Effective Nonlinear Coefficient Research Articles

Few-layer Ta2CTx nanosheets-based mode-locked fiber lasers

In this paper, two-dimensional (2D) few-layer Ta2CTx nanosheets are fabricated by liquid phase exfoliation (LPE) method. The nonlinear optical absorption properties are studied by Z-scan and I-scan techniques, revealing excellent saturable absorption response with an effective nonlinear absorption coefficient of -92.2 cm/MW@1064 nm. The saturation intensity and modulation depth for 1064 nm and 1550 nm are determined to be 79 and 51 MW/cm2, 9.9% and 4.5%, respectively. Furthermore, by decorating few-layer Ta2CTx nanosheets onto microfiber, few-layer Ta2CTx saturable absorber (SA) is fabricated and applied in Yb-doped and Er-doped fiber lasers (YDFLs and EDFLs). Not only a normal mode-locked operation but also square-wave pulse (SWP) are realized by increasing the length of the laser cavity at 1.5 µm, highlighting the great potential of few-layer Ta2CTx nanosheets as an optical modulator. The maximum pulse duration of 5.56 ns is also the widest SWP width that can be realized with 2D materials without filtering device in the cavity. Our work provides a platform for exploring novel SAs materials and nonlinear phenomena in mode-locked fiber lasers.

Near-infrared all-fiber mode-locked laser based on vanadium carbide nanosheets

Vanadium carbide (V2C), a newly developed MXene, has been theoretically predicted to be an excellent nonlinear optical materials. Here, few-layer V2CTx nanosheets were synthesized by liquid phase exfoliation (LPE) method. Z-scan measurement was performed to explore their third-order nonlinear optical properties, highlighting the strong nonlinearities of few-layer V2CTx nanosheets. And the effective nonlinear absorption coefficient was determined to be − 98.3 cm/MW, corresponding to the imaginary part of the third-order nonlinear effects was obtained to be − 1.106 × 10−8 esu. In addition, microfiber-based few-layer V2CTx saturable absorber (SA) was fabricated by optical deposition method and the saturable absorption characteristic was measured by I-scan technique. The Yb-doped and Er-doped fiber lasers (YDFLs and EDFLs) were performed by inserting microfiber-based few-layer V2CTx SA into the ring cavity. And the stable mode-locked operation was realized with super high signal- noise ratio (SNR). Our work systematically reveals that few-layer V2CTx nanosheets should be an excellent SA for ultrafast photonics in the near-infrared band.

Photonic crystal fiber supporting 394 orbital angular momentum modes with flat dispersion, low nonlinear coefficient, and high mode quality

A photonic crystal fiber (PCF) with an SSK2 dense crown glass ring is designed and analyzed. After optimization of the radius of the central air hole and thickness of the annular region, 394 orbital angular momentum (OAM) modes in the range of 1.48 to 1.62 μm can be transmitted stably. The effective refractive index, effective index difference, dispersion, effective mode area, nonlinear coefficient, numerical aperture (NA), mode quality, and confinement loss are analyzed numerically by the finite element method. The results show that the effective index difference of all the OAM modes is greater than 1 × 10 − 4 and they can propagate stably in the PCF. Besides, the fiber shows flat dispersion with a minimum variation of 8.55 ps / ( km · nm ) , very small nonlinear coefficient of less than 0.232 W − 1 · km − 1, as well as high mode quality bigger than 94.57%. This high-performance PCF has immense application potential in optical fiber communication.

Third-order optical nonlinearity in Ti2C MXene for Q-switching operation at 1–2 μm

Two-dimensional (2D) transition metal carbides/nitrides (MXene) possess the peculiar physical and electronic properties. In this paper, we reported the wideband third-order optical nonlinearities in Ti2C MXene from 1 to 2 μm. The maximum effective nonlinear absorption coefficients were −0.56 cm/MW, −0.702 cm/MW and −0.62 cm/MW at 1, 1.3 and 2 μm, respectively. Moreover, two-photon absorption effect was also investigated. Based on the Ti2C MXene saturable absorber, passively Q-switched bulk lasers operating at 1, 1.34 and 2 μm were realized for the first time. The minimum pulse duration was obtained as 128 ns at 1064 nm.

