Enhanced optical nonlinear absorption of graded Au-TiO_2 composite films

This paper reports that single-layer and graded Au-TiO2 granular composite films with Au atom content 15%- 66% were prepared by using reactive co-sputtering technique. The third-order optical nonlinearity of single-layer and graded composite films was investigated by using s- and p-polarized Z-scans in femtosecond time scale. The nonlinear absorption coefficient βeff of single-layer Au-TiO2 films is measured to be -2.3×10^3-0.76×10^3 cm/GW with Au atom content 15%-66%. The βeff value of the 10-layer Au-TiO2 graded film is enhanced to be -2.1×10^4cm/GW calculated from p-polarized Z-scans, which is about ten times the maximum βeff of single-layer films. Broadened response in the wavelength region 730-860 nm of the enhanced optical nonlinearity of graded Au-TiO2 composite films was also investigated.

Size-dependent nonlinear absorption and refraction of Ag nanoparticles excited by femtosecond lasers

Silver （Ag） nanoparticles with different average sizes are prepared, and the nonlinear absorption and refraction of these nanoparticles are investigated with femtosecond laser pulses at 800 nm. The smallest Ag nanoparticles show insignificant nonlinear absorption, whereas the larger ones show saturable absorption. By considering the previously reported positive nonlinear absorption of 9 nm Ag nanopartieles, the nonlinear absorptions of Ag nanopartieles are found to be size-dependeut. All these nonlinear absorptions can be compatibly explained from the viewpoints of electronic transitions, energy bands and electronic structures in the conduction band of Ag nanoparticles. The nonlinear refraction is attributed to the effect of hot electrons arising from the intraband transition in the s p conduction band of Ag nanoparticles.

Nonresonant and Resonant Nonlinear Absorption of CdSe-Based Nanoplatelets

We present a comprehensive understanding of the nonHneer absorption characteristics of CdSe- based nanoplatelets （NPLs） synthesized by the solution-phase method and the colloidal atomic layer deposition approach through Z- scan techniques at 532nm with picosecond pulses. The CdSe NPLs exhibit strong two-photon induced free carrier absorption （effective three-photon absorption） upon the nonresonant excitation, resulting in a remarkable optical limiting behavior with the limiting threshold of approximately 75 GW/cm2. A nonlinear optical switching from saturable absorption （SA） to reverse saturable absorption （RSA） with increasing the laser intensity is observed when coating CdSe NPLs with a monolayer of CdS shell to realize the resonant absorption. The SA behavior originates from the ground state bleaching and the RSA behavior is attributed to the free carrier absorption. These findings explicitly demonstrate the potential applications of CdSe-based NPLs in nonlinear optoelectronics such as optical limiting devices, optical pulse compressors and optical switching devices.

2D Nb_(2)CT_(x) MXene/MoS_(2) heterostructure construction for nonlinear optical absorption modulation

Two-dimensional(2D)nonlinear optical mediums with high and tunable light modulation capability can significantly stimulate the development of ultrathin,compact,and integrated optoelectronics devices and photonic elements.2D carbides and nitrides of transition metals(MXenes)are a new class of 2D materials with excellent intrinsic and strong light-matter interaction characteristics.However,the current understanding of their photo-physical properties and strategies for improving optical performance is insufficient.To address this issue,we rationally designed and in situ synthesized a 2D Nb_(2)C/MoS_(2) heterostructure that outperforms pristine Nb2C in both linear and nonlinear optical performance.Excellent agreement between experimental and theoretical results demonstrated that the Nb_(2)C/MoS_(2) inherited the preponderance of Nb_(2)C and MoS_(2) in absorption at different wavelengths,resulting in the broadband enhanced optical absorption characteristics.In addition to linear optical modulation,we also achieved stronger near infrared nonlinear optical modulation,with a nonlinear absorption coefficient of Nb_(2)C/MoS_(2) being more than two times that of the pristine Nb_(2)C.These results were supported by the band alinement model which was determined by the X-ray photoelectron spectroscopy(XPS)experiment and first-principal theory calculation.The presented facile synthesis approach and robust light modulation strategy pave the way for broadband optoelectronic devices and optical modulators.

A Reaction-diffusion System with Nonlinear Absorption Terms and Boundary Flux

This paper deals with a reaction-diffusion system with nonlinear absorption terms and boundary flux. As results of interactions among the six nonlinear terms in the system, some sufficient conditions on global existence and finite time blow-up of the solutions are described via all the six nonlinear exponents appearing in the six nonlinear terms. In addition, we also show the influence of the coefficients of the absorption terms as well as the geometry of the domain to the global existence and finite time blow-up of the solutions for some cases. At last, some numerical results are given.

