transitions when the photon energy falls below twice the Fermi energy, creating electroabsorption modulation. Extinction ratios exceeding 10 dB have been achieved with modulation bandwidths approaching 40 GHz, competitive with conventional semiconductor modulators.
Waveguide-integrated graphene modulators maximize interaction between the optical mode and the graphene layer for efficient modulation with minimal device length. The graphene can be positioned on top of the waveguide, where evanescent field overlap provides coupling, or integrated within slot waveguides that concentrate the field at the graphene position. Double-layer graphene structures with a dielectric spacer enable push-pull operation that enhances modulation depth.
Phase modulation using graphene exploits the accompanying change in refractive index when absorption is modified. The strong electrorefractive effect enables phase shifters for Mach-Zehnder modulators and other interferometric devices. Graphene phase shifters provide compact alternatives to long thermal phase shifters in silicon photonics, with potential for higher speed and lower power consumption.
Transition Metal Dichalcogenides
Electronic and Optical Structure
Transition metal dichalcogenides (TMDCs) with formula MX2, where M is a transition metal (Mo, W) and X is a chalcogen (S, Se, Te), undergo a dramatic transformation when thinned to monolayers. Bulk TMDCs are indirect band gap semiconductors, but quantum confinement converts them to direct band gap materials in monolayer form. This transition produces band gaps in the visible spectrum: 1.9 eV for MoS2, 1.65 eV for MoSe2, 2.0 eV for WS2, and 1.65 eV for WSe2.
The direct band gap enables efficient light emission that is absent in bulk crystals. Photoluminescence quantum yields in monolayer TMDCs can exceed 90% under appropriate conditions, rivaling conventional III-V semiconductors. The emission wavelength corresponds to the band gap, placing these materials in the red to near-infrared spectral region with potential for visible light sources and display applications.
Strong spin-orbit coupling in TMDCs, arising from the heavy metal atoms, splits the valence band by hundreds of millielectronvolts. Combined with broken inversion symmetry in monolayers, this creates two inequivalent valleys at the K and K' points of the Brillouin zone with opposite spin and valley indices. Optical selection rules couple circularly polarized light selectively to each valley, enabling valley-selective excitation and the emerging field of valleytronics.
Excitons and Many-Body Effects
Excitons in monolayer TMDCs exhibit binding energies of several hundred millielectronvolts, far exceeding typical semiconductor values of tens of millielectronvolts. This strong binding results from reduced dielectric screening in two dimensions and the heavy effective masses of carriers. Consequently, excitons dominate the optical response even at room temperature, with excitonic absorption peaks clearly visible in transmission spectra.
The exciton landscape in TMDCs is rich, including not only the bright A and B excitons corresponding to the spin-orbit split valence bands but also various dark states and charged excitons (trions). Dark excitons with spin-forbidden optical transitions can have longer lifetimes, potentially useful for certain applications. Trions form when an exciton binds an additional electron or hole, producing absorption and emission features sensitive to doping level.
At elevated carrier densities, excitons interact to form higher-order complexes including biexcitons and potentially excitonic molecules. The strong Coulomb interactions in two dimensions enhance these many-body effects compared to conventional semiconductors. Understanding and controlling exciton interactions is essential for applications in quantum light sources, nonlinear optics, and excitonic circuits.
Light Emission and Light-Emitting Devices
Monolayer TMDCs emit light efficiently upon optical or electrical excitation, with potential applications in displays, lighting, and quantum photonics. Photoluminescence occurs at the exciton resonance energy, with linewidths of tens of millielectronvolts reflecting both homogeneous broadening and inhomogeneous contributions from disorder. Low-temperature measurements on high-quality samples reveal linewidths approaching the homogeneous limit.
Electroluminescent devices inject electrons and holes from contacts into the monolayer where they form excitons and recombine radiatively. Vertical heterostructure devices with graphene electrodes achieve efficient injection while maintaining optical access to the emitting layer. The device architecture resembles an organic light-emitting diode but with an atomically thin active region, offering ultimate miniaturization of light sources.
Single-photon emission from localized states in TMDCs enables quantum light sources operating in the visible spectrum. Strain or disorder creates localized potentials that trap excitons, producing discrete emission lines with antibunched photon statistics characteristic of single-quantum emitters. Site-controlled strain engineering through nanopillars or other structures enables deterministic positioning of single-photon sources for integration with photonic circuits.
TMDC Photodetectors
TMDC photodetectors exploit the strong absorption at excitonic resonances and the tunable band gap across the visible to near-infrared spectrum. Phototransistor configurations using TMDC channels achieve photoconductive gain through photogating, where trapped carriers modify the channel conductivity, producing responsivities of thousands of amperes per watt. The trade-off is reduced speed due to the slow response of trapped carriers.
Vertical heterostructure photodetectors stack TMDCs with graphene electrodes to create efficient photovoltaic devices. Absorbed photons generate electron-hole pairs that separate at the graphene-TMDC interface, producing photocurrent without applied bias. The transparent graphene electrodes allow illumination through the contact, maximizing absorption in the active layer. Response times in the nanosecond range have been demonstrated.
Integrating TMDC photodetectors with waveguides extends the absorption path for efficient detection with fast response. The thin active layer couples evanescently to waveguide modes over lengths that compensate for the weak per-pass absorption. Silicon photonics platforms provide natural hosts for such hybrid integration, potentially enabling visible-wavelength detection capabilities on silicon chips.
Black Phosphorus
Structure and Band Gap
Black phosphorus consists of phosphorus atoms arranged in puckered honeycomb layers held together by van der Waals forces. Unlike the hexagonal lattice of graphene, the orthorhombic crystal structure creates strong in-plane anisotropy, with distinct armchair and zigzag directions. This anisotropy manifests in all physical properties including electrical conductivity, thermal transport, and optical absorption.
The band gap of black phosphorus varies dramatically with layer number, ranging from approximately 0.3 eV in bulk to 2.0 eV in monolayer (phosphorene). This tunability spans the mid-infrared through visible spectrum, bridging the gap between graphene (no gap) and TMDCs (visible gaps). The mid-infrared coverage is particularly valuable for thermal imaging, molecular spectroscopy, and free-space communications where few other materials provide convenient operation.
