# The thinnest optical amplifier ever

## 1 Ultrafast lasers

The famous French painter Théodore Géricault (1791-1824), pioneer of the Romantic movement, was fascinated by horses. One of his paintings titled Le Derby de 1821 à Epsom, shown in fig.1, depicts a horse race. Géricault paints horses at full gallop with the front legs extended forward and the hind legs extended to the rear, and all feet off the ground. This representation of the horse galloping phase, which is commonly found in early 19th century paintings, cannot be verified by visual inspection, due to the phenomenon of the persistence of vision, causing the brain to retain images cast on the retina for approximately 20 milliseconds.

When in 1878, Eadweard Muybridge invented flash photography, he started experimenting with twelve different cameras, taking pictures of a galloping horse, shown in fig. 2, with exposure times of 1 millisecond. Are galloping horses really exhibiting front and hind legs extended outwards as Géricault painted? The human eye is not able to break down the action at the quick gaits of the gallop. But Muybridge could go beyond the human eye and freeze the horse motion, i.e. resolve the gallop with enough temporal resolution to claim that during the jump horse’s legs are gathered together and not spread out (red frame in fig. 2).

In the end, what Géricault had previously painted was wrong.

Few decades after these pioneering flash photography experiments, stroboscopic photography was invented by Harold Edgerton at MIT, and it finally became possible to freeze even faster motions, like a bullet passing through an apple, or the fall of a water droplet, which is as fast as a microsecond (10–6 s).

What if we want to look at much less massive objects? Can we use similar principles to take pictures of molecules in motion? Atoms within molecules move with an approximate speed $v\sim 10^3$ m/s and their motion occurs over a typical length scale corresponding to the inter-atomic distance $d\sim 10^{–10}$m. Therefore, the required temporal resolution is

$\Delta t = d/v = 10^{-13}\mathrm{s} = 100$ fs.

Light-induced conformational changes in molecules (or in more complex systems) and also chemical reactions thus occur on a femtosecond (1 fs = 10–15 s) time scale. Electronics, which is limited to gigahertz bandwidths, i.e. sub-nanosecond time-scales, is not fast enough to allow monitoring such dynamics. In order to freeze the molecular motion we should use a “camera” with a flash of light lasting not more than 100 fs. Indeed, if a scene is illuminated for a time much longer than the relevant motion, then the scene becomes blurred and it is not possible to visualise the characteristic dynamics. Does such a special ultrafast camera exist?

The invention of the LASER (acronym for Light Amplification by Stimulated Emission of Radiation) in 1960 by Theodor Maiman, followed by the discovery of the mode-locking regime in 1965, made these ultrashort light flashes real. Nowadays, lasers can be exploited to record movies of molecular motions. An ultrashort laser pulse indeed can provide the femtosecond shutter speed that allows to freeze the motion of atoms within molecules. In other words, the ultrashort light pulse acts as a camera flash light, and it is able to probe the motion by stroboscopy, i.e., by impulsively illuminating the sample under investigation at different delays.

Fundamental photoinduced processes in molecules and solids, like electron-electron or electron-phonon coupling, energy transfer and charge transfer, occur on femtosecond time scales. In the last 40 years, the development of ultrafast laser sources capable of generating ultrashort pulses (down to less than 10 fs, corresponding to just a few cycles of oscillation of the carrier wave of light), made possible and established a new branch of physics, aimed at using light flashes to pump and probe the sample under investigation with femtosecond temporal resolution: ultrafast spectroscopy. Ultrashort light sources are at the basis of transient spectroscopy setups.

Lasers, which have revolutionized our daily life, are based on the capability to amplify light, i.e. to increase its intensity, using specific active media. Essential photonic applications, like optical fibers for ultra-high-speed communications, barcode readers, high-precision surgery with light scalpels, indeed rely on intense laser light sources at specific working wavelengths, i.e. they are based on the possibility to selectively enhance the laser intensity in the wavelength range of interest. A great variety of materials can be used as light amplifiers, from gases to liquids and solids, all of which have macroscopic size. These lasers typically exploit the population inversion between specific electronic and vibrational levels to enable coherent light amplification by stimulated emission, and thus operate at a given set of frequencies with limited or no tunability.

A different kind of light amplifier is the Optical Parametric Amplifier (OPA), which exploits a second-order nonlinear optical process that enables light amplification at virtually any wavelength. In an OPA a nonlinear crystal is illuminated by two laser beams, i.e. the pump, which provides the energy for the amplification, and the signal, the weak beam that needs to be amplified. When the OPA process occurs in the nonlinear crystal the pump beam transfers energy to the signal, which is amplified at the output, and, according to energy conservation, a new beam at the difference frequency between pump and signal, the idler, is generated.