Ultrafast nonlinear absorption and nonlinear refraction in few-layer oxidized black phosphorus

We experimentally investigated the nonlinear optical response in few-layer oxidized black phosphorus(OBP) by the femtosecond Z-scan measurement technique, and found that OBP not only possesses strong ultrafast saturable absorption but also a nonlinear self-defocusing effect that is absent in black phosphorus(BP). The saturable absorption property originates mainly from the direct band structure, which is still maintained in OBP. The emergence of self-defocusing might originate from the combined consequences of the oxygen-induced defects in BP. Our experimental findings might constitute the first experimental evidence on how to dynamically tune its nonlinear property, offering an inroad in tailoring its optical properties through chemical modification(oxidation, introducing defects, etc.). The versatile ultrafast nonlinear optical properties(saturable absorption and self-defocusing) imply a significant potential of the layered OBP in the development of unprecedented optoelectronic devices, such as mode lockers, optical switches, laser beam shapers, and wavelength converters.

Nonlinear Refractive Index and Absorption Coefficient of Single-Shell Semiconductor Carbon Nanotube

The nonlinear refractive index and absorption coefficient of single\|shell semiconductor carbon nanotubes(CN s ) are calculated based on the two\|band approximation and Genkin\|Mednis approach. The results of nonlinear refractive index and absorption coefficient reach the order of 10 -8 and 10 -4 cm 2\5W -1 separately, which indicates that CN s have wonderful nonlinear optical properties. Taking into account the temperature effect and overlapping of σ and π orbits, the effect of relaxation term and chiral angle is discussed. The results show that the smaller the relaxation term, the larger the nonlinear absorption coefficient and refractive index. At the same time, CN s with different chiral angles have different results due to their different energy gap.

Effect of Si δ-Doping on the Linear and Nonlinear Optical Absorptions and Refractive Index Changes in InAlN/GaN Single Quantum Wells

In the framework of effective mass approximation, we theoretically investigate the electronic structure of the Si δ-doped InAIN/GaN single quantum well by solving numerically the coupled equations Schrodinger-Poisson self-consistently. The linear, nonlinear optical absorption coefficients and relative refractive index changes are calculated as functions of the doping concentration and its thickness. The obtained results show that the position and the amplitude of the linear and total optical absorption coefficients and the refractive index changes can be modified by varying the doping concentration and its thickness. In addition, it is found that the maximum of the optical absorption can be red-shifted or blue-shifted by varying the doping concentration. The obtained results are important for the design of various electronic components such as high-power FETs and infrared photonic devices.

Effect of size and indium-composition on linear and nonlinear optical absorption of InGaN/GaN lens-shaped quantum dot

Based on the Schr ¨odinger equation for envelope function in the effective mass approximation, linear and nonlinear optical absorption coefficients in a multi-subband lens quantum dot are investigated. The effects of quantum dot size on the interband and intraband transitions energy are also analyzed. The finite element method is used to calculate the eigenvalues and eigenfunctions. Strain and In-mole-fraction effects are also studied, and the results reveal that with the decrease of the In-mole fraction, the amplitudes of linear and nonlinear absorption coefficients increase. The present computed results show that the absorption coefficients of transitions between the first excited states are stronger than those of the ground states. In addition, it has been found that the quantum dot size affects the amplitudes and peak positions of linear and nonlinear absorption coefficients while the incident optical intensity strongly affects the nonlinear absorption coefficients.

Observation of Two-Photon Absorption and Nonlinear Refraction in AlN

Two-photon absorption （TPA） and nonlinear refraction in AlN single crystals are revealed with the single beam Z-scan technique. A large TPA coefficient of 134-3 cm/CW at 355 nm and third-order nonlinear refractive indices of-1.91±0.38×10-13 cm2/W at 355nm, 1.79±0.36 × 10-13 cm2/W at 532nm and 1.61±0.32 ×10-12 cm2/W at 1064nm are derived. It is inferred that the TPA-generated free carriers are responsible for the large negative nonlinear refractive index at 355 nm, while the oxygen impurity induced bandgap narrowing may account for the large third-order nonlinear refractive indices at 532nm and 1064nm. The large nonlinear optical responses of AIN promise wide applications in the deep ultraviolet nonlinear optical devices.

