Current State of the Art Nonlinear Optical Materials Cmos Compatible Review

1 Introduction

Layered materials have recently emerged as a promising course of materials for optoelectronics [one]. These materials possess dissimilar ring gaps leading to a big range of conductivities and the ability to emit and detect lite at different wavelength ranges [1]. For example, graphene has no band gap and behaves like a metallic; semiconducting transition metal dichalcogenides (TMDCs), such as WS_ii, MoS₂, MoSe₂ and WSe₂, and black phosphorous have band gaps on the club of 1–2.5 eV, and with its very wide ring gap (~six eV) hexagonal boron nitride (h-BN) is an excellent insulator. Going beyond usual conductivity, exotic backdrop like superconductivity (TaS₂, NbSe_two) [2], [iii], ferroelectricity (CuInP_iiSouthward₆) [4], and ferromagnetism (Cr₂Ge₂Te_vi, CrI_three) [five], [6], [7] have been recently reported in these atomically thin materials. Effigy 1A and B testify the schematic of the atomic structure for a typical TMDC and graphene. While the majority of the research in these materials has focused on cloth label, optical spectroscopy and electrical transport measurements, integration of these materials with nanophotonic and nanoelectronic devices is gaining attention. Such integration efforts are primarily motivated past the ease of transferring these extremely thin materials on any substrate without needing explicit lattice matching. Unlike many other quantum confined structures, such as 3-V quantum wells or cocky-assembled quantum dots, these materials stick to the substrate via van der Waals forcefulness, and do not require expensive molecular beam epitaxy processes, or wafer bonding. This provides a unique opportunity to develop hybrid photonic platforms where the fabrication processes of the active and passive devices can be completely decoupled. Big-calibration, passive photonic integrated circuits will be made using existing foundry systems [9], and subsequently layered materials will be transferred on the pre-made photonic chip to build the active devices, including modulators, detectors, low-cal sources (lasers or light-emitting diodes) and nonlinear optical switches.

Figure 1:

Atomic structure of layered 2D materials.

Crystal structures and SHG spectroscopy of common layered materials. Schematic of (A) layered transition metal dichalcogenide (TMDC) textile and (B) graphene. (C) The hexagonal crystal structure of TMDCs. The two directions shown are the zig-zag (show in blueish) and arm-chair (shown in red) directions. (D) Due to the vi-fold symmetry in the crystal construction, a six-fold pattern is observed in polarization resolved 2nd harmonic generation experiment. Thus, based on the 2d harmonic point, crystal axes can exist mapped out. Effigy 1D is reprinted from Ref. [8].

Over the last decade, the growth and all-encompassing label of these materials have revealed their potential for various electronic and optoelectronic applications. Graphene, inarguably the most studied layered material [ten], has found applications in building transistors [11], radio-frequency devices [12], and electronic sensors [13]. In the optoelectronics community, the large electro-optic tunability [14], [15] and potent photo-absorption [16] of graphene generated not bad interest. Nonetheless, the farthermost thinness of the material, the source of the unusual properties and unprecedented material compatibility of these layered materials besides limits the effective light-matter interaction for optoelectronic device applications. To solve this trouble, optical device engineers take used various nanophotonic devices integrated with graphene to raise the light-thing interaction. For example, using nanophotonic waveguides integrated with graphene, the effective light-matter interaction can be increased to build an electro-optic modulator [17], [18], or a photo-detector with loftier efficiency [19], [xx], [21]. Further light-matter enhancement and reduction in the size of the device is possible using optical resonators, including photonic crystals [22], [23], ring resonators [xviii] and plasmonic resonators [24], [25], [26]. Optical resonators enhance the lite-matter interaction past confining the low-cal both temporally and spatially. For a crenel, the extents of the temporal and spatial confinement are quantitatively given by the quality factor (Q) and mode volume (V), respectively [27]. This trend of integrating graphene with nanophotonic devices continued with TMDCs [28], [29], [30]. Cavity integrated TMDCs take been used to demonstrate optically pumped lasing [31], [32], [33], crenel-enhanced electroluminescence [34] and strongly coupled exciton-polaritons [35], [36]. In all these devices, the enhancement due to the cavity depends on the Purcell gene F _p ~Q/V [27], [37].

