Nonlinear optics

In plain words

Light changing colour as it passes through a material. Normally a material responds in proportion to the light falling on it, and the colour stays the same. With intense light, such as a laser pulse, part of the response follows the square or the cube of the light’s field, and new colours appear: light at twice or three times the frequency, or pairs of split from one. Thin layers convert little simply because they are thin, but some are so strongly nonlinear for their thickness that they are studied as chip-sized frequency converters and sources of entangled photons.

As the site uses it

The device interest is a naturally polar, chemically stable semiconductor for compact nonlinear optics and photodetection.

RhSeCl, RhTeCl · Rhodium chalcohalides

The mixed bonding breaks symmetries that simpler compounds keep, giving polar Janus semiconductors, giant spin splitting, ferroelectric layers, exceptionally strong nonlinear optics and layered photocatalysts.

The materials

Going deeper

Intense light drives a response in the square and the cube of its field, and new frequencies appear. The square term needs a crystal without a centre of inversion – only ferroelectric NbOI₂, not TaOI₂, doubles the frequency – while the cube term does not. Run backwards, the square term splits one photon into an entangled pair.

Beyond proportional

In everyday optics the electrons of a material follow the light’s electric field in step, and the light that comes out has the colour that went in. Push harder, with the field of a focused laser pulse, and the response gains parts that grow with the square and the cube of the field. Those parts oscillate at twice and three times the light’s frequency, so a material lit at 1560 nm can give light at 780 and at 520 nm.

The square term needs a crystal without a centre of inversion – in a symmetric crystal it cancels – which is why doubles as a test of symmetry. The cube term has no such condition. Of the oxide iodides NbOI₂ and TaOI₂, only NbOI₂ gives second-harmonic light, while both give third-harmonic light about as efficiently as a of WS₂, growing as the square of the thickness up to about 30 nm (Tang and colleagues, 2024).

Thin but strong

Conversion builds up as light travels through a crystal, as long as the light it generates keeps in step with the light that makes it; over a coherence length, often a few micrometres, the two drift apart and the gain reverses – the reason bulk converters need phase matching. A layer a few nanometres thick never gets that far, so it needs no phase matching at all, but it also has almost no length to convert in, and its output stays small.

Some layered crystals are so strongly nonlinear for their thickness that the trade is still attractive, and stacking can recover part of the length: in twisted stacks of -MoS₂ arranged so that the generated light keeps adding up, frequency doubling and photon-pair generation were both enhanced (Tang and colleagues, 2024). Bulk crystals of the same family are already in use: GaSe is an established crystal for generating radiation and converting infrared light.

Pairs of photons

Run backwards, the square term splits one photon into two of lower energy, born together – spontaneous parametric down-conversion, the standard source of entangled photons. Thin layers make such a source microscopic. boron nitride, free of the strong light emission that limits 2D , gave more than 120 coincident pairs per second, with a coincidence-to-accidental ratio above 200, entangled in polarisation, with the entangled state chosen by turning the pump’s polarisation (Liang and colleagues, 2025).

Ferroelectric layers add a possible switch: their second-order response follows their polarisation, so reversing it electrically could reverse the response – one of the open questions for the oxide .

For specialists

Optical response beyond linear order in the field, P = ε₀(χ⁽¹⁾E + χ⁽²⁾E² + χ⁽³⁾E³ + …). Second-order processes – second-harmonic and sum-frequency generation, spontaneous parametric down-conversion – need symmetry; third-order ones – third-harmonic generation, the optical – occur in any material. Layers much thinner than the coherence length need no phase matching but convert weakly; stacking can compensate, as in twisted 3R-MoS₂ stacks that quasi-phase-match frequency doubling and photon-pair generation. Rhombohedral BN, free of the that limits 2D semiconductors, gives polarisation-entangled photon pairs whose Bell state is set by the pump polarisation.