Black phosphorus maintains a direct band gap at all thicknesses, ensuring efficient optical transitions regardless of layer number. The moderate effective masses, intermediate between graphene and TMDCs, provide reasonable carrier mobility while maintaining strong optical absorption. These balanced properties make black phosphorus attractive for optoelectronic applications across a uniquely broad spectral range.
Anisotropic Optical Properties
The puckered crystal structure of black phosphorus produces strongly anisotropic optical properties with different absorption coefficients for light polarized along the armchair and zigzag directions. The absorption edge and excitonic features shift by hundreds of millielectronvolts between polarizations, enabling polarization-sensitive photodetection and linear dichroism studies. This natural birefringence exceeds that of most conventional optical materials.
Excitons in black phosphorus exhibit large binding energies that increase with decreasing layer number, reaching hundreds of millielectronvolts in few-layer samples. The anisotropic effective masses create elliptical exciton wave functions with different spatial extent along the two in-plane directions. These anisotropic excitons produce dichroic absorption and emission that can be controlled through crystal orientation.
Plasmonic excitations in doped black phosphorus inherit the crystalline anisotropy, supporting hyperbolic dispersion where the effective dielectric function has opposite signs along different directions. This hyperbolic response enables unusual propagation effects including negative refraction and enhanced optical density of states, with potential applications in super-resolution imaging and thermal emission control.
Mid-Infrared Applications
Black phosphorus photodetectors address the mid-infrared spectral region where few semiconductor materials combine direct band gaps with high carrier mobility. Photoconductive and photovoltaic devices demonstrate detection at wavelengths beyond 4 micrometers, covering molecular fingerprint absorption bands valuable for chemical sensing. Room-temperature operation at these wavelengths distinguishes black phosphorus from narrow-gap semiconductors requiring cooling.
Polarization-sensitive mid-infrared detection exploits the strong dichroism of black phosphorus without requiring external polarizers. The photocurrent varies as the square of the cosine of the angle between light polarization and the armchair direction, enabling compact polarimetric sensors for imaging and remote sensing. This intrinsic polarization sensitivity simplifies device design while providing functionality difficult to achieve otherwise.
Thermal imaging applications benefit from the atmospheric transmission window around 3-5 micrometers where black phosphorus absorption can be optimized through thickness selection. The relatively high operating temperature compared to mercury cadmium telluride detectors reduces system complexity and cost, potentially enabling widespread deployment of mid-infrared imaging.
Stability and Passivation
Black phosphorus degrades rapidly when exposed to ambient oxygen and water, with the surface reacting to form phosphorus oxides that disrupt electronic and optical properties. Visible degradation occurs within hours of air exposure, creating bubble-like features on the surface. This environmental sensitivity presents a significant challenge for device fabrication and long-term operation.
Encapsulation with hexagonal boron nitride provides effective protection by creating an inert barrier against atmospheric species. Boron nitride-encapsulated devices maintain their properties for extended periods, with high-quality interfaces that preserve carrier mobility. The encapsulation must be performed in inert atmosphere to prevent degradation during the fabrication process.
Alternative passivation strategies include atomic layer deposition of aluminum oxide, organic surface treatments, and covalent functionalization. Each approach offers trade-offs between protection effectiveness, process complexity, and impact on underlying properties. Developing scalable passivation remains essential for practical applications of black phosphorus photonics.
Hexagonal Boron Nitride
Wide Band Gap Optics
Hexagonal boron nitride (hBN) is a wide band gap insulator with a gap around 6 eV, placing its optical activity in the deep ultraviolet region. The layered structure analogous to graphene enables exfoliation into atomically thin sheets, though the insulating character precludes the electronic applications of graphene. Instead, hBN serves critical roles as a dielectric, encapsulant, and platform for quantum light sources.
Deep ultraviolet emission from hBN occurs through excitonic recombination near the band edge, with potential applications in sterilization, photolithography, and spectroscopy. Lasing has been demonstrated in hBN under intense optical pumping, though achieving practical UV light sources remains challenging. The wide band gap also makes hBN transparent throughout the visible and infrared spectrum, valuable for optical windows and encapsulation.
Phonon polaritons in hBN result from coupling of infrared light to optical phonons, creating hybridized excitations that propagate along the crystal. The in-plane and out-of-plane optical phonons have different frequencies, producing two Reststrahlen bands where the material exhibits metallic-like optical response. These phonon polaritons enable subwavelength infrared imaging, thermal management, and novel optical components operating in the mid-infrared.
Single-Photon Emitters
Hexagonal boron nitride hosts bright single-photon emitters that operate at room temperature, distinguishing them from most solid-state quantum emitters requiring cryogenic conditions. These emitters, likely associated with crystal defects, produce narrow emission lines spanning the visible spectrum from blue through red depending on the specific defect type. Photon antibunching measurements confirm single-photon character with g2(0) values approaching zero.
The emission properties including wavelength, brightness, and polarization vary between individual emitters, reflecting the diversity of defect structures present in hBN samples. Emission rates exceeding millions of photons per second have been observed, with photostability allowing continuous operation over extended periods. The combination of brightness, stability, and room-temperature operation makes hBN emitters attractive for quantum technology applications.
Creating emitters at controlled locations remains challenging because the defect formation process is not fully understood. Various approaches including electron irradiation, ion implantation, and plasma treatment create emitters but with limited spatial control. Strain engineering influences emission properties, enabling some degree of wavelength tuning and potentially site-selective activation of emitters.
Role in Van der Waals Heterostructures
Hexagonal boron nitride serves as the ideal substrate and encapsulant for other two-dimensional materials, providing atomically flat surfaces free of dangling bonds and charge traps. Graphene and TMDC devices on hBN substrates exhibit dramatically improved performance including higher carrier mobility, sharper optical resonances, and reduced disorder compared to devices on silicon oxide substrates.
The encapsulation geometry sandwiches the active two-dimensional material between top and bottom hBN layers, protecting it from environmental degradation while maintaining optical access. Light can pass through the transparent hBN for optical measurements, while the insulating character allows electrostatic gating through the hBN dielectric. This architecture has become standard for high-quality two-dimensional material devices.