Two-photon absorption and stimulated emission in poly-crystalline Zinc Selenide with femtosecond laser excitation

The optical nonlinearity in polycrystalline zinc selenide(ZnSe),excited with 775 nm,1 kHz femtosecond laser pulses was investigated via the nonlinear transmission with material thickness and the Z scan technique.The measured two photon absorption coefficientβwas intensity dependent,inferring that reverse saturated absorption(RSA)is also relevant dur-ing high intensity excitation in ZnSe.At low peak intensity I<5 GW cm^(-2),we findβ=3.5 cm GW^(-1) at 775 nm.The spec-tral properties of the broad blueish two-photon induced fluorescence(460 nm-500 nm)was studied,displaying self-ab-sorption near the band edge while the upper state lifetime was measured to be τ_(e)~3.3 ns.Stimulated emission was ob-served when pumping a 0.5 mm thick polycrystalline ZnSe sample within an optical cavity,confirmed by significant line narrowing fromΔλ=11 nm(cavity blocked)toΔλ=2.8 nm at peak wavelength λ_(p)=475 nm while the upper state life-time also decreased.These results suggest that with more optimum pumping conditions and crystal cooling,polycrystal-line ZnSe might reach lasing threshold via two-photon pumping atλ=775 nm.

FDTD Numerical Simulation of Absorption of Microwaves in an Unmagnetized Atmosphere Plasma

Numerical simulations based on the finite-difference-time-domain （FDTD） approximation to multi-fluid equations for positive ions, negative ions and electrons are used to study high frequency electromagnetic wave propagation and absorption in an unmagnetized plasma layer. The interaction between the incident high frequency wave and the plasma layer shows that the existence of negative ions and the nonlinear effect reduces the power absorption capability of the plasma. Parameter dependences of the effects are calculated and discussed.

Nonlinear optical characterization of phosphate glasses based on ZnO using the Z-scan technique

The nonlinear optical properties of a phosphate vitreous system [（ZnO）x-（MgO）30-x-（P2O5）70], where x=8, 10, 15, 18, and 20 mol% synthesized through the melt-quenching technique have been investigated by using the Z-scan technique. In the experiment, a continuous-wave laser with a wavelength of 405 nm was utilized to determine the sign and value of the nonlinear refractive （NLR） index and the absorption coefficient with closed and opened apertures of the Z-scan setup. The NLR index was found to increase with the ZnO concentration in the glass samples by an order of 10-10 cm2·W-1. The real and imaginary parts of the third-order nonlinear susceptibility were calculated by referring to the NLR index （n2） and absorption coefficient （β） of the samples. The value of the third-order nonlinear susceptibility was presented by nonlinear refractive or absorptive behavior of phosphate glasses for proper utilization in nonlinear optical devices. Based on the measurement, the positive sign of the NLR index shows a self-focusing phenomenon. The figures of merit for each sample were calculated to judge the potential of phosphate glasses for application in optical switching.

Thermal Nonlinearity of Functionalized Graphene Enhanced by Gold Nanorods

The nonlinearity of functionalized and nonfunctionlaized graphene as well as gold nanorods were investigated using the Z-scan system with an Ar＋ laser beam tuned at a wavelength of 514 nm in a CW （continuous wave） regime that was in resonance with AuNRs （gold nanorods）. Z-scan experimental study indicated that functionalized graphene had a negative nonlinear refraction with self-defocusing performance. The result concluded that gold nanorods （average length was 36 ± 3 nm, and the average diameter was 12 ± 2 nm） enhance the thermal nonlinear properties of graphene oxide materials. Gold nanorods were proved to enhance the nonlinear absorption by 50%, and there was a large enhancement on the thermal nonlinear refraction and the thermo-optical coefficient （dn/dT）. It was observed that the AuFG （functionalized graphene film with gold nanorods） presented a large thermal nonlinear refraction. The value of the nonlinear refraction （nl＇） of FG and AuFG samples was shifted from -0.533 x 10.7 cm2/W to -2.92 x 10-7 cm2/W. There was a large enhancement in thermal refraction value that was about five factors larger than the nonlinear refraction of the host material （FG） and much larger （4 orders of magnitude） than that for AuNRs.

Quantization of electromagnetic field in quadratic continuous nonlinear absorptive dielectrics

This paper reports that in the quantization of electromagnetic field in the dielectrics, the wave equation with regard to the Green function is analytically solved by a direct integral method for a quadratic continuous nonlinear absorptive dielectric medium. The quantization of the electromagnetic field in such a nonlinear absorptive dielectric is carried out for which the material dielectric function is assumed as a separable variable about the frequency and the space coordinate. The vacuum field fluctuations for different spatial continuous variations of dielectric function are numerically calculated, which shows that the present result is self-consistent.