Where this comes from

Third harmonic generation in thin NbOI₂ and TaOI₂ Tang et al. · Nanomaterials 14, 412 (2024) cited by 17
Quasi-phase-matching enabled by van der Waals stacking Tang et al. · Nature Communications 15, 9979 (2024)
Tunable polarization entangled photon-pair source in rhombohedral boron nitride Liang et al. · Science Advances 11, eadt3710 (2025)

In the news

The newest items in the site’s news feed that use the term, one from each source.

Journal 19 Oct 2026 Nano Letters

Nonlinear Optical Fingerprints of Defects in Hexagonal Boron Nitride

Hexagonal boron nitride (h-BN) defects are promising building blocks for quantum and , yet their nonlinear optical signatures remain poorly understood. We use calculations to determine the polarization-resolved linear, second-order, and third-order susceptibilities of multilayer h-BN…

ExperimentTheoryhBN

Journal 17 Oct 2026 Journal of Materials Chemistry C

Investigation of broadband nonlinear optical absorption and refraction properties of 2D Mo 2 Ga 2 C and Mo 2 C nanosheets

The Mo 2 C and Mo 2 Ga 2 C were synthesized through and (LPE), utilizing multilayer Mo 2 Ga 2 C as the precursor. The...

Experiment

Journal 10 Oct 2026 Advanced Functional Materials

Optical Signature of Moiré Superlattices Formed by Twisted SrTiO3 Membranes

formed at the interfaces of mismatched lattices have attracted significant interest over the past decade due to their large tunability of band parameters and interactions among electrons, , and lattices. Superlattices made from twisted perovskite oxides may have strong structure and potential…

Experiment

Search the news for this term

Photon

The smallest possible amount of light – one indivisible packet of it. The packets of a given colour all carry the same energy, and blue ones carry more than red: that is why ultraviolet light gives you sunburn and red light, however bright, does not. A semiconductor absorbs only photons with enough energy to cross its band gap and gives light back at about the gap’s energy – which is why LEDs of different colours are made from different semiconductors.

The quantum of the electromagnetic field, with energy E = hν and momentum h/λ but no mass or charge. Visible photons carry about 1.7–3.1 eV, comparable to the band gaps of semiconducting TMDCs, but a momentum far smaller than the crystal momenta across the Brillouin zone, so optical transitions are vertical and an indirect gap needs a phonon to make up the difference. Single-photon emission is established by antibunching in photon-correlation measurements.

Full explanation

Second-harmonic generation (SHG)

Shine intense light on a crystal and a little of it comes back at exactly twice the frequency – half the wavelength, which is how a green laser pointer turns invisible infrared into green light. It happens only if the crystal has no centre of symmetry, which makes it a quick, contactless test of symmetry, layer number and crystal orientation.

A second-order nonlinear response, forbidden in centrosymmetric media, so in 2H TMDCs it appears for odd layer numbers and vanishes for even ones. The polarisation dependence gives crystal orientation, and so the twist angle in a stack; the intensity follows layer number and strain; and it detects broken inversion symmetry in ferroelectric and magnetic layers where no other quick probe exists.

Full explanation

Ferroelectricity

A material that holds an electric polarisation – one side slightly positive, the other slightly negative – with no voltage applied, and that can be flipped by a large enough field – the coercive field – and stay flipped. That memory of the last field applied is what makes it useful for storing data.

A spontaneous, switchable electric polarisation produced by a structural distortion that breaks inversion symmetry. In 2D the usual obstacle – depolarising fields destroying the polarisation as a film thins – is sidestepped in three ways: in-plane polarisation, layered compounds whose dipoles survive to the monolayer such as CuInP₂S₆ and In₂Se₃, and sliding ferroelectricity, where the polarisation belongs to the interface between layers rather than to the layers themselves.

Full explanation

Terahertz (THz)

Light that vibrates about a trillion times a second, between microwaves and infrared. Its photons carry only a few thousandths of an electronvolt – the energies of lattice vibrations and of free charges being jostled – so terahertz light can measure how well a 2D layer conducts without touching it. It has long been hard to make and to detect, a stretch of the spectrum called the terahertz gap, and 2D materials are studied as new sources, detectors and switches for it.