Current OPA setups exploit bulk (millimeter thick) nonlinear crystals, e.g. $\beta$-barium borate (BBO). The miniaturization trend, which has dominated the world of electronics, enabling the realization of powerful consumer devices such as smartphones and tablets, is now moving to the laser world, the so-called field of photonics. Despite their high amplification efficiency, standard nonlinear crystals are not suited for integrated photonics applications since they cannot be reduced to nanometer thickness. The implementation of broadband and highly efficient optical amplifiers with ultracompact footprints is essential for new photonic nanotechnologies required to address rising demands for fast and energy-efficient information processing at the nanoscale. Ideal candidates that promise to revolutionize future technology with next-generation ultrafast and ultrathin devices are two-dimensional (2D) materials.

## 2 Two-dimensional materials

Most of us are familiar with graphite, the grey material made of carbon atoms which is inside our pencils. Graphite consists of several layers of carbon atoms covalently bound to form a hexagonal honeycomb structure (see fig. 3). By using mechanical exfoliation with a scotch tape it became possible, in 2004, to isolate just a single atomic layer of graphite, which is called graphene. Being merely one atom thick, graphene is the prototypical 2D material. Although the existence of 2D materials has been predicted since decades, it was experimentally proven only in 2004, when graphene was isolated for the first time from graphite, its bulk counterpart. Graphene is a centrosymmetric sp2 bonded carbon sheet and it is a gapless semimetal that shows remarkably high electrical mobility, exceeding 15000 cm2V–1s–1 at room temperature (10 times more than standard semiconductors like GaAs), high thermal conductivity (10 times higher than silver), and high mechanical strength (over 300 times stronger than steel). The absence of the energy gap guarantees ultrafast speeds and ultra-broad bandwidths in graphene-based devices.

The discovery of graphene triggered the research on other and similar 2D materials, with the promise and the challenge to revolutionize future technology with next-generation ultrafast and ultrathin devices. In 2005 the first monolayer (1L) of MoS2, a semiconducting Transition Metal Dichalcogenide (TMD), was exfoliated for the first time. Being three-atom thick (see fig. 4), 1L-TMDs are still considered 2D materials. Similar to graphene, 1L-TMDs can be exfoliated starting from their bulk compounds of the type MX2 crystallizing in a graphite like structure, where M is a transition metal atom (Mo, W) and X is a chalcogen (S, Se), e.g. MoS2, MoSe2, WS2 and WSe2. Being 2D direct bandgap semiconductors, 1L-TMDs are at the forefront of both scientific and technical innovation and in many optoelectronic applications they can complement graphene, which is a gapless semimetal.

Graphene and TMDs paved the way to the discovery of innumerable new classes of 2D materials: insulators, semiconductors, metal, semimetals, ferromagnets and antiferromagnets. Hundreds of 2D compounds have been predicted to be stable in ambient conditions.

Due to the weak interlayer van der Waals forces, 2D materials can be stacked together forming the so-called van der Waals (vdW) heterostructures (HSs). Like the individual single layers, vdW HSs can be formed either by direct growth or by exfoliation and stacking process, one on top of the other. The possibility to create an innumerable quantity of new atomically thin quantum materials with ad hoc physical properties is opening new fascinating opportunities in the field of photonics and optoelectronics (photodetectors, LEDs, plasmonic devices, sensors, tunneling devices, and even flexible and wearable devices), and also integrated linear and nonlinear optics. Inventing a new technology beyond the three dimensions may push electronics, currently based on silicon (three-dimensional), towards thinner and thinner devices. This is not so relevant if we think of a 1-mm-thick smartphone replacing a 5-mm-thick one, but groundbreaking for future aerospace, or even medical, technology. For instance, imagine an ultrathin temporary tattoo sensor which is able to monitor vital health parameters, directly from the skin. Going beyond the three dimensions opens the door to a new world of electronics and photonics with thinner and more compact devices.

## 3 Amplifying light at the nanoscale

The superposition principle – stating that the total response of a generic linear system to multiple external stimuli is equivalent to the sum of the individual responses to every individual stimulus – has constituted a long-standing building block in physics, as in particular optics and quantum mechanics. Indeed, photons in vacuum are known not to interact with each other. However, photons can interact with each other in photonic materials owing to the inherent nonlinear response of matter to external electromagnetic stimuli, which enables several photonic applications such as frequency conversion, all-optical signal processing, and non-classical sources of radiation. In particular, parametric down-conversion – namely the annihilation of a pump photon into a pair of photons of lower energies (signal and idler) – constitutes the underpinning physical mechanism enabling optical parametric oscillation (OPO), which has been exploited in tunable sources of coherent radiation and for the generation of entangled photons and squeezed states of light. Similarly, Optical Parametric Amplification (OPA) is a second-order nonlinear process, in which the pump beam amplifies a weak signal beam, and, according to energy conservation, generates a new beam at the so-called idler frequency, i.e. the difference between pump and signal frequencies.