Fourier Transform Analysis on Random Quasi-Phase-Matched Nonlinear Optical Interactions

The Fourier transform method is adopted to analyze random quasi-phase matched (RQPM) nonlinear frequency conversion problems in polycrystalline materials. By treating the material as random signals of effective nonlinear coefficient ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> ) along the beam path, fast Fourier transform (FFT) operations directly produce the generated field amplitude versus spatial frequency mismatch (Δ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> /2π), which relates to all the possible RQPM nonlinear interactions. Thus, the RQPM bandwidth is intuitive from the wavelength-dependent results. More importantly, the Fourier transform treatment greatly decreases the computational amount by orders compared with the traditional step-by-step integration method. The quantitative simulation of RQPM difference frequency generation (DFG) with three variable wavelengths is realized for the first time.

Dispersion and nonlinearity properties of small solid-core photonic fibers with As2Se3 substrate

Characteristics of As2Se3 photonic crystal fibers (PCFs) with a solid-core and small-core diameter are numerically investigated in the long-wavelength range (from 2 to 10 μm). A full modal analysis and optical properties of designed photonic crystal fibers with lattice constant Λ and filling factor d/Λ are presented in terms of chromatic dispersion, effective refractive index, nonlinear coefficients, and confinement loss. The simulation results show that a high nonlinear coefficient of 4410.303 W–1·km–1 and a low confinement loss of 10−20 dB·km–1 can simultaneously be achieved in the proposed PCFs at a 4.5 μm wavelength. Chromatic dispersions are flat. The values of dispersion increase with increasing filling factor d/Λ and decrease with the increase in lattice constant Λ. In particular, some chromatic dispersion curves also cut the zero-dispersion line at two points. The flat dispersion feature, high nonlinearity, and small confinement loss of the proposed photonic crystal fiber structure make it suitable for supercontinuum.

Large Optical Nonlinearity of Dielectric Nanocavity-Assisted Mie Resonances Strongly Coupled to an Epsilon-near-Zero Mode.

Strong coupling provides a powerful way to modify the nonlinear optical properties of materials. The coupling strength of the state-of-the-art strongly coupled systems is restricted by a weak-field confinement of the cavity, which limits the enhancement of the optical nonlinearity. Here, we investigate a strong coupling between Mie resonant modes of high-index dielectric nanocavities and an epsilon-near-zero mode of an ultrathin indium tin oxide film and obtain an anticrossing splitting of 220 meV. Static nonlinear optical measurements reveal a large enhancement in the intensity-independent effective optical nonlinear coefficients, reaching more than 3 orders of magnitude at the coupled resonance. In addition, we observe a transient response of ∼300 fs for the coupled system. The ultrafast and large optical nonlinear coefficients presented here offer a new route towards strong coupling-assisted high-speed photonics.

Three-band plasmon induced transparency effect based on four-disk resonator coupled waveguide system

