Abstract

Regulating nonlinear optical (NLO) absorption and refraction properties of graphene is significant in nonlinear photonics. In this work, the functionalizing strategy of quantum dots (QDs) was used for the regulation of the NLO properties of reduced graphene oxide (rGO) with Au nanospheres and Au@CdS core-shells. The third-order NLO properties of rGO-Au and rGO-Au@CdS nanocomposites were investigated by Z-scan technique with 38 ps laser pulses at 532 nm wavelength. The saturation absorption (SA) of rGO was weakened when it was combined with Au nanospheres and switched to reverse saturation absorption (RSA) when combined with Au@CdS core-shells as irradiance intensity increased. The strength of RSA was tunable with the size of Au@CdS core-shells. Meanwhile, the nonlinear susceptibility of rGO was weakened with the complex Au but was tunable with the complex Au@CdS and realized two times enhancement. The effect of charge transfer mechanism was proposed to explain the regulated effect.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

In the past decade, since graphene was successfully stripped by A.Geim and K.Novoselov at Manchester University, the synthesis, NLO properties and device applications of 2D layered materials have attracted widespread attention [13]. Stimulated by the success of graphene, other 2D materials, such as graphitic carbon nitride [4,5], topological insulators [6,7], black phosphorus [810], transition metal dichalcogenides [1113], and metalorganic frameworks [1416], have also developed rapidly. Due to the excellent NLO properties of 2D materials, their application in photonics has become one of the most attractive fields [17]. However, for the demand of practical applications, suitable NLO properties of materials need to be found, which has always been an eternal topic in the field of nonlinear photonics. Therefore, the regulation of the NLO properties of 2D materials has become obviously very significant.

Graphene is the most typical representative of these 2D materials. Except for its unique properties, a bundant chemical groups such as −OH and −C = O on the surface of graphene also make it an ideal substrate for the deposition of other functional materials [18]. Hitherto, graphene has always been used as an important part of functional composites, compounded with various organic and inorganic components [19,20]. Previous studies have shown that the combination of QDs on the surface of graphene would affect its NLO properties. For example, Liu et al. obtained the enhanced NLO properties of Bi2S3/rGO composite [21]. Zhang et al. observed the enhanced optical nonlinearity of graphene-γMnS [22], Khanzadeh et al. improved the NLO properties of graphene oxide in mixed with Ag2S@ZnS core-shells [23], and He et al. studied the mechanism of superior optical limiting of graphene oxide covalently functionalized with up-conversion NaYF4:Yb3+/Er3+nanoparticles [24]. These results suggested that functionalizing graphene with QDs would be a way to regulate its NLO properties.

Metal-based composite nanocrystals (NCs) have attracted increasing attention for their possible improvement in optical, electronic and catalytic functionalities [25,26]. Among them, great progress has been made in the fabrication of core-shell heterostructures by assembling metal as the core and semiconductor as the shell. The metal core acted as a conductive scaffold and supported charge transfer, and the surface isobaric resonance of nanostructures greatly enhanced the local electric field, which not only improved the photocatalytic efficiency and luminescence efficiency [27,28], but also changed the optical response and nonlinear behaviors [23].

Taking advantages of the core-shell heterostructure and graphene, we prepared the Au nanospheres and Au@CdS core-shells on the surface of rGO, the aim of which is to study the regulation and enhancement of NLO properties of rGO. Metal Au nanosphere was employed as the core because of its high chemical stability, conductivity and high specific surface area, and CdS with different size was used as the shell due to its strong photoelectric response and photoelectric conversion, which is beneficial for the charge transfer that influences the NLO properties. The results show that both the nonlinear optical absorption and the third order susceptibility of rGO in combining with Au and Au@CdS QDs were regulated.

2. Experiments

2.1 Synthesis of rGO-Au and rGO-Au@CdS

Graphene oxide (GO) was synthesized by modified Hummers method. The resulting GO suspension (50 mL, 0.1 mg/mL) was mixed with 0.5 ml of chloroauric acid. Adding 1.5 g of trisodium citrate dihydrate and 0.0037 g of sodium borohydride to 50 ml of ultra-pure water and stir well. Then, took out 1 ml of the above solution and added it to the mixture of GO and chloroauric acid, followed by stirring at room temperature for 1 h and resting for 2 h. After the solution was red wine, 0.01 ml hydrazine hydrate was added and stirred at 90°C for 1 h. After cooling, the rGO-Au solution was obtained. Cadmium nitrate and L(+)-Cysteine were used to prepare Cys/Cd2+ mixture with a molar concentration of 10 mM, and the molal concentration ratio of Cys to Cd2+ was 2:1. Appropriate amount of ammonium hydroxide was added to adjust the hydrogen ion concentration of the mixture. Adding 5 ml of Cys/Cd2+ prepared to 10 mL rGO-Au solution, diluted with 15 mL ultra-pure water, and ultrasonic processing was performed for 15 min. Transfer the mixture prepared to the 50 mL lining of tetrafluoroethylene in stainless steel reactor. After sealing, it was heated to 130°C and kept for 6 h. It was cooled to room temperature naturally and thoroughly washed with ethanol and deionized water to remove the unreacted impurities. In this paper, we prepared three kinds of rGO-Au@CdS composites labeled as S1, S2 and S3 with different reaction durations of 5 h, 6 h and 7 h, respectively. The schematic diagram of rGO-Au@CdS composite nanostructure fabrication is shown in Fig. 1.

 figure: Fig. 1.

Fig. 1. Schematic diagram of rGO-Au@CdS