The success of optical resonators to heighten the light-thing interaction in layered materials motivated researchers to study cavity nonlinear optics using these materials. Due to their bosonic and chargeless nature, the interaction strength betwixt photons is very weak and nonlinear optical effects appear but at very loftier ability. This remains an outstanding claiming to exist overcome for eyes to be used for any compute applications. However, the required power can be lowered using optical resonators. For a cavity-enhanced 2nd-guild χ ⁽²⁾ (third-social club χ ⁽³⁾) nonlinear switch, the threshold ability is proportional to 5/Q ⁱⁱⁱ (V/Q ²) [38]. The ability of nano-cavities to spatially confine light of wavelength λ to an extremely small mode volume [V~(λ/n)³ where n is the refractive index of the cavity cloth], and store calorie-free for a few nanoseconds (τ _ph =Qλ/2πc) provides an opportunity to realize optical nonlinearity at the few photon level. Thus, cavities can significantly enhance the intrinsic optical nonlinearity of the layered materials. In this paper, we review the recent progress in the field of crenel nonlinear eyes with layered materials. We note that the nonlinearity of layered materials is comparable to that doable of existing textile systems, including breakthrough confined structures and bulk materials. Notwithstanding, the ability to integrate these materials with any material systems provides an excellent opportunity to build hybrid integrated nonlinear photonic systems. Apart from the cavity-enhanced second-society and third-order nonlinear eyes, the layered materials exhibit saturable assimilation and nonlinear polariton-polariton interaction. Finally, the layered materials host defect centers, which are essentially two-level systems, and will provide a road to obtain single photon nonlinearity. Along with reviewing the existing works, we will lay out the outstanding challenges and several future directions of the crenel nonlinear eyes with these emerging layered material systems.

two Nonlinear processes in layered materials

In recent years, several experiments with stand-alone layered materials measured their nonlinear optical coefficients. Table 1 summarizes the measured χ ⁽²⁾ and χ ⁽ⁱⁱⁱ⁾ coefficients for different layered materials. The large χ ⁽²⁾ values near ~800 nm originate from the energetic proximity of the excitons in TMDCs, and thus generally come up with large losses [8], [46], [47], [48], [51]. These experiments also clearly showed that the 2d-order nonlinearity in TMDCs is the strongest at the single layer limit. With an even number of layers, this nonlinearity disappears, as the material becomes centrosymmetric. Thus, the nonlinear signal works as a convenient microscopy tool for probing the number of layers in the TMDC crystal. Additionally, a half dozen-fold polarization pattern is plant in the second harmonic signal reflecting the hexagonal crystal structure of the TMDCs (Figure 1C and D). Thus, nonlinear spectroscopy of the layered materials has become an indispensable tool to determine the crystalline orientation, thickness uniformity, layer stacking, and unmarried-crystal domain size of atomically thin films [47], [49], [52], [53]. In fact, this technique is critical for creating the heterostructures of TMDC layers, as the relative crystal orientation determines the heterostructure'southward electronic ring construction [54]. Researchers accept also demonstrated that the centrosymmetry of bilayer MoS₂ can be broken with a static electrical field, enabling second harmonic generation (SHG) [55]. Note that this electrical field-induced SHG can potentially create opportunities for electro-optic switching applications. Another way to break the symmetry will be via straining the bilayers. Straining monolayers and bilayers of MoS₂, researchers take already demonstrated band gap engineering and photoluminescence (PL) control [56], [57], [58]. All the same, strain induced nonlinear optics with layered matierlas have yet to be reported. In add-on to experimental measurements, several enquiry groups take reported atomistic simulation studies to judge the nonlinear coefficients for dissimilar layered materials [59], [60], [61], and have also analyzed the effect of substrates [62]. This piece of work models the nonlinearity of layered materials as zero-thickness interfaces, and showed that without careful theoretical modelling, the extracted value of the nonlinear coefficient can be largely exaggerated.

Table 1:

Reported nonlinear optical coefficients in layered materials: SI unit for χ ^(three) -coefficients is m ²/V ² and for χ ⁽²⁾ -coefficients is 1000/V.

Fabric [Ref]	Type of NLO (χ(3), χ(2))	Approx. λ(nm)	Value (SI unit)
Graphene [39]	χ (3)	800	1.4×10−15
Graphene [40]	χ (3)	1550	iii.25×ten−19
BP [41]	χ (3)	1550	1.4×10−19
MoStwo [42]	χ (3)	1550	two.nine×x−nineteen
GaSe [43]	χ (3)	1550	1.7×10−sixteen
ReS2 [44]	χ (iii)	1550	5.three×x−eighteen
WSeii [45]	χ (2)	1550	sixty×10−12
WS2 [46]	χ (2)	800	10×10−9
MoS2 [47]	χ (2)	800	100×10−9
WSeii [48]	χ (2)	800	10×10−9
h-BN [49]	χ (ii)	800	ane×ten−eleven
GaSe [50]	χ (2)	1550	700×10−12

Most studies with TMDCs have focused on pumping about the exciton resonance (~800 nm) and creating a second harmonic to a higher place the band gap at ~400 nm. A more than interesting regime from an application signal of view is to pump almost 1550 nm and create a 2nd harmonic signal at 775 nm. This wavelength range is especially important for interfacing with telecommunication technologies. Such nonlinear devices could exist utilized for optical bistability for a telecommunications wavelength light amplification by stimulated emission of radiation [63]. In this wavelength range, the absorbent loss at the fundamental frequency is as well minimal. Researchers have demonstrated SHG nether pump near 1550 nm in stand up-alone, monolayer WSe₂ [45] and in GaSe [fifty]. In WSe₂, researchers also demonstrated electric field controlled SHG showing the nonlinear optical effect far from the excitonic frequency is strongest at twice the exciton frequency. Thus, by changing the exciton frequency, ane tin can alter the effective nonlinearity. The reported χ ⁽ⁱⁱ⁾ values for WSe₂ are effectually 60 pm/V at 1550 nm and for GaSe, the χ ^(two) value is estimated to be at least one order of magnitude larger (Table ane).