Electromagnetic radiation of roughly 0.1–10 THz: wavelengths from 3 mm to 30 µm, photon energies from 0.4 to 40 meV (1 THz ≈ 4.1 meV ≈ 33 cm⁻¹). Time-domain spectroscopy records the transmitted field in amplitude and phase, so the complex sheet conductivity of a monolayer follows without contacts, and a Drude fit gives its Drude weight and scattering time, and from them carrier density and mobility; with an optical pump it follows photocarriers on picosecond scales. Interlayer shear and breathing modes, superconducting gaps, antiferromagnetic magnons and graphene plasmons all fall in this window. Graphene and Dirac semimetals serve as broadband detectors and gate-tuned modulators, and ferromagnet/heavy-metal bilayers, in which 2D layers such as PtTe₂ can replace the heavy metal, turn femtosecond pulses into terahertz bursts through the inverse spin Hall effect.

Full explanation

Bernal and rhombohedral stacking

The two ways graphene sheets usually sit on one another in graphite. In Bernal, or AB, stacking every second layer lines up with the one two below it; in rhombohedral, or ABC, stacking each layer is shifted the same way as the one before, so the pattern repeats only every third layer. Natural graphite is mostly Bernal with some rhombohedral regions, and the difference matters: a few rhombohedral layers have very flat electron bands, and such flakes have turned out to superconduct and to hold unusual kinds of magnetism.

The two common stacking sequences of graphene layers: Bernal (AB, hexagonal graphite) and rhombohedral (ABC), which differ in the lateral position of every third layer; 3R TMDCs follow the same rhombohedral sequence. In the simplest model the low-energy bands of N-layer ABC graphene disperse as the Nth power of momentum and sit on the two outer layers, so they flatten with thickness and a perpendicular displacement field opens a tunable gap; Bernal multilayers instead decompose into bilayer-like bands plus, for odd N, a monolayer-like one. Rhombohedral stacking is metastable and relaxes to Bernal under heat, strain or processing.

Full explanation

Chalcogenide, halide and pnictide

Family names for compounds, taken from the element in them that carries the negative charge. Chalcogenides contain sulfur, selenium or tellurium; halides contain fluorine, chlorine, bromine or iodine; pnictides contain phosphorus, arsenic, antimony or bismuth. Most layered crystals belong to one of these families, and the catalogue groups many of them that way.

Compounds named for their most electronegative constituent: chalcogenides of group 16 (S, Se, Te; oxides are conventionally counted apart), halides of group 17 (F, Cl, Br, I) and pnictides of group 15 (P, As, Sb, Bi; nitrides usually keep their own name). Down each group the anion grows larger and less electronegative, so bonding turns more covalent, gaps shrink and spin–orbit coupling grows. Chalcogenides give the MX₂ semiconductors and metals, halides mostly ionic, often magnetic insulators built from edge-sharing octahedra, and pnictides many metals, semimetals and the parents of the iron-based superconductors; mixed-anion compounds such as oxychalcogenides and chalcohalides combine two.

Full explanation

Silicon photonics

Guiding light instead of electricity through tiny channels on a silicon chip, made with the same factories and tools as ordinary computer chips. Light carries data faster and with less loss over distance, so such chips already connect the servers in data centres. Silicon itself is poor at a few jobs: it hardly emits light, cannot detect the infrared light used in fibre networks, and switches light only weakly. 2D materials laid on top of the light channels are one way to add the missing functions.

Photonic integrated circuits in silicon-on-insulator, in which submicron silicon waveguides, with their high index contrast to the buried oxide, route light at telecom wavelengths through splitters, rings and gratings made with CMOS tools; germanium detectors and silicon carrier-depletion modulators are standard, and lasers are bonded or grown from III–V semiconductors. 2D materials couple to the evanescent field of the waveguide: graphene gives broadband, fast modulators and photodetectors that can be integrated at wafer scale, thin MoTe₂ and black phosphorus emit and detect in the near infrared, and low-loss phase-change Sb₂S₃ and Sb₂Se₃ give non-volatile switches and tuning. The obstacles are wafer-scale transfer or growth, contacts, optical loss and reproducibility to foundry standards.