Beyond passive roles, hBN contributes active functionality in heterostructure devices. Tunneling through thin hBN barriers creates defined junction characteristics for light-emitting devices and photodetectors. The hyperbolic phonon polaritons in hBN can couple to plasmons in adjacent graphene layers, creating hybrid modes with properties tunable through both layers.
MXenes for Photonics
Structure and Synthesis
MXenes are a family of two-dimensional transition metal carbides, nitrides, and carbonitrides with the general formula Mn+1XnTx, where M is a transition metal, X is carbon or nitrogen, and T represents surface terminations including oxygen, hydroxyl, and fluorine groups. These materials are produced by selectively etching the A layers from MAX phase precursors, creating accordion-like structures that can be delaminated into individual sheets.
The rich compositional space of MXenes encompasses dozens of confirmed compositions with properties tunable through the choice of metal, X element, and surface termination. Titanium carbide Ti3C2Tx is the most studied MXene, exhibiting metallic conductivity and strong optical absorption. The combination of metallic character with solution processability distinguishes MXenes from other two-dimensional materials.
Synthesis typically involves etching in hydrofluoric acid or milder fluoride-containing etchants, followed by sonication or mechanical shearing to delaminate the layered product. The resulting colloidal suspensions can be processed into films, coatings, and composites through various deposition techniques. This solution processability enables large-area device fabrication impractical with mechanically exfoliated materials.
Optical Properties
MXenes exhibit broad optical absorption spanning ultraviolet through near-infrared wavelengths, with specific features determined by the composition. The metallic density of states produces free-carrier absorption in the infrared, while interband transitions create absorption features at higher energies. The overall absorption can exceed 90% for films only tens of nanometers thick, making MXenes effective light absorbers despite their modest thickness.
Localized surface plasmon resonances occur in MXene nanoparticles and nanostructures, analogous to metallic nanoparticle plasmonics. The plasmonic response depends on particle dimensions and can be tuned through morphology control during synthesis. These plasmonic properties enable applications in sensing, photothermal therapy, and surface-enhanced spectroscopy.
Nonlinear optical properties of MXenes include strong saturable absorption useful for passive mode-locking of lasers and optical limiting for eye and sensor protection. The saturable absorption arises from absorption bleaching as carriers fill available states under intense illumination. MXene saturable absorbers have demonstrated mode-locking across wavelength ranges from visible to mid-infrared in various laser systems.
Electromagnetic Interference Shielding
The high electrical conductivity and strong absorption of MXenes make them exceptionally effective electromagnetic interference (EMI) shielding materials. Films only micrometers thick can attenuate electromagnetic radiation by more than 90 dB, exceeding the performance of much thicker conventional shields. The combination of reflection at conductive interfaces and absorption within the material contributes to the shielding effectiveness.
The tunable electromagnetic properties allow optimization for specific frequency ranges and shielding requirements. Low-frequency shielding benefits from high conductivity and thickness, while high-frequency shielding can exploit magnetic permeability in certain MXene compositions. The ability to process MXenes into flexible films and coatings enables conformal shielding for complex geometries.
Transparent conductive films for EMI shielding in displays and windows represent an important application where MXenes can balance optical transparency with electromagnetic attenuation. Patterned MXene meshes and sparse films achieve this balance, blocking electromagnetic radiation while allowing visible light transmission for practical devices.
Photothermal Applications
The strong optical absorption and efficient conversion to heat make MXenes effective photothermal agents. Under solar illumination, MXene films can reach temperatures sufficient for water purification through evaporation, with demonstrated solar-to-vapor conversion efficiencies exceeding 80%. The localized heating concentrates at the surface where evaporation occurs, minimizing heat loss to the bulk water.
Biomedical photothermal therapy uses MXene nanoparticles to convert near-infrared light into localized heating for cancer treatment. The particles accumulate in tumors through enhanced permeation and retention, then generate lethal temperatures upon laser illumination. Preliminary studies demonstrate tumor ablation in animal models with minimal damage to surrounding tissue.
Photoacoustic imaging exploits the same photothermal conversion to generate acoustic waves from pulsed laser illumination. MXene contrast agents provide strong photoacoustic signals with biocompatibility suitable for in vivo imaging. The combination of imaging and therapy in single nanoparticle systems enables theranostic applications that simultaneously diagnose and treat disease.
Van der Waals Heterostructures
Assembly Techniques
Van der Waals heterostructures are assembled by stacking individual two-dimensional materials layer by layer, held together by van der Waals forces without requiring epitaxial lattice matching. The assembly process typically uses polymer stamps or similar transfer methods to pick up flakes from their growth or exfoliation substrates and place them with controlled alignment onto target locations. Sequential transfers build up complex stacks with designed layer sequences.
Dry transfer techniques avoid liquid contact with the flakes, preserving clean interfaces essential for high-quality devices. Polymer stamps made from materials like polycarbonate or polydimethylsiloxane can be manipulated under microscopes with micromanipulators for precise positioning. Temperature control during transfer aids adhesion and release at appropriate steps.
Scalable assembly methods beyond manual stacking are needed for practical applications. Robotic assembly systems automate the pick-and-place process for improved throughput. Direct growth of heterostructures through sequential chemical vapor deposition eliminates the transfer step entirely, though interface quality remains challenging. Advances in both transfer and growth approaches continue improving heterostructure fabrication.
Interlayer Excitons
Interlayer excitons form in heterostructures when the electron and hole reside in different layers, typically occurring when band alignment creates a type-II heterojunction. These spatially indirect excitons have reduced overlap between electron and hole wave functions, dramatically extending their lifetime compared to intralayer excitons. Lifetimes ranging from nanoseconds to microseconds have been observed, compared to picoseconds for intralayer species.
The long lifetime makes interlayer excitons suitable for studying excitonic phenomena including Bose-Einstein condensation, superfluidity, and excitonic circuits. The permanent electric dipole moment from the spatial separation enables control through applied electric fields, providing tunability of exciton energy and transport. These properties are valuable for both fundamental studies and potential device applications.