In addition to second-lodge nonlinear processes, third-order nonlinear processes take besides been studied using layered materials. Being centrosymmetric, graphene does non possess intrinsic 2nd-social club nonlinearity, and hence graphene is primarily studied for tertiary-order nonlinear processes. Several research papers explore third harmonic generation [39], cascaded third harmonic generation [64], and four wave mixing [65]. Layer-dependent third harmonic generation is too recently reported in black phosphorous [41]. In TMDCs, researchers have demonstrated intensity-dependent refractive index past exploiting the third-guild nonlinearity [66].

We note that, the measured values of the nonlinear coefficients in infrared wavelengths (~1500 nm) are comparable to the χ ⁽³⁾ of bulk silicon (~10^−nineteen m²/V²) or the χ ⁽²⁾ of majority Iii–V materials, such as GaAs or GaP (~100×10⁻¹² m/V), as a research article has pointed out in the by [67]. Thus, the utility of nonlinear layered materials does non necessarily originate from a large nonlinearity per se, just rather from their tunable optical nonlinearity, their ease of integration onto capricious substrates, ease of patterning, and the possibility of creating a hybrid platform. For example, complementary metal-oxide-semiconductor (CMOS)-compatible materials, such every bit silicon and silicon nitride, lack second-club optical nonlinearity. By integrating layered materials on height of them, we tin can realize second-lodge nonlinearity in a CMOS uniform style. Thus, in our opinion, the true benefit of layered materials lies in creating hybrid, active photonic systems.

iii Cavity-enhanced second harmonic generation

While at that place is pregnant enquiry progress in the nonlinear optics of layered materials, the extreme thinness of the cloth poses a serious trouble for applied applications. This problem can be ameliorated by using an optical resonator to heighten the effective nonlinearity. While the constructive nonlinearity in a layered material clad cavity is proportional to the material nonlinearity, the textile interacts simply with a small portion of the field on the surface. Hence it is important to guess the constructive nonlinearity in the presence of an optical resonator.

iii.1 Modeling of the nonlinear cavity

In a recent work, Majumdar et al. [68] analyzed the effective nonlinearity of a layered material clad nano-cavity for 2nd-order nonlinear optics. They assume that the optical cavity is formed in a dielectric slab with the field contour varying sinusoidally inside the slab, and decomposable exponentially outside (Effigy 2A). While such a model is a simplification, and neglects the bodily style profiles of the crenel, information technology allows the authors to obtain a closed class analytical expression, which provides an intuitive understanding of the effective nonlinearity. They observe that the nonlinear interaction force 1000_nl is given by [68]:

Figure two:

Modeling of nonlinear layered textile integrated optical resonator.

(A) The theoretical model to gauge the effective nonlinearity for a layered material placed on top of the cavity assumes the cavity mode follows a cosine office inside the slab, and decays exponentially outside the slab. (B) Schematic of a disk with patterned layered fabric on meridian: by intelligently patterning the cloth on peak, the mode profiles are not significantly altered, just the nonlinear overlap tin be significantly improved.

ℏ g n fifty ≈ ( ℏ ω o 2 ε o ) 3 / 2 2 χ ( ii ) d S 3 3 ε 3 / 2 π σ x σ y ,

where ħ is the reduced Planck's constant, ω_o is the fundamental athwart frequency, χ ⁽²⁾ is the value of the second-club nonlinear coefficient, d is the thickness of the layered materials, ε is the dielectric constant of the layered material, S signifies the ratio of the field strength at the surface and middle of the slab, and σ _x and σ _y are the confinement length of the optical field inside the resonator along 10 and y directions. Note that, a stronger localization within the nonlinear material volition increase the nonlinear interaction force. A cavity helps to confine light and thus reduces both σ _x and σ _y . They also find that the interaction force depends on the product of the nonlinear coefficient and the material thickness, as one would expect. Thus, the small thickness of the layered materials indeed limits the interaction strength. Nevertheless, the analytical expression likewise shows that past enhancing the field on the surface, i.due east. by increasing the value of S, the effective nonlinearity tin be significantly enhanced. This criterion necessitates rethinking the design of the dielectric optical cavities, where the field is by and large minimized on the surface to reduce the loss. In a more recent paper, the authors have likewise shown that layered materials provide a novel way to satisfy phase-matching condition in second-order nonlinear optics as elaborated below.