In order to reduce power consumption and realize ultrafast response time and dynamic tunability, a plasmonic waveguide system based on four disk resonators is designed. A plasmon induced transparency effect is theoretically analyzed by using two different methods: one is the direct destructive interference between bright mode resonator and dark mode resonator, and the other is the indirect coupling through a plasmonic waveguide. Owing to the giant effective nonlinear Kerr coefficient of the graphene-Ag composite material structure and the enhancement characteristics of slow light response to optical Kerr effect, the pump intensity of PIT system for changing the phase shift of transmission spectrum is greatly reduced. An ultrafast response time of 1 ps is achieved, and 0.4π, 0.8π, 1.2π, 1.6π and 2π-phase shift of the transmission spectrum in the plasmon induced transparency system are achieved with the intensity of the pump light as low as 2.34, 4.68, 7.02, 9.36, 11.7 MW/cm&lt;sup&gt;–2&lt;/sup&gt;, respectively. In this work, a plasmonic waveguide coupled directly by two small disk resonators is employed, because two small disk resonators play a role of the slit between the waveguide and the resonators, and also act as two separate resonators side-coupled with a plasmonic waveguide, which leads to the more efficient coupling of electromagnetic energy in the waveguide into the big disk resonators to form resonance and easier storage of light in the resonator. The triple-band plasmon induced transparency (PIT) effect and slow light properties of the model are analyzed by the expression of the deduced theoretical transmittance based on the coupled mode theory, indicating that they are very consistent with the finite-difference time-domain simulations. The results show that the transmission peak of the system is over 80% and the maximum group index is as high as 368. Furthermore, the disk resonators are easy to fabricate and the size of the entire PIT structure is &lt; 0.5 μm&lt;sup&gt;2&lt;/sup&gt;, which is beneficial to the design of optoelectronic device on-chip integration. The research results have important application prospects in highly integrating optical circuits and networks, and also provide the ideas for the design and fabrication of multi-channel optical filter and light storage devices with low power consumption, ultrafast nonlinear response, ultracompact and dynamical tunability.

Surface functionalization of Ta4C3 MXene for broadband ultrafast photonics in the near-infrared region

Recently, MXene has set off a great research boom in the optoelectronic field benefiting from its strong conductivity, eminent broadband absorption, and tailorable electronic/optical properties. In this paper, two-dimensional tantalum carbide (Ta4C3) MXene nanosheets were successfully synthesized based on a two-step liquid exfoliation strategy. Firstly, the role of surface termination with different adsorption structures on the electronic and diverse optical properties of Ta4C3Tx MXene were firstly investigated theoretically via first-principles with density functional theory. Interestingly, the simulation revealed that the oxidized and hydroxylated Ta4C3 MXene featured significantly enhanced optical absorption properties in the near-infrared (NIR) band compared with the pristine bare Ta4C3 nanosheets. Besides, the third-order nonlinear optical (NLO) characteristics of the surfaced terminated Ta4C3 nanosheets were measured by the typical Z-scan techniques at 1 μm. The maximum effective nonlinear absorption coefficient was determined to be -0.78 cm/GW, indicating the great potential as a nonlinear material in NIR band. The nonlinear refractive index, real and imaginary parts of the third-order NLO susceptibility were also obtained. Furthermore, the endowment as an excellent broadband optical modulator was strongly acknowledged utilizing Ta4C3 MXene as saturable absorbers for NIR mode-locking operation at 1044 nm and 1557 nm, respectively. Both highly stable dissipative soliton and traditional soliton pulses were generated. Our results demonstrated the excellent broadband nonlinear absorption in NIR regime of terminal functionalized Ta4C3 MXene and might open a new avenue to the Ta4C3-based advanced ultrafast photonic devices.