Moire patterns arising from lattice mismatch or twist angle between layers modulate the interlayer exciton properties across the heterostructure. Periodic modulation of the local atomic registry creates a moire potential that can trap excitons at specific locations, forming arrays of localized states. These trapped excitons can function as quantum emitters with spatially periodic arrangement determined by the moire pattern.
Charge Transfer and Separation
Ultrafast charge transfer across heterostructure interfaces occurs on femtosecond timescales, driven by the type-II band alignment that favors electron and hole separation. Electrons transfer to the layer with lower conduction band while holes accumulate in the layer with higher valence band. This rapid separation competes favorably with intralayer recombination, enabling efficient extraction of photogenerated carriers.
Photovoltaic devices exploit the charge separation to generate electrical power from absorbed light. The built-in potential at the heterojunction separates carriers without requiring external bias, producing photocurrent at zero applied voltage. Power conversion efficiencies remain modest compared to bulk semiconductors but continue improving with optimized device architectures and material quality.
The separated carriers can be extracted through graphene electrodes that provide Ohmic contact to both electrons and holes. Vertical heterostructures with graphene contacts above and below the active heterojunction enable efficient carrier collection while maintaining optical access for illumination. The atomically thin architecture minimizes carrier transport distances, reducing recombination losses.
Designer Optical Properties
Heterostructure assembly enables engineering of optical properties unachievable in individual materials. Stacking materials with different band gaps creates systems with multiple absorption edges and emission lines. Coupling between layers hybridizes electronic states, producing new spectral features that depend on layer sequence, thickness, and alignment.
Optical microcavities incorporating two-dimensional materials couple cavity photons with material excitations to form polaritons. Strong light-matter coupling produces Rabi splitting observable in reflectance spectra, with polariton properties controllable through cavity design and material selection. Exciton-polaritons in TMDC-based microcavities demonstrate coherent phenomena including stimulated scattering and potentially Bose-Einstein condensation.
Metasurfaces using patterned two-dimensional material heterostructures manipulate light through subwavelength structuring. The atomically thin active layers enable dynamic tuning through electrical gating impossible in bulk metasurfaces. Reconfigurable metalenses, beam steering devices, and holographic displays represent potential applications of tunable two-dimensional metasurfaces.
Twisted Bilayer Systems
Moire Physics
Twisted bilayer systems exhibit moire patterns when two layers are rotated relative to each other, creating a superlattice with periodicity determined by the twist angle. For small twist angles, the moire period can reach tens of nanometers, introducing a new length scale that profoundly affects electronic and optical properties. The local atomic registry varies across the moire unit cell, creating spatially modulated interlayer coupling.
The moire potential acts as a periodic perturbation that folds electronic bands into a reduced Brillouin zone and opens gaps at zone boundaries. Near specific "magic angles" around 1.1 degrees in twisted bilayer graphene, flat bands emerge where the electronic bandwidth approaches zero. These flat bands enhance electron correlation effects, leading to exotic phases including superconductivity and correlated insulating states.
Optical properties reflect the modified electronic structure, with new absorption features appearing at energies corresponding to flat band transitions. The strong spatial variation of local band structure across the moire pattern produces corresponding variations in local optical properties, observable through near-field microscopy and tip-enhanced spectroscopy.
Twisted TMDC Bilayers
Twisted bilayers of transition metal dichalcogenides create moire patterns that modulate excitonic properties across the superlattice. The variation in local atomic registry produces a moire potential for interlayer excitons, trapping them at specific locations within the pattern. Arrays of trapped excitons with regular spacing determined by the twist angle form spontaneously without lithographic patterning.
Single-photon emission from moire-trapped excitons has been observed, with the spatial periodicity of the moire pattern organizing the emitters into regular arrays. The twist angle provides a control parameter for adjusting the array periodicity and potentially the emission properties. This self-organized approach to quantum emitter arrays complements deterministic fabrication methods.
Collective phenomena among moire-trapped excitons become accessible when the trapping potential is strong enough to localize excitons but weak enough to allow tunneling between sites. Dipolar interactions between excitons in neighboring traps can produce correlated states analogous to those in quantum simulator platforms. The optical addressability of excitons enables both control and readout of such many-body states.
Twist-Angle Control and Characterization
Precise twist-angle control during heterostructure assembly determines the resulting moire period and associated properties. Alignment techniques using crystal edges, second-harmonic generation polarimetry, or atomic force microscopy imaging of flake orientations enable angle accuracy within a fraction of a degree. In situ rotation stages allow fine-tuning of the twist angle after initial assembly.
Characterizing the actual twist angle in fabricated devices requires techniques sensitive to the moire structure. Second-harmonic generation imaging reveals the moire period through its influence on the local nonlinear response. Scanning tunneling microscopy directly images the moire pattern with atomic resolution, though it requires conductive samples and ultra-high vacuum conditions.
Inhomogeneity in twist angle across a sample, arising from strain or fabrication imperfections, produces spatial variation in properties that must be accounted for in device design. Local strain can cause twist angle to vary continuously across a flake, creating a gradient in moire properties. Understanding and controlling this inhomogeneity remains important for reproducible device performance.
Exciton-Polaritons
Strong Light-Matter Coupling
Exciton-polaritons are hybrid quasiparticles formed when excitonic transitions couple strongly to confined photon modes in optical cavities. The coupling strength must exceed both exciton and photon decay rates to reach the strong coupling regime where the hybrid nature is clearly manifest. Two-dimensional materials with their large exciton binding energies and oscillator strengths are particularly favorable for achieving strong coupling at room temperature.
The strong coupling produces two polariton branches separated by the Rabi splitting, observable as an anticrossing in angle-resolved reflectance or photoluminescence spectra. The splitting magnitude indicates the coupling strength, with values exceeding 50 meV demonstrated in TMDC-based cavities. The polariton dispersion interpolates between photon-like and exciton-like character depending on the detuning between cavity mode and exciton resonance.