In deriving the analytical expression of the nonlinear interaction strength, information technology was previously assumed that the phase-matching condition is fully satisfied. In 2d-social club nonlinear optics, the phase-matching condition is equivalent to satisfying the momentum conservation of the interacting waves [69]. In a nano-crenel, satisfying this condition amounts to having a good modal overlap between the cardinal and the second harmonic modes. Moreover, for high efficiency, the crenel needs to support modes at both frequencies. Satisfying both of these requirements is difficult, and to date, the proposed designs require stringent fabrication tolerance, and often involve significant computational resources [70]. A single monolayer does non significantly change the bars mode profiles in the cavities as the interaction is evanescent in nature, and due to the extreme thinness of the fabric, only slightly perturbs the cavity style. Thus, 2nd materials provide an excellent opportunity to decouple the cavity design and nonlinear material blueprint. Starting with whatever crenel, and intelligently patterning second materials on tiptop of it, the phase-matching condition can be satisfied. A schematic of a nano-resonator with patterned 2D material on tiptop is shown in Figure 2B. Our theoretical analysis shows that such patterning tin maintain a adept overlap integral, and thus retain significant effective nonlinearity, fifty-fifty when the modes are largely mismatched [71].

The model described above primarily works for a dielectric optical resonator, and currently virtually of the reported results on cavity nonlinear eyes with layered materials involve dielectric resonators. Still, plasmonic resonators already are being used to heighten the linear properties of the layered materials [72], including light emission [32], [73], electro-optic modulation [25] and photograph-detection [74]. Recently, evidence of polariton germination has besides been observed in plasmonic cavities [75]. Plasmonic resonators tin too be engineered to accept multiple resonances [73], and thus tin be ideal for second and 3rd harmonic generation. While the quality factors of plasmonic resonances are significantly lower compared to dielectric resonators due to metallic losses, they provide an extremely small mode book to which significantly enhances the calorie-free-thing interaction. Additionally, plasmonic effects can be exploited to confine low-cal to lie in a single plane, where the layered cloth can be placed. Thus, plasmonic resonators are expected to play an important office in enhancing nonlinear optical effects in layered materials. Another of import research direction could be to develop hybrid plasmonic-dielectric resonators to realize both high Q equally is characteristic of dielectric cavities, with the depression 5 that is characteristic of plasmonic cavities.

3.2 Second harmonic generation with single mode cavity

Electric current experimental efforts on SHG with layered materials are primarily focused on a single crenel mode coupled to exfoliated layered materials. Using a tungsten diselenide (WSe_two) clad silicon photonic crystal cavity, Fryett et al. [76] showed enhanced SHG. In this work they used a pulsed laser operating within the telecommunication ring (~1550 nm). Effigy 3A shows the scanning electron micrograph of a WSe_ii clad silicon photonic crystal cavity. The cavity modes are near 1490 nm. When the crenel is resonantly excited using a pulsed light amplification by stimulated emission of radiation, they observed a stiff second harmonic signal around 745 nm (Figure 3B). In the second harmonic signal, they observed a Gaussian background which comes from the doubling of the laser wavelengths, which are off-resonant from the cavity. In this background, they observed a Lorentzian acme at exactly the one-half-wavelength of the cavity resonance, signifying the cavity-enhanced SHG. The reported enhancement is merely ~100, primarily considering of the lack of a cavity mode at the second harmonic frequency and low Q-factor of the cavity (Q~100). Moreover, silicon absorbs a significant corporeality of second harmonic indicate. A promising solution will be to brand a doubly resonant crenel out of wide bandgap materials, such as silicon nitride [thirty] or silicon dioxide [78]. Researchers also recently demonstrated continuous moving ridge (CW) SHG using GaSe coupled with silicon photonic crystal cavity with a pump light amplification by stimulated emission of radiation at ~1550 nm [79]. The required optical power in this work is only microwatts, primarily due to the high Q-gene and small mode-volume of the photonic crystal cavities.

Figure three:

Cavity-enhanced second-gild nonlinear optics with layered materials.

(A) Scanning electron micrograph (SEM) of a WSe₂-clad silicon photonic crystal cavity. (B) Measured spectrum of the second harmonic signal shows the Gaussian background with a Lorentzian peak signifying the crenel resonance. (C) Schematic of a distributed Bragg reflector (DBR) cavity with MoS₂ placed in between two mirrors. The DBR is fabricated of alternating layers of silicon dioxide and silicon nitride. (D) The measured intensity of the second harmonic generated calorie-free shows a articulate enhancement due to the crenel. Figures (A) and (B) are reprinted from Ref. [76]; Figures (C) and (D) are reprinted from Ref. [77].