Floquet Edge Multicolor Solitons

AbstractTopological insulators are unique physical structures that are insulators in their bulk, but support currents at their edges which can be unidirectional and topologically protected from scattering on disorder and inhomogeneities. Photonic topological insulators can be crafted in materials that exhibit a strong nonlinear response, thus opening the door to the exploration of the interplay between nonlinearity and topological effects. Among the fascinating new phenomena arising from this interplay is the formation of topological edge solitons—hybrid asymmetric states localized across and along the interface due to different physical mechanisms. Such solitons have so far been studied only in materials with Kerr‐type, or cubic, nonlinearity. Here, the first example of the topological edge soliton supported by parametric interactions in nonlinear media is presented. Such solitons exist in Floquet topological insulators realized in arrays of helical waveguides made of a phase‐matchable material. Floquet edge solitons bifurcate from topological edge states in the spectrum of the fundamental frequency wave and remain localized over propagation distances drastically exceeding the helix period, while travelling along the edge of the structure. A theory of such states is developed. It is shown that multicolor solitons in a Floquet system exists in the vicinity of (formally infinite) set of linear resonances determined by the Floquet phase matching conditions. Away from resonance, soliton envelopes can be described by a period‐averaged single nonlinear Schrödinger equation with an effective cubic nonlinear coefficient whose magnitude and sign depend on the overall phase‐mismatch between the fundamental frequency and second harmonic waves. Such total phase‐mismatch includes the intrinsic mismatch and the geometrically‐induced mismatch introduced by the array, and its value reveals one of the genuine effects exhibited by the Floquet quadratic solitons. The results open fundamental new prospects for the exploration of a range of parametric frequency‐mixing phenomena in photonic Floquet quadratic nonlinear media.

Cascaded chirped quasi-phase-matching grating for broad spectrum generation via a complementary reciprocal lattice vector

Broad spectra are of interest for a variety of applications, including pulse compression and ultrafast optical signal processing. We report a scheme of a cascaded chirped quasi-phase-matching (QPM) grating with a complementary reciprocal lattice vector bandwidth. The large reciprocal lattice vector bandwidth provided by first- and second-order QPM can simultaneously achieve second and third harmonic generations. Combined the effective nonlinear coefficient model with the transfer function method, it reveals that spectrum width increased with increasing fundamental wave bandwidth, reciprocal lattice vector bandwidth, chirp rate, and crystal length. The two-section cascaded chirped QPM grating can offer a reciprocal lattice vector bandwidth as large as 0.3 to 1.26 μm − 1, which corresponds to a broadband spectrum covering 450 to 820 nm upon illumination with a tunable femtosecond laser. The proposed grating could extend supercontinuum generation toward potential spectroscopic applications.

Third-order nonlinear properties and reverse absorption behavior in layered Ti3C2 MXene in the near infrared region

Two-dimensional transition metal carbides/nitrides (MXenes) have attracted a lot of attention as optical materials owing to their unique electronic and optical features. In this paper, we demonstrated the nonlinear optical response of Ti3C2 MXene in the near infrared (NIR) regime at 1 and 1.3 µm. The nonlinear optical absorption behavior was systematically studied by the open/closed aperture (OA/CA) Z-scan techniques. Under a low excitation intensity, the saturable absorption dominated the optical nonlinear process, and the maximum effective nonlinear absorption coefficients βeff were −0.59 cm/MW and −0.68 cm/MW at 1 and 1.3 µm, respectively. The nonlinear refractive index n2 and the third-order susceptibility of Ti3C2 Mxene at 1 µm were −2.18 ×10−2 cm2/GW and 3.65×10−3 esu, respectively. While with the excitation laser at 1.3 µm, the nonlinear refractive index n2 was −1.64×10−2 cm2/GW and the third-order susceptibility was 2.75×10−3 esu. With the increase of incident optical intensity, the two-photon absorption (TPA) process was observed, leading to the reverse absorption phenomenon. Our results confirmed that Ti3C2 MXene possessed intensity-depended nonlinear optical properties, which could be applied in various nonlinear optical devices.

Recalibration of the nonlinear optical coefficients of BaGa4Se7 crystal using second-harmonic-generation method

Nonlinear optical coefficients are important parameters for nonlinear optical crystals. Based on the previously disclosed BaGa4Se7 crystal coefficients, the optimum phase-matching direction with the largest effective nonlinear optical coefficient appears in the second octant (90∘<θ<180∘, 0∘<ϕ<90∘). In this study, a recalibration was performed using the second-harmonic-generation method, and it was confirmed that the optimum phase-matching direction of the BaGa4Se7 crystal is located in its XZ principal plane (ϕ=0∘). Therefore, this study will serve as a good reference for future applications of this excellent crystal.