Cavity architectures for two-dimensional material polaritons include distributed Bragg reflector microcavities, open cavities with adjustable mirror spacing, and plasmonic nanocavities. Each architecture offers different trade-offs between mode volume, quality factor, and tunability. Plasmonic cavities achieve the smallest mode volumes for strongest coupling but suffer from significant ohmic losses.
Polariton Condensation
Polaritons can undergo Bose-Einstein condensation when sufficient population accumulates in low-energy states below a critical temperature. Unlike atomic condensates requiring ultracold temperatures, polariton condensates can form at elevated temperatures because the small polariton effective mass produces large thermal de Broglie wavelengths. Room-temperature condensation has been achieved in various material systems including organic semiconductors and, more recently, TMDC monolayers.
The condensate exhibits macroscopic coherence manifest as narrowing of the emission linewidth and long-range spatial coherence across the condensate extent. Interference patterns from different parts of the condensate demonstrate the phase coherence characteristic of condensed matter. The coherent emission constitutes polariton lasing, distinct from conventional lasing by its equilibrium or quasi-equilibrium character.
Polariton condensates in two-dimensional materials benefit from the strong exciton binding that maintains the bosonic character at room temperature. The valley degree of freedom in TMDCs adds additional richness, enabling valley-polarized condensates that emit circularly polarized light. Controlling the valley polarization through optical pumping or magnetic fields provides a route to chiral photonic devices.
Nonlinear Polariton Physics
The excitonic component of polaritons provides nonlinear interactions that pure photon systems lack. Polariton-polariton interactions arising from the underlying exciton-exciton interactions enable effects including bistability, soliton formation, and quantum correlations. The strength of these interactions makes polariton systems attractive platforms for studying nonlinear quantum optics and simulating interacting quantum systems.
Optical parametric oscillation in polariton systems converts pump photons into signal and idler polaritons through the nonlinear interaction. The process can be either stimulated by an existing population or occur spontaneously, generating entangled polariton pairs analogous to parametric down-conversion in nonlinear crystals. The strong interaction enhances the conversion efficiency compared to conventional nonlinear optical processes.
Polariton blockade, where the interaction energy shift prevents multiple polariton occupation of a mode, would enable single-polariton nonlinearity valuable for quantum information processing. Achieving this regime requires reducing the mode volume to enhance interactions while maintaining sufficient lifetime. Current research explores deeply subwavelength plasmonic cavities and moire-trapped exciton-polaritons as paths toward this goal.
Valley Photonics
Valley Optical Selection Rules
The two inequivalent K and K' valleys in monolayer TMDCs couple selectively to light of opposite circular polarization due to the combined effects of broken inversion symmetry and time-reversal symmetry. Right-circularly polarized light excites carriers in the K valley while left-circularly polarized light excites the K' valley, and vice versa for emission. This valley-dependent optical selection rule enables optical writing and reading of valley information.
The degree of circular polarization in emission reflects the valley polarization of the excited carrier population. Under circularly polarized excitation, emission maintains substantial circular polarization even at room temperature, indicating that valley depolarization is slower than radiative recombination. Factors affecting valley lifetime include intervalley scattering, exchange interactions, and sample quality.
Valley coherence, referring to the phase relationship between superposition states of K and K' valleys, produces linearly polarized emission with orientation depending on the coherent superposition. Creating and detecting valley coherence requires linearly polarized excitation and careful analysis of emission polarization. Valley coherence times provide information about dephasing mechanisms complementary to population relaxation studies.
Valley-Polarized Devices
Light-emitting devices that generate circularly polarized light without external optical elements exploit the valley optical selection rules. Electrical injection into a specific valley, achieved through spin-polarized contacts or magnetic field effects, produces emission with net circular polarization. Such valley-polarized LEDs could simplify optical systems requiring circular polarization for applications in displays, communications, and sensing.
Valleytronic transistors use the valley index as an information carrier analogous to charge in conventional electronics or spin in spintronics. Generating, manipulating, and detecting valley polarization electrically would enable new device paradigms exploiting this degree of freedom. Current research explores mechanisms for electrical valley injection and detection, facing challenges from the lack of direct valley-charge coupling.
Valley Hall effect, where carriers in opposite valleys deflect to opposite transverse directions in an electric field, provides a mechanism for spatial separation of valley populations. This effect arises from the Berry curvature associated with the valley electronic structure and occurs even without magnetic field. Exploiting the valley Hall effect for device functionality requires controlling the anomalous velocity contributions and detecting the resulting charge accumulation.
Magnetic Field Effects
Magnetic fields break time-reversal symmetry and lift the valley degeneracy through the valley Zeeman effect. The two valleys shift in opposite energy directions, with splitting proportional to the applied field and an effective g-factor that differs from the free electron value. Fields of several Tesla produce splittings of several millielectronvolts, sufficient to polarize valley populations at cryogenic temperatures.
The magnetic circular dichroism arising from valley Zeeman splitting enables wavelength-selective valley excitation that depends on the applied field. Tuning the excitation wavelength to the energy of one valley while detuning from the other enhances the achievable valley polarization. Combined with temperature control of thermal valley population, substantial valley polarization can be achieved.
Proximity effects from magnetic substrates can induce effective magnetic fields in adjacent two-dimensional materials without external field application. Ferromagnetic insulators including EuS and CrI3 have demonstrated proximity-induced valley splitting in nearby TMDC layers. This approach could enable local control of valley properties through patterned magnetic structures.
Strain Engineering
Effects of Strain on Optical Properties
Mechanical strain modifies the electronic band structure of two-dimensional materials, shifting band edges and modifying optical transition energies. Tensile strain generally reduces band gaps while compressive strain increases them, with sensitivity coefficients of tens of millielectronvolts per percent strain. This strain sensitivity enables continuous tuning of emission and absorption wavelengths through mechanical deformation.
The relationship between strain and optical properties can be highly anisotropic, particularly for materials like black phosphorus with strongly direction-dependent electronic structure. Uniaxial strain along specific crystallographic directions produces different effects than strain along other directions or biaxial strain. Understanding the strain tensor coupling to optical properties enables targeted modification through controlled deformation.