In some other experiment, 24-hour interval et al. [77] demonstrated SHG using MoS_two integrated inside a distributed Bragg reflector (DBR) cavity (Figure 3C and D). In this experiment, the DBR is formed by using alternating layers of silicon nitride and silicon dioxide to minimize the absorption of light. Here, the SHG is observed under pulsed excitation at 800 nm. The reported enhancement is ~x. The lower enhancement cistron tin can exist attributed to low Q-cistron of ~xx, and the large manner-volume of the DBR cavity. An open hemiconfocal cavity geometry [80] might be more suitable to reduce the mode volume and thus further enhance the nonlinearity.

3.three Second harmonic generation with double mode cavity

The enhancement cistron can be significantly increased past using cavity modes both at the fundamental and the second harmonic frequency. Such mode engineering is theoretically hard at the nano-scale, merely can be easily realized in a DBR-based Fabry-Perot cavity. However, inevitable fabrication errors prevent the cavity modes from appearing exactly at the desired resonance wavelengths. Yi et al. [81] solved this problem by creating a mechanically tunable Fabry-Perot cavity, where the bottom mirror is a DBR, and the meridian mirror is a capacitively actuated silver mirror (Figure 4A). The capacitive tuning enables changing the cavity length, and thus cavity resonances. Via mechanical tuning, it is possible to bring both the fundamental and the 2d harmonic modes to the desired frequencies. In this experiment, they used MoS_two as the nonlinear textile, and despite their low cavity Q-factor, the reported enhancement is ~3000 (Figure 4B and C). This experiment used a pulsed excitation near 930 nm. Further improvement is possible by improving the cavity Q-factor, and reducing the mode-book, which is oftentimes very large in Fabry-Perot cavities.

Figure 4:

2d harmonic generation in double-style cavity.

(A) Schematic of the mechanically tunable Fabry-Perot cavity with embedded MoS₂. (B) The frequency conversion efficiency is increased due to the presence of the crenel. (C) By applying the voltage, the cavity modes can exist tuned, and a large enhancement can be achieved when the cavity is tuned such that modes appear at the fundamental and harmonic frequencies. Figures are reprinted with permission from Ref. [81]. Copyright (2016) American Chemic Society.

Stage-matched SHG was also recently reported in a silicon photonic waveguide using MoSe₂ [82]. Past technology the waveguide cross-department, the effective mode-indices of the fundamental and 2d harmonic modes are matched, which ensures the stage-matching of the light at the fundamental and 2d harmonic frequencies. Similar methods have been used for designing phase-matched ring resonators for cavity nonlinear optics using aluminum nitride [83]. Such a phase-matched ring integrated with layered materials tin enhance the efficiency of the 2nd-order nonlinear processes.

All the existing experiments so far take reported significantly lower SHG efficiency, compared to the theoretical predictions. For a given power, the efficiency can be improved past increasing the quality factor and reducing the mode volume. Another limiting factor might exist the transfer of the layered materials, which generally involves organic polymers, and might innovate excess loss coming from the polymer residues. Having the resonances at both the fundamental and the 2nd harmonic frequencies will also increase the efficiency significantly. Forth with innovating cavity structures, new layered materials with stronger nonlinear optical backdrop, such equally multiferroics [84], can also improve the overall efficiency of SHG.

4 Third-society nonlinear processes

While most of the recent works on cavity nonlinear eyes using layered materials primarily focused on 2nd-club nonlinear optics, the first demonstration of cavity nonlinear optics was with third-social club nonlinearity of graphene. Gu et al. [85] demonstrated optical bistability and regenerative oscillation using a graphene-clad silicon photonic crystal cavity. Figure 5A shows the fabricated photonic crystal cavity which is coupled to a waveguide. Graphene is transferred onto the crenel, and under ~1562 nm CW excitation optical bistability is observed (Figure 5B). The threshold power where the bistable behavior appears in graphene-silicon resonator is lower than that observed with a bare silicon photonic crystal cavity.

Effigy 5:

Optical bistability with graphene-clad silicon photonic crystal cavity.

(A) Scanning electron micrograph (SEM) of the graphene-clad photonic crystal crenel; (B) output ability as a function of the input ability clearly shows the signature of optical bistability. The figures are reprinted from Ref. [85].