We have recently shown that two-dimensional semiconductors, which are known to possess a remarkably high nonlinear optical response, enable single-pass collinear optical parametric amplification at the atomic scale, thus achieving the ultimate thickness limit for the OPA process. Our experimental results refer to the semiconducting 1L-TMDs, particularly monolayer MoSe2, MoS2, WSe2, and WS2, which have the advantage of a direct bandgap ranging from 1.55 eV to 1.98 eV.

In this experiment we use large-area (mm size) monolayer samples prepared using a gold-assisted exfoliation technique from bulk TMDs. They are subsequently transferred on top of 500 μm thick SiO2 substrates. A 40× reflective objective illuminates the samples with two collinearly synchronized femtosecond laser beams, i.e. the pump and the signal beam, respectively. Following energy conservation, part of the pump photons are annihilated into pairs of signal and idler photons (see sketch in fig. 5). We choose to measure the emitted idler beam, as a fingerprint of the amplification process because of its background-free detection.

Figure 6 demonstrates the ultra broadband tunability – only limited by the signal beam tunability – and quantifies the efficiency of the single-pass OPA process in semiconducting 1L-TMDs. Figure 6a reports the emitted normalized idler spectra measured on one of the four TMD samples, i.e. MoSe2 in a broad energy range (1.9 eV – 2.3 eV). Figure 6b reports the absolute values of the effective generated idler power (color dots) measured on the four semiconducting 1L-TMDs excited by pump and signal beams with fluences of ~77 μJ cm−2 (power of ~48 μW and spot of ~1 μm) and ~5 mJ cm−2 (power of ~12.7 mW and spot diameter of ~2 μm), respectively. The observed ultrabroad bandwidth of the OPA process is only limited by the laser tunability and it is related to the atomic thickness of the nonlinear optical material, which eliminates any phase mismatch.

Although the intrinsic single-pass OPA gain of 1L-TMDs is still limited by the sub-nm propagation length, the atomic thickness has innumerable advantages in novel ultrathin device configurations. Approaching the high amplification gain regime while preserving the nanometer thickness of the nonlinear crystal is still an open challenge in the world of nanophotonics. The gain of the second-order parametric process in our experimental conditions scales quadratically with the thickness of the nonlinear optical material. The gain of an OPA could be boosted, in principle, by increasing the propagation length through the active media, i.e. by using a stack of $N$ different TMD monolayers with controlled twist angle the amplification gain increases by a factor $N^2$, while still keeping nanometer thickness. Here we perform a proof-of-principle demonstration of this concept for 1-3 layers of mechanically stacked WS2 monolayer flakes, shown in fig. 7, assembled into a perfectly oriented heterostructure. In the micrograph of fig. 7a we can distinguish 1L, 2L and 3L-WS2 regions.

Figure 7b shows the idler spectrum emitted at 2.14 eV from the different numbers of WS2 layers, excited with pump and signal photon energies of 3.11 eV and 0.97 eV, respectively. The measured idler intensity indeed scales nearly quadratically with the layer number. The measured nonlinear gain enhancement in $N =$ 1, 2, 3 layers has a slight deviation from the expected $N^2$ enhancement because of absorption effects. Upon tuning the pump photon energy below the WS2 gap one would obtain the expected $N^2$ enhancement.

Our experimental and theoretical investigations provide the first evidence of single-pass light amplification through 1L-TMDs. The amplification efficiencies of the four measured semiconducting TMDs, i.e. MoS2, MoSe2, WS2, and WSe2, are comparable and that they are independent of the signal frequency, thus enabling an ultra broadband functionality. The measured broadband behaviour and efficiency of the nonlinear process are fully reproduced by first-principle calculations. Furthermore, artificial stacking of suitably aligned monolayer TMDs provides a route towards the quadratic scaling of the nonlinear optical gain with the layer number, while still maintaining the ultrabroad bandwidth enabled by the nanometer thickness regime.

The future applications of an atomic thickness nonlinear optical amplifier are innumerable. We could even think of covering an entire integrated optical circuit with an “atomic sheet” of a 2D material to create a quantum light generator over atomic length scales. Our results shed light on second-order parametric processes in 1L-TMDs, paving the way to the scaling and the integration of 2D materials in future photonic applications, such as 2D all optical amplifiers, single-photon nanoemitters and integrated sources of entangled photons for quantum information.