Exciton binding energies also respond to strain through modifications of dielectric screening and effective masses. The competition between band gap shifts and binding energy changes determines the net effect on excitonic transition energies. In some cases, these effects partially compensate, while in others they add constructively to enhance tunability.
Strain-Induced Single-Photon Emitters
Localized strain creates potential wells that trap excitons, producing discrete emission lines characteristic of single-quantum emitters. Nanostructures including pillars, ridges, and edges concentrate strain in adjacent two-dimensional materials, defining the locations where emitters form. The emission wavelength correlates with local strain magnitude, providing a route to wavelength-controlled quantum light sources.
Deterministic positioning of strain-induced emitters enables integration with photonic structures for enhanced extraction efficiency and controlled emission properties. Placing emitters at antinodes of optical cavities enhances the Purcell factor and emission rate. Arrays of regularly positioned emitters could provide multiple sources for quantum information applications requiring identical photons.
The strain-emission relationship allows wavelength tuning of individual emitters through in situ strain modification. Piezoelectric actuators or flexible substrates provide dynamic control over the strain environment, shifting emission wavelengths by tens of nanometers. This tunability enables matching emission wavelengths between different emitters or to cavity resonances for strong coupling.
Funneling and Guiding Excitons
Strain gradients create energy gradients that drive exciton drift toward regions of maximum tensile strain where the band gap is reduced. This exciton funneling concentrates optical excitation into defined regions, potentially enabling efficient light harvesting and localized emission. Engineered strain profiles can guide excitons along designed paths to collection points.
Wrinkles and bubbles in two-dimensional materials create strain distributions that naturally funnel excitons. The curved geometry at bubble edges produces large strains that attract excitons from surrounding flat regions. Understanding and controlling these naturally occurring strain features provides insights applicable to deliberately engineered structures.
The combination of strain funneling with heterostructure band alignment enables sophisticated control over carrier dynamics. Excitons funneled to specific locations can then transfer across heterojunctions for charge separation or emission. This multistep process could enhance efficiency in photovoltaic or light-emitting devices by spatially separating absorption and conversion functions.
Electrostatic Tuning
Gate-Tunable Optical Properties
Electrostatic gating controls the carrier density in two-dimensional materials, modifying optical properties through band filling, many-body effects, and screening. In graphene, gating shifts the Fermi level, controlling the onset of Pauli blocking and enabling electroabsorption modulation across a broad spectral range. In TMDCs, gating modifies exciton binding energies and creates charged exciton species with distinct spectral signatures.
The formation of trions, charged exciton complexes, upon doping produces new absorption and emission features distinct from neutral excitons. Trion emission can dominate under heavy doping, shifting the photoluminescence spectrum and modifying quantum yield. Controlling the trion population through gating enables switching between neutral and charged exciton regimes with different optical properties.
Many-body interactions among carriers modify the optical response beyond single-particle effects. Band gap renormalization at elevated carrier densities shifts absorption edges, while screening weakens exciton binding. These competing effects determine the net response to gating, which can be non-monotonic as carrier density increases.
Ionic Gating
Ionic liquid or polymer electrolyte gates achieve higher carrier densities than solid dielectric gates by forming electric double layers at the material surface. Carrier densities exceeding 10^14 per square centimeter are achievable, sufficient to access phenomena including superconductivity and insulator-metal transitions. The high capacitance of the double layer produces these densities at modest gate voltages.
Optical properties under ionic gating span from intrinsic through heavily doped regimes, enabling study of evolution with carrier density. The gradual filling of bands can be tracked through spectroscopic measurements, revealing the development of Fermi edge singularities and many-body effects. Comparison with theoretical predictions tests understanding of the underlying physics.
Practical considerations for ionic gating include the slow switching speed limited by ion mobility and the operational temperature range constrained by electrolyte properties. Solid polymer electrolytes offer improved stability compared to ionic liquids at the cost of somewhat reduced capacitance. Integration with device structures requires careful design to prevent electrolyte degradation and ensure reproducible operation.
Ferroelectric Gating
Ferroelectric substrates or gate dielectrics provide non-volatile doping through their remnant polarization. The polarization-induced surface charge persists without applied voltage, enabling memory functionality where optical properties depend on the ferroelectric state. Switching the ferroelectric polarization toggles between different doping levels and corresponding optical responses.
Local polarization writing using scanning probe techniques creates patterned doping profiles in adjacent two-dimensional materials. The spatial resolution approaches the ferroelectric domain wall width, enabling nanoscale definition of optical property variations. Lateral p-n junctions and more complex doping patterns can be written and erased through polarization manipulation.
Combining ferroelectric gating with other tuning mechanisms provides multiple control parameters for complex device functionality. The non-volatile ferroelectric state sets a baseline while additional electrostatic or optical modulation provides dynamic control. Such multi-parameter devices could implement reconfigurable optical functions or serve as memory elements in optical information processing.
Photodetectors
Device Architectures
Two-dimensional material photodetectors span diverse architectures optimized for different performance metrics. Photoconductors use a single channel material with ohmic contacts, relying on photogenerated carriers to modify conductivity. Phototransistors add a gate electrode for additional control and potential gain through photogating effects. Photodiodes use heterojunctions or Schottky contacts to create built-in fields for photovoltaic operation.
Vertical heterostructure photodetectors stack active layers between transparent electrodes, maximizing absorption while maintaining short carrier transit distances. The vertical geometry simplifies achieving uniform fields across the active region compared to lateral devices where fringe effects complicate the electric field distribution. Graphene electrodes provide the combination of transparency and conductivity needed for efficient carrier extraction.
Waveguide-integrated photodetectors place two-dimensional materials in the evanescent field of guided optical modes, increasing interaction length for improved absorption. This approach is particularly valuable for graphene detectors where single-pass absorption is limited. The integration with silicon photonics platforms enables hybrid systems combining silicon waveguiding with two-dimensional material detection.
Performance Metrics
Responsivity measures the photocurrent produced per unit incident optical power, with units of amperes per watt. High responsivity requires efficient absorption and carrier collection, with possible gain through photoconductive or photogating mechanisms. Values ranging from milliamperes per watt for simple graphene devices to thousands of amperes per watt for optimized phototransistors have been demonstrated.