In the authors' opinion, withal, the 3rd-order nonlinearity with 2D materials is not as attractive as second-lodge nonlinear optics from an application indicate of view. As most materials already possess strong third-society nonlinearity, and the measured values of nonlinearity for graphene and black phosphorous are nigh the same gild of magnitude as silicon, the application area of third-order nonlinear optics with layered material is debatable [67]. Yet, for many applications, requiring loftier power operation, silicon is not platonic due to high 2-photon absorption when operating at the telecommunication wavelength. In those applications, silicon nitride and silicon dioxide are gaining popularity due to their wide band gaps [86]. The magnitude of the third-order nonlinear coefficient in layered materials is higher compared to that of the nitride (χ ^(three)~one×10⁻²⁰ m ²/V ²) [87] or oxide (χ ⁽³⁾~two.5×x⁻²² m ²/V ²) [69], and will play an important role in realizing low-ability nonlinear optics.

five Saturable absorption

Another promising nonlinear optical effect in layered materials is their saturable absorption. Due to the extreme thinness of layered materials, their photograph-absorption can be easily saturated with low optical power. A common application of saturable assimilation is the integration into optical cavities to generate pulsed light amplification by stimulated emission of radiation sources, both in cobweb and free space systems. Many contempo papers on pulsed lasers have utilized layered 2d materials as the saturable absorption cloth of choice [88], [89], [90]. Virtually of these works used graphene every bit the saturable absorber. I particularly appealing aspect of graphene is its broadband absorption due to its lack of a band gap, which allows mode-locking over a large wavelength range, including in the mid-infrared wavelengths. Figure 6A shows an experimental setup with a graphene saturable absorption mirror [88]. In this piece of work, stable mode-locked laser pulses as short equally 729 fs were obtained with a repetition rate of 98.vii MHz and an average output ability of 60.2 mW at ~ii μm (Figure 6B). In improver to the free-infinite setup, saturable absorption in graphene was used in a fiber laser to demonstrate mode-locking (Figure 6C) [89]. In this piece of work, they created a passively manner-locked erbium-doped fiber laser working at 1559 nm, with 460 fs pulse elapsing (Figure 6D). Recently, several works reported like mode-locked laser systems with a variety of atomically thin materials including black phosphorous [91], MoS₂ [92] and WS_ii [93]. Additionally, researchers have used blackness phosphorous, WS₂ and MoS₂ solutions as saturable absorbers to construct passively Q-switched Nd:YVO_iv lasers, with pulse durations of few nanoseconds [94].

Figure 6:

second material based mode-locking.

(A) Experimental setup of the fashion-locked light amplification by stimulated emission of radiation based on the graphene saturable absorption mirror; (B) CW mode-locked pulse trains in nanosecond and millisecond time scales; (C) graphene mode-locked fiber laser where the fashion-locker associates contains a graphene flake. (D) Auto-correlation trace of output pulses showing the pulse repetition rate of 19 MHz. Figures (A) and (B) are reprinted from Ref. [88]. Figures (C) and (D) are reprinted with permission from Ref. [89]. Copyright (2010) American Chemical Gild.

EDF, erbium-doped cobweb; ISO, isolator; PC, polarization controller; WDM, wavelength division multiplexer.

half dozen Nonlinear exciton-polaritons

Then far, most of the nonlinear optical furnishings we discussed are observed with low-cal sources off-resonant from the exciton. Very nearly the exciton resonances, a large nonlinearity can be realized using the polaritonic system formed past stiff coupling between the cavity-bars photons, and the excitons in the layered materials. Recent works reported ascertainment of strongly coupled exciton-polaritons using layered materials, including MoS_two and bilayer MoSe₂ [35], [36]. Figure 7A shows the schematic of the open DBR cavity used to demonstrate stiff coupling between the crenel mode and the exciton [35]. The open cavity compages allows tuning the cavity resonance by mechanically displacing one of the crenel mirrors. When the cavity mode is tuned across the excitonic resonance, anti-crossing between the cavity way and the exciton is observed, signifying strong coupling and polariton germination. Figure 7B shows the upper and lower polaritons measured in PL.

Figure 7:

Exciton-polaritons in layered materials.

(A) Schematic of the open up distributed Bragg reflector (DBR) cavity with layered fabric inside the crenel. The peak mirror of the cavity can be mechanically displaced to tune the cavity resonance. (B) Photoluminescence spectrum of the strongly coupled exciton-polariton arrangement clearly shows the upper and lower polaritons. The figures are reprinted from Ref. [35].

Exciton-polaritons using quantum wells have been previously used to extensively written report "quantum fluids of light" [95]. At low excitation power, the exciton-polariton system behaves linearly as the exciton-exciton interaction is weak. Bose-Einstein condensation (BEC) of exciton-polaritons has also been observed by several groups [96], [97]. The polaritons take much smaller effective mass compared to atoms due to their photonic components, and thus the BEC can be realized at a much college temperature. Moreover, the extremely large binding energy (~0.ii–0.8 eV) in TMDC excitons can potentially allow creation of polaritons and condensates at room temperature. Such condensation has not yet been observed in layered materials, but is theoretically predicted [98]. Theory also predicts observation of topological polaritons [99] and exciton-mediated superconductivity using the TMDC exciton-polaritons [100]. With college excitation power, withal, one cannot create an arbitrary number of excitons [97]. Thus, the fermionic nature of the constituent electron and hole in the exciton-polariton becomes more than prominent in high density exciton-polaritons, and strong polariton-polariton repulsion tin can be observed. When the exciton density reaches the Mott density, the exciton-polariton system can potentially exhibit BEC-BCS crossover [97]. Thus, layered material based exciton-polaritons and their condensates tin potentially provide a strongly nonlinear cloth platform.