Band structure tuning of g-C3N4 via sulfur doping for broadband near-infrared ultrafast photonic applications

Abstract Graphitic carbon nitride (g-C3N4) featuring a stable heptazine ring structure and high polymerization degree, was indexed as a high thermochemical stability material, attracting rising research enthusiasm for diverse applications. However, the poor near-infrared (NIR) optical absorption and resulting limited NIR applications were pronounced for g-C3N4 due to its large bandgap of 2.7 eV. In the present work, sulfur-doping was manifested by first-principles calculations to introduce impurity level and result in anisotropic spin splitting in g-C3N4 for enhancing broadband nonlinear optical characteristics in NIR regime. The modified sulfur-doped g-C3N4 (S-C3N4) exhibited the maximum effective nonlinear absorption coefficient to be −0.82 cm/GW. Pulse duration within hundred nanoseconds was realized with high modulation stability employing S-C3N4 as saturable absorber in Q-switching operations. Moreover, broadband ultrafast photonics properties were successfully demonstrated in constructed ytterbium-doped and erbium-doped fiber lasers, generating highly stable dissipative soliton and traditional soliton mode-locking pulses. The presented S-C3N4 nanomaterial with remarkable nonlinear optical performances might explicitly boost the development and application of g-C3N4 materials in advanced optoelectronic and ultrafast photonic devices.

Optical parametric generation in biaxial KTA crystal under pumping by YAG:Nd laser in arbitrary directions

Herein, on the basis of expressions for the refractive indices of isonormal waves, the possibility of performing collinear phase matching for optical parametric generation in arbitrary directions of a biaxial KTA crystal under pumping by radiation of a YAG:Nd laser is analyzed. The tuning curves that determine the tuning range of the signal and idler for type-I and II-type phase-matching and arbitrary angles θ and φ in cases where the tuning is carried out along the angle θ at a fixed angle φ and vice versa are calculated. The effective nonlinear coefficient is determined. It is shown that their maximum value is achieved аt a polar angle θ = 90° and type-II phase-matching. For the case of generation of eye-safe radiation the spectral and angular phase matching widths were estimated, as well as gain widths of KTA-OPO under monochromatic pumping.

High-Q, submicron-confined chalcogenide microring resonators.

We demonstrate high quality (Q) factor microring resonators in high index-contrast GeSbSe chalcogenide glass waveguides using electron-beam lithography followed by plasma dry etching. A microring resonator with a radius of 90 μm shows an intrinsic Q factor of 4.1 × 105 in the telecom band. Thanks to the submicron waveguide dimension, the effective nonlinear coefficient was determined to be up to ∼110 W-1m-1 at 1550 nm, yielding a larger figure-of-merit compared with previously reported submicron chalcogenide waveguides. Such a high Q factor, combined with the large nonlinear coefficient and high confinement, shows the great potential of the GeSbSe microring resonator as a competitive platform in integrated nonlinear photonics.

Enhancing Si3N4 Waveguide Nonlinearity with Heterogeneous Integration of Few-Layer WS2.

The heterogeneous integration of low-dimensional materials with photonic waveguides has spurred wide research interest. Here, we report on the experimental investigation and the numerical modeling of enhanced nonlinear pulse broadening in silicon nitride waveguides with the heterogeneous integration of few-layer WS2. After transferring a few-layer WS2 flake of ∼14.8 μm length, the pulse spectral broadening in a dispersion-engineered silicon nitride waveguide has been enhanced by ∼48.8% in bandwidth. Through numerical modeling, an effective nonlinear coefficient higher than 600 m–1 W-1 has been retrieved for the heterogeneous waveguide indicating an enhancement factor of larger than 300 with respect to the pristine waveguide at a wavelength of 800 nm. With further advances in two-dimensional material fabrication and integration techniques, on-chip heterostructures will offer another degree of freedom for waveguide engineering, enabling high-performance nonlinear optical devices, such as frequency combs and quantum light sources.