Detectivity normalizes responsivity by noise to quantify the minimum detectable signal, enabling comparison between devices of different areas and bandwidths. The specific detectivity D* accounts for the noise equivalent power and provides a figure of merit for comparing detection capability. Two-dimensional material detectors achieve D* values approaching commercial infrared detectors in favorable cases.
Response speed determines the bandwidth available for detecting modulated signals or fast transient events. Intrinsic carrier lifetimes in two-dimensional materials are typically picoseconds to nanoseconds, enabling terahertz bandwidths in principle. Practical device speeds are often limited by RC time constants of contact resistances and parasitic capacitances rather than intrinsic material properties.
Spectral Range and Tunability
The diverse band gaps across the two-dimensional materials family enable photodetection spanning ultraviolet through far-infrared wavelengths. Wide band gap materials including hBN detect in the ultraviolet. TMDCs cover the visible and near-infrared through their excitonic transitions. Black phosphorus extends into the mid-infrared. Graphene detects across this entire range due to its gapless band structure.
Wavelength selectivity through band gap engineering tailors response to specific spectral regions. Layer number variation in black phosphorus and TMDCs shifts the band edge, while composition variation in alloy systems provides additional tunability. Integration of different materials in heterostructure devices can create multispectral detectors with separate channels for different wavelength bands.
Dynamic tunability through electrostatic gating modifies the spectral response during device operation. Shifting the Fermi level in graphene controls the onset of interband absorption. Modifying exciton energies in TMDCs shifts spectral features. This electrical tunability enables reconfigurable detection capabilities and potentially hyperspectral imaging without mechanical filter wheels.
Modulators
Electroabsorption Modulators
Graphene electroabsorption modulators control light transmission through gate-induced Fermi level shifts that modify interband absorption. The broadband operation spans visible through infrared wavelengths where interband transitions are relevant. Modulation depths exceeding 10 dB have been achieved with bandwidths approaching 40 GHz, competitive with conventional semiconductor modulators.
Device optimization balances extinction ratio against insertion loss and power consumption. Longer interaction lengths increase modulation depth but add absorption and device capacitance. Double-layer graphene structures enable push-pull operation where both layers contribute to modulation, improving performance for given device dimensions.
TMDC-based electroabsorption modulators exploit the gate-dependent excitonic absorption, achieving strong modulation at specific wavelengths corresponding to exciton resonances. The narrow spectral features provide wavelength selectivity but limit broadband operation. Combining multiple TMDC layers with different band gaps could extend the operational wavelength range.
Phase Modulators
The real part of the refractive index in two-dimensional materials also responds to gating, enabling phase modulation for interferometric devices. Graphene phase shifters provide tens of degrees of phase shift per micrometer of interaction length with voltage swings of a few volts. This strong electrorefractive effect arises from the Kramers-Kronig relation between absorption and refractive index changes.
Mach-Zehnder modulators incorporating graphene phase shifters convert phase modulation to amplitude modulation through interference. The inherent trade-off between modulator length and capacitance that limits speed in all modulators applies here, though the strong effect in graphene enables shorter devices than required with weaker electrorefractive materials.
Ring resonator modulators use graphene-induced phase shifts to tune resonance conditions, switching transmission between on-resonance and off-resonance states. The resonant enhancement concentrates the modulation effect at specific wavelengths, enabling high extinction ratios with modest phase shifts. Wavelength-division multiplexed systems could use arrays of ring modulators at different resonance wavelengths.
All-Optical Modulation
All-optical modulation in two-dimensional materials uses intense control beams to modify the transmission of weaker signal beams through saturable absorption and other nonlinear effects. The ultrafast carrier dynamics enable femtosecond switching speeds far exceeding electrical modulation. Applications include pulse shaping, optical switching, and signal regeneration.
Saturable absorption occurs when intense light bleaches the absorption by filling available electronic states. The absorption recovers as carriers relax, with timescales ranging from femtoseconds for carrier thermalization to picoseconds for recombination. The saturation intensity depends on material and wavelength, with graphene exhibiting low saturation intensity due to its limited density of states.
Cross-phase modulation uses the refractive index change induced by a control beam to modify the phase of a co-propagating signal. The large nonlinear index coefficient of two-dimensional materials produces significant phase shifts at moderate intensities. Cascading multiple stages or using resonant enhancement can achieve the large phase shifts needed for practical optical processing.
Light Sources
Electroluminescent Devices
Light-emitting devices based on two-dimensional materials achieve electroluminescence through electrical injection of carriers that recombine radiatively. TMDC monolayers with their direct band gaps and strong exciton emission are the primary candidates for efficient light sources. Device architectures must address the challenges of injecting both electrons and holes into the atomically thin active layer.
Vertical tunnel junctions with graphene electrodes separated from the TMDC by thin hBN tunnel barriers provide controlled injection. The tunnel barriers prevent direct graphene-TMDC contact that would quench emission through fast charge transfer. Adjusting the injection balance through asymmetric barriers or applied bias optimizes radiative efficiency.
Lateral p-n junctions created through split gates that locally dope adjacent regions enable current flow through the junction where electrons and holes recombine. The emission localizes at the junction, potentially enabling defined pixel locations for display applications. External quantum efficiencies approaching 10% have been demonstrated, comparable to organic LEDs.
Single-Photon Sources
Localized emitters in two-dimensional materials produce antibunched photon streams characteristic of single-quantum emitters. Sources in hBN operate at room temperature with high brightness, while TMDC-based emitters typically require cryogenic conditions for optimal purity. The visible emission wavelengths of these sources complement infrared sources based on semiconductor quantum dots.
Creating emitters at controlled locations enables integration with photonic structures for enhanced performance. Strain engineering using nanopatterned substrates positions emitters deterministically, while the surrounding photonic crystal or cavity structure modifies the emission rate and collection efficiency. Site-controlled emitters eliminate the need for statistical searching to find suitable sources.
Indistinguishability of photons from two-dimensional material emitters remains less developed than for established platforms like quantum dots. Spectral diffusion and phonon coupling degrade indistinguishability, requiring optimization of the local environment and potentially dynamic feedback to lock emission wavelengths. Progress in this area will determine suitability for quantum information applications requiring photon interference.