Additionally, the extreme thinness of the layered materials allows for straightforward patterning past etching. Thus, one can easily blueprint them to create small islands of layered materials, which should comport like breakthrough dots (Figure 8A). The size and position of these islands can be easily controlled by lithography [101]. Operation of such quantum dot like structures has been theoretically analyzed [102]. In TMDCs with excitonic Bohr radius of simply 1 nm, theoretical analysis showed that when the radius of the patterned fabric reaches a few tens of nm, single photon nonlinear eyes can be observed [103]. Specifically, polaritonic blockade can be realized in these quantum dot like structures. The ability to deterministically position these structures via lithography can potentially create an assortment of interacting single photon nonlinear systems (Figure 8B). Researchers have already designed and fabricated an array of linear cavities [104], [105]. The addition of the single photon nonlinearity in each of these cavities will create a testbed to study not-equilibrium quantum many body physics with correlated photons [106], [107], [108].

Figure 8:

Patterned quantum dots in layered materials.

(A) By patterning layered 2D materials, nosotros can create quantum dot similar structures, where the exciton-exciton interaction can be significantly enhanced. (B) These patterned quantum dots can exist placed in an array and coupled with an array of interacting optical resonators. Thus, a network of nonlinear nodes tin be created.

7 Unmarried photon nonlinear eyes

Several theoretical proposals explored the feasibility of reaching single photon nonlinear eyes using the second-order and 3rd-order optical nonlinear materials, coupled to optical resonators [109], [110]. As layered materials can be integrated with high-Q silicon or silicon nitride cavities, it is indeed possible to reach unmarried photon nonlinear optics using the off-resonant nonlinearity. However, the quality cistron needed to achieve the single photon nonlinear optical regime is generally very loftier, ~ten^v–10^{half dozen}, and it is non yet articulate whether such a high Q can exist reached with a polymer-based transfer process of layered materials. The creation of the quantum dot similar structures by lithography is promising, but the result of etching on the non-radiative excitonic decay charge per unit is not clear.

A more than straightforward route would be to exploit breakthrough emitters in layered materials. Recently several research groups accept reported unmarried breakthrough emitters in layered materials, especially in TMDCs and in h-BN [111], [112], [113], [114]. These single emitters originate from the localized defects in the crystals [115]. Figure 9A shows the scanning PL data from a chemic vapor deposition-grown WSe_ii flake, where the bright defects can be clearly identified. When such a bright spot is spatially separated, the measured spectrum shows narrow lines, indicative of single defects (Figure 9B). Via 2d-lodge autocorrelation measurements nether both CW and pulsed excitation (Figure 9C and D), a thou ⁽²⁾ (0)<0.v is measured, which unambiguously proves unmarried photon emission from these defects. Via coupling two-level quantum emitters, such as breakthrough dots, with an optical cavity, strong nonlinear optical effects, such as single photon switching [116], [117], [118] and photon blockade [119], [120], [121] have been observed. A similar performance is expected from the defects in layered materials as well. To this stop, Tran et al. [122] have coupled the single defects in h-BN to plasmonic resonators. The plasmonic pillars enhanced the overall brightness of the emitters by a gene of two. These emitters are also recently excited by two-photon processes [123]. Recently, enhancement of the quantum emitters in WSe_ii was also observed using silver nanowires, where the emission was coupled to a surface plasmon polariton mode [124]. Finally, very recently, scalable growth of defects in layered material has been demonstrated [125]. In this work, monolayers of WSe_ii and WS₂ were transferred in a templated vertical silica nano-pillar, and with high probability the defects were localized virtually the pillar. The wavelength of the defect emission besides can exist controlled by the colonnade bore. Such adequacy of deterministic positioning and wavelength choice tin can solve the long-standing problem of stochastic positioning and large inhomogeneous broadening of quantum dots, which have largely limited the scalable operation of quantum dots, and other quantum emitters. The defects in layered materials thus can provide a scalable platform of single photon nonlinear devices.

Effigy 9:

Single quantum emitters in layered materials.

(A) Photoluminescence intensity map of narrow emission lines over 25 μm×25 μm area. The dashed triangle indicates the position of the monolayer; (B) photoluminescence spectrum of localized emitters. The left inset is a high-resolution spectrum of a defect emission. The right inset is a zoom-in of the monolayer valley exciton emission; ascertainment of photon anti-bunching with (C) CW and (D) pulsed excitation. The dip at cipher fourth dimension-filibuster indicates presence of single photons. This figure is reprinted from Ref. [111].