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Sensor

A device that turns something in its surroundings – a gas, a magnetic field, a pressure, a molecule in blood – into an electrical signal. 2D materials make unusually sensitive sensors because every atom is on the surface: a few molecules landing on a single layer change how well it conducts. Graphene also makes very good magnetic-field sensors. The hard part is not sensitivity but selectivity – responding to one thing and ignoring everything else – and staying stable for years.

Transducers in which a stimulus changes an electrical property of a 2D layer: chemiresistive and field-effect gas and humidity sensors, in which adsorbates transfer charge and shift the conductance (graphene registered single NO₂ molecules in 2007); Hall sensors, in which graphene’s low carrier density and high mobility give a large, temperature-stable Hall voltage; biosensors with receptors on a graphene or MoS₂ channel that bind target molecules; and strain, pressure and light sensors. Sensitivity comes from the all-surface geometry and the low density of states; the limits are selectivity, drift and hysteresis from humidity and contamination, recovery time, device-to-device variation and calibration, addressed by functionalisation, encapsulation and arrays read by pattern recognition.

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Density functional theory (DFT)

The workhorse calculation of materials physics. Rather than following every electron, it works with the electron density and a recipe for how electrons avoid one another – which makes a whole crystal cheap enough to compute, and makes the accuracy depend entirely on that recipe.

Ground-state electronic structure from the density, exact in principle by Hohenberg–Kohn and made practical by the Kohn–Sham equations with an approximate exchange–correlation functional. Two dimensions need care: a vacuum gap wide enough that periodic images stop interacting or a truncated Coulomb interaction, a dispersion correction for interlayer binding, and the knowledge that semi-local functionals underestimate gaps – hybrid functionals narrow that error at far higher cost, and quantitative gaps and optical spectra need GW and Bethe–Salpeter on top.

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Etching

Removing material on purpose, with a chemical or a plasma. In chip-making it carves patterns: a stencil of light-sensitive polymer protects some areas while a plasma eats away the rest. For 2D materials etching has three jobs: cutting flakes into shaped devices, thinning a crystal one layer at a time, and – for MXenes – making the material in the first place. There it dissolves one kind of atom out of a layered ceramic so that the remaining sheets come apart.

Material removal by chemical reaction in a liquid (wet etching) or by reactive and physical processes in a plasma (dry etching, including reactive ion etching with oxygen-, fluorine- or chlorine-based chemistries, and atomic layer etching). For 2D materials it patterns channels and Hall bars through resist masks – oxygen plasma for graphene, fluorine-based plasmas for hBN and TMDCs – exposes edges in encapsulated stacks for edge contacts, thins crystals layer by layer, and selectively removes the A element, usually aluminium, from MAX phases with hydrofluoric acid or fluoride-containing acids to make MXenes. Its side effects are edge roughness and damage, residues, doping and plasma-induced defects in neighbouring layers, so the etched edge and its electronic states have to be considered in narrow devices.

Full explanation

Spin

A built-in property of every electron that makes it a tiny magnet. Measure it along any direction and you only ever find one of two answers, ‘up’ or ‘down’. Despite the name, nothing is actually spinning – the word stuck from an early picture – but the magnetism is real: countless electron spins lined up are what make a fridge magnet stick. Spintronics tries to carry information in spin rather than in charge.

The intrinsic angular momentum of the electron, ħ/2, with a magnetic moment of almost exactly one Bohr magneton; a measurement along any axis yields one of two values. In solids spin couples to orbital motion through spin–orbit coupling and to other spins through exchange; in 2D materials it sets magnetic order, spin–valley locking and how long a spin survives as a carrier of information.

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