Plasmonic Light Sources
Electrical excitation of graphene plasmons produces mid-infrared emission through intraband carrier heating. When current flows through a constriction, carriers accelerate and emit plasmons that can couple to free-space radiation through antenna structures. This mechanism provides an electrically driven mid-infrared source using only graphene and metallic contacts.
The emission spectrum is broad, reflecting the thermal distribution of hot carriers, with intensity increasing at higher current densities. The spectral peak can be tuned through the plasmonic resonance of the antenna structure and the gated carrier density in the graphene. Nanosecond switching times enable modulated emission for communications or time-resolved spectroscopy.
Thermal emission from electrically heated two-dimensional materials provides another route to light generation, with the emission spectrum determined by the material temperature and emissivity. The rapid thermal response of atomically thin materials enables fast modulation of thermal emission. Selective emitters exploiting plasmonic resonances can narrow the emission spectrum below the blackbody limit.
Nonlinear Optics
Second-Harmonic Generation
Second-harmonic generation (SHG) in two-dimensional materials produces light at twice the frequency of the incident fundamental beam. Broken inversion symmetry is required for SHG, present in odd-layer TMDCs but absent in centrosymmetric graphene and even-layer stacks. The SHG signal provides a sensitive probe of layer number, crystal orientation, and stacking order.
The second-order susceptibility of monolayer TMDCs is among the largest known, producing strong SHG from atomically thin samples. Resonant enhancement occurs when fundamental or harmonic frequencies match excitonic transitions, increasing conversion efficiency by orders of magnitude. The enhancement is accompanied by increased sensitivity to sample quality and environmental conditions.
Mapping SHG across samples reveals spatial variations in crystal properties that are otherwise difficult to detect. Domain boundaries, strain distributions, and stacking faults all modify the local SHG response. This characterization capability complements structural techniques like electron microscopy while providing information about electronic structure relevant to device performance.
Third-Order Nonlinearities
Third-order nonlinear processes including third-harmonic generation, four-wave mixing, and the optical Kerr effect occur in all materials regardless of symmetry. Graphene exhibits particularly strong third-order response due to its unique band structure, with nonlinear coefficients exceeding those of typical bulk materials by orders of magnitude. The combination of strong nonlinearity and ultrafast response makes graphene attractive for nonlinear photonic devices.
Four-wave mixing in graphene enables wavelength conversion and signal processing functions. Two pump photons combine with a signal photon to generate an idler at a new wavelength determined by energy conservation. The conversion efficiency depends on pump intensity and phase matching conditions, with demonstrations showing practical conversion levels in waveguide-integrated devices.
The optical Kerr effect produces intensity-dependent refractive index changes useful for self-phase modulation, cross-phase modulation, and optical switching. The large Kerr coefficient of graphene enables significant phase shifts at modest intensities, though the accompanying absorption complicates purely phase-based applications. Two-photon absorption also occurs at sufficient intensity, providing another nonlinear mechanism with applications in saturable absorption and limiting.
High-Harmonic Generation
High-harmonic generation (HHG) produces coherent radiation at many multiples of the driving laser frequency through highly nonperturbative electron dynamics. Two-dimensional materials support HHG with distinct characteristics arising from their confined geometry and modified band structure. The combination of strong in-plane fields and reduced dimensionality creates favorable conditions for efficient harmonic production.
Graphene HHG shows unusual scaling with driver intensity and polarization dependence reflecting the Dirac cone band structure. The harmonics encode information about carrier dynamics on attosecond timescales, providing a probe of ultrafast processes in the material. Theoretical understanding continues developing as experiments explore different driving conditions and material systems.
HHG from TMDCs and other two-dimensional semiconductors exhibits resonant enhancement when harmonics coincide with excitonic features. The interplay between intraband and interband contributions creates complex spectral and temporal structure in the emitted harmonics. Exploiting these effects for controlled extreme ultraviolet light sources remains an active research direction.
Applications in Mode-Locking
Saturable absorbers based on two-dimensional materials enable passive mode-locking of lasers across wavelengths from visible through mid-infrared. Graphene provides the broadest spectral coverage due to its gapless absorption, with demonstrated mode-locking from 800 nm to beyond 3 micrometers. TMDCs and black phosphorus offer saturable absorption at wavelengths matched to their respective band gaps.
The fast recovery time of two-dimensional material saturable absorbers supports generation of ultrashort pulses. Carrier thermalization on tens of femtoseconds sets the initial absorption recovery, while full recovery occurs on picosecond timescales. This fast-slow double response provides both pulse shaping and stabilization against Q-switching instabilities.
Integration of saturable absorbers into laser cavities takes various forms including direct deposition on cavity mirrors, embedding in polymer films, and coupling to waveguide lasers. The mechanical flexibility of two-dimensional materials enables conformal coating of curved surfaces. Reliable, low-cost saturable absorbers based on solution-processed materials could enable widespread adoption of mode-locked lasers.
Conclusion
Two-dimensional materials have established themselves as a powerful platform for photonics, offering unique properties unavailable in conventional bulk or thin-film materials. The atomic-scale thickness provides ultimate optical confinement and interaction strength, while the diverse family of materials covers wavelengths from ultraviolet through far-infrared. Electrical tunability through gating enables dynamic control of optical properties that would require complex external components in traditional photonic systems.
The field continues advancing rapidly on multiple fronts. Device performance metrics improve as materials quality increases and device architectures are optimized. New materials join the two-dimensional family, expanding the available property space. Heterostructure engineering creates designer optical responses through controlled layer stacking. These advances translate into demonstrated devices including high-speed photodetectors, efficient modulators, quantum light sources, and mode-locked lasers.
Challenges remain in achieving the reproducibility and scalability needed for widespread application. Large-area synthesis with controlled properties, reliable device fabrication at scale, and integration with existing photonic platforms all require continued development. Stability under ambient conditions and long-term reliability must be demonstrated for practical devices. Addressing these challenges will determine how broadly two-dimensional materials photonics impacts technology beyond the laboratory.