8 Outlook

The field of the cavity nonlinear eyes with layered materials is in its infancy. The majority of researchers working with layered materials still primarily focus on the spectroscopy and textile characterization, and the effort on integration with nanophotonic resonant structures is relatively contempo. However, the unprecedented material compatibility, easy availability of the materials, and unique optoelectronic properties of the layered materials accept very speedily generated strong involvement in the nanophotonics community. Hence, we are hopeful that integration of layered materials with nanophotonic devices will enable more fundamentally new scientific studies, and novel low-power applications in the near futurity. Equally explained earlier, all the reported nonlinearities tin be enhanced by improving the cavities (larger Q and smaller Five), and this will surely bulldoze future research on cavity nonlinear optics with layered cloth systems. In this department, we elaborate on some of the new and more speculative research directions involving cavity nonlinear optics with layered materials.

8.1 Phase transition layered materials

Stage transition in layered materials, such as MoTe₂ and WTe_ii has been predicted [126], [127], [128]. Majority stage alter materials, such equally GeSbTe (GST), have recently generated a lot of interest in the field of integrated nanophotonics due to the large change in the refractive index associated with the structural change in GST [129], [130], [131]. Coupled with an optical resonator, such large change in refractive index will enable optical bistability, where the output optical power is a strongly nonlinear role of the input optical power. I major problem of GST, however, is the large amount of loss in the visible and nearly-infrared frequency. The layered stage change materials take a wider ring gap, and tin provide a new way to realize a very large change in the refractive indices, while maintaining a low loss.

eight.2 Heterostructure of layered materials

Several groups take reported fabrication and characterization of heterostructures of layered materials [132], [133]. One especially interesting aspect of the heterostructure is the observation of long-lived inter-layer excitons, where the electron and holes are separated into different layers. This prevents the recombination of the electron and pigsty pair, and thus long-lived exciton states can be realized. The implication of such long-lived excitons for nonlinear optics is non articulate, and can potentially constitute a new inquiry field. For example, what are the implications for exciton-polaritons and exciton-polaritons BEC with long-lived excitons? Furthermore, by separating unlike TMDC layers past h-BN, a multi-quantum well-like structure tin be realized, where the thickness of the nonlinear fabric can be varied. Researchers have already demonstrated stronger exciton-photon coupling in bilayer MoSe₂ separated by h-BN [35]. With Due north layers, we expect the coupling strength to increase by a factor of Due north .

8.3 Valley exciton-polaritons

TMDCs showroom unique spin-valley physics, which primarily stems from the combination of 2 features. Offset, the band gap is at the +K and –G "Dirac valleys", not at the Brillouin zone eye. This gives the electron states a "valley alphabetize" (or pseudospin) in improver to real spin [134], [135]. Optical selection rules are such that right hand circularly polarized light (σ⁺) couples only to 1 valley and left hand circularly polarized light (σ⁻) couples to the other, providing the commencement solid-state arrangement in which dynamic control of valley pseudospin is possible [134], [136], [137], [138], [139], [140], [141], [142]. 2nd, the strong spin-orbit coupling locks the real spin at the band edges to the valley alphabetize [134]. Spontaneous transitions between these spin-states are unlikely due to the large mismatch between momentum vectors. Several research groups have observed valley physics in the exciton-polariton system [143], [144], [145]. Surprisingly, the results show that the hybridization with cavity photons makes it easier to notice the spin-valley physics at room temperature [143], and for materials, where the exciton does not ordinarily demonstrate strong spin-valley physics [145]. However, the spin-valley physics remained largely ignored in the cavity nonlinear optics with monolayer materials. In Iii-V quantum well systems, researchers demonstrated a helicity dependent polariton-polariton interaction. Exploiting such an issue, multistability in helicity is observed in exciton-polariton systems [146], [147]. Similar effects are expected with TMDC exciton-polaritons equally well. The multistable devices can enable multi-state optical logic.

8.iv Hyperbolic metamaterial with layered materials

In all the nonlinear systems nosotros take considered in this article and so far, the layered materials only provide the required nonlinearity and the cavity is formed past another, linear material. However, it is possible to fabricate a whole photonic structure using layered materials. For example, using graphene and h-BN layered structures, researchers predicted that a hyperbolic metamaterial can be created [148], [149]. Hyperbolic metamaterials are promising candidates for enhancing the nonlinear optical interaction [150]. Thus, it is possible to build a nonlinear nanophotonic organisation solely fabricated out of layered materials. This will open a completely new field of research.

Acknowledgments

The authors acknowledge useful word with Professor Vinod Menon, Professor Xiaodong Xu and Professor Feng Wang. This piece of work is supported past the National Scientific discipline Foundation under grant NSF-EFRI-1433496, and the Air Strength Office of Scientific Research-Young Investigator Program under grant FA9550-fifteen-1-0150.

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