Enhanced Kerr nonlinearity in a quantized four-level graphene nanostructure

In this paper, a new model is proposed for manipulating the Kerr nonlinearity of right-hand circular probe light in a monolayer of graphene nanostructure. By using the density matrix equations and quantum optical approach, the third-order susceptibility of probe light is explored numerically. It is realized that the enhanced Kerr nonlinearity with zero linear absorption can be provided by selecting the appropriate quantities of controllable parameters, such as Rabi frequency and elliptical parameter of elliptical polarized coupling field. Our results may be useful applications in future all-optical system devices in nanostructures.

Realization of high-performance tri-layer graphene saturable absorber mirror fabricated via a one-step transfer process

Graphene,as a saturable absorber(SA),has attracted much attention for its application in ultrashort pulse fiber lasers due to its ultrafast interband carrier relaxation and ultra-broadband wavelength operation.Nevertheless,during the stacking process of monolayer graphene layer,the induced nonuniform contact at the interface of graphene layers deteriorate the device performance.Herein,we report the fabrication of graphene saturable absorber mirrors(SAMs)via a one-step transfer process and the realization of the much enlarged modulation depth and the much reduced nonsaturable loss with tri-layer graphene(TLG)than single-layer graphene(SLG)due to the improved uniform contact at the interface.Moreover,the operation of 1550 nm mode-locked Er-doped fiber laser with the TLG SAM exhibits excellent output characteristics of the maximum output power of 9.9 mW,a slope efficiency of 2.4%and a pulse width of 714 fs.Our findings are expected to pave the way toward high-performance ultrashort pulse fiber lasers based on graphene SAs.

Optical Limiting Response in Er^(3+)-Doped TeO_2-Nb_2O_5-ZnO Glass

The nonlinear absorption properties of Er^3＋ doped telluride glass were investigated with picosecond laser pulses. The optical limiting response was measured with a transmission technique and reverse saturable absorption （RSA） with a Z-scan technique, which proved that the glass was a promising material for practical optical limiters. The experimental resulted showed that the excited absorption was responsible for the measured RSA, resulting in the optical limiting response. The measured data could be well simulated with a rate equation model to obtain the absorption cross sections of the excited state.

Thickness dependency of nonlinear optical properties in ITO/Sn composite films

In this study,a batch of indium tin oxide(ITO)/Sn composites with different ratios was obtained based on the principle of thermal evaporation by an electron beam.The crystalline structure,surface shape,and optical characterization of the films were researched using an X-ray diffractometer,an atomic force microscope,a UV-Vis-NIR dual-beam spectrophotometer,and an open-hole Z-scan system.By varying the relative thickness ratio of the ITO/Sn bilayer film,tunable nonlinear optical properties were achieved.The nonlinear saturation absorption coefficientβmaximum of the ITO/Sn composites is−10.5×10^(−7)cm/W,approximately 21 and 1.72 times more enhanced compared to monolayer ITO and Sn,respectively.Moreover,the improvement of the sample nonlinear performance was verified using finite-difference in temporal domain simulations.

Nonlinear optical absorption of few-layer molybdenum diselenide （MoSe2） for passively mode-locked soliton fiber laser [Invited]

In this paper,both nonlinear saturable absorption and two-photon absorption（TPA） of few-layer molybdenum diselenide（MoSe2） were observed at 1.56 μm wavelength and further applied to mode-locked ultrafast fiber laser for the first time to our knowledge.Few-layer MoSe2 nanosheets were prepared by liquid-phase exfoliation method and characterized by x ray diffractometer,Raman spectroscopy,and atomic force microscopy.The obtained fewlayer MoSe2 dispersion is further composited with a polymer material for convenient fabrication of MoSe2 thin films.Then,we investigated the nonlinear optical（NLO） absorption property of the few-layer MoSe2 film using a balanced twin-detector measurement technique.Both the saturable absorption and TPA effects of the few-layer MoSe2 film were found by increasing the input optical intensity.The saturable absorption shows a modulation depth of 0.63% and a low nonsaturable loss of 3.5%,corresponding to the relative modulation depth of 18%.The TPA effect occurred when the input optical intensity exceeds 260 MW∕cm2.Furthermore,we experimentally exploit the saturable absorption of few-layer MoSe2 film to mode lock an all-fiber erbium-doped fiber laser.Stable soliton mode locking at 1558 nm center wavelength is achieved with pulse duration of 1.45 ps.It was also observed that the TPA process suppresses the mode-locking operation in the case of higher optical intensity.Our results indicate that layered MoSe2,as another two-dimensional nanomaterial,can provide excellent NLO properties（e.g.,saturable absorption and TPA） for potential applications in ultrashort pulse generation and optical limiting.