Enhanced optical nonlinearities in Ti3C2 MXene decorated Fe3O4 nanocomposites for highly stable ultrafast pulse generation

In the present work, we proposed a facile strategy to synthesize the Fe3O4/Ti3C2 MXene composite. The morphology and structures of Fe3O4/Ti3C2 MXene were investigated to confirm the interaction. Moreover, the conventional open- and closed-aperture (OA/CA) Z-scan experiments were implemented to work out the nonlinear optical properties at 1 μm. The large effective nonlinear absorption coefficient βeff, nonlinear refractive index n2, third-order susceptibility |χ(3)| were −4.39 cm MW−1, -2.9 × 10−3 cm2 GW−1, 1.5 × 10−10 esu, respectively. In addition, based on the photogenerated carrier separation and transfer model, a set of rate equations was established to interpreter the nonlinear optical dynamics. The recovery lifetimes were estimated in ∼10 ps level, while the carrier separation and transfer times were in sub-ps level. Furthermore, the tapered-microfiber Fe3O4/Ti3C2 MXene composite was employed as the saturable absorber in the Er-doped fiber laser (EDFL) and the Yb-doped fiber laser (YDFL). In the EDFL, a conventional soliton operation was realized at 1555 nm with a minimum pulse duration of 773 fs and a high signal-to-noise ratio (SNR) of 72 dB. While in the YDFL, a dissipative soliton was achieved with a pulse duration of 677 ps and a high SNR of 82 dB. Our work confirmed that Fe3O4/Ti3C2 MXene hybrid possesses excellent nonlinear optical properties and benefits the ultrafast photonics applications.

Investigation and analysis of the optical Kerr nonlinear effect caused by metal nanocomposite on the performance of nonlinear hybrid plasmonic waveguide

In this paper, a nonlinear hybrid plasmonic waveguide (HPW) with a layer of metal-nanocomposite as nonlinear Kerr material with the high nonlinear response, long propagation length and tight light confinement for processing and active control of optical signals for nonlinear applications has been proposed. The effective parameters of the nonlinear layer due to third-order susceptibility in the HPW structure, which includes the nonlinear metal-nanocomposite layer, have been analyzed by using the Maxwell-Garnett theory. The presence of metal nanoparticles in the nanocomposite host medium improves the nonlinear effect of the proposed HPW structure. Also, the effect of radius, volume fraction, host medium permittivity related to nanoparticles and nanocomposite on the performance and output results of effective nonlinearity coefficient, propagation length, effective mode area, confinement factor has been simulated by using FEM numerical solution method in TM mode. The proposed nonlinear hybrid plasmonic waveguide is an ideal option for design and application in nonlinear all-optical integrated circuits.

Investigation of 1064-nm Pumped Type II SPDC in Potassium Niobate for Generation of High Spectral Purity Photon Pairs

The generation and detection of nonclassical light of about 2 μm has good potential in an emerging field of high-sensitivity metrology, especially gravitational wave detection, as well as free-space quantum communication. A pair of photons is generated through a spontaneous parametric down-conversion (SPDC) process in a nonlinear optic crystal, which can be properly entangled in a spatial region where two beams with each polarization overlap or in a Sagnac-loop interferometer configuration. We investigated theoretically and numerically Type II SPDC in a potassium niobate (KNbO3, KN) crystal, which is useful as a material platform for generating photon pairs of high spectral purity in the 2-μm range. The technique is based on the frequency degenerate SPDC under Type II extended phase matching (EPM). We described the EPM characteristics of KN and showed that it is practically feasible for a 1064-nm pumped SPDC under moderate temperature conditions. The effective nonlinear optic coefficient of KN is at least four-times larger than those of other crystals using the Type II EPM approach, which implies a significant improvement in SPDC efficiency. The joint spectral analysis showed that a pair of photons can be generated with a high purity of 0.995 through proper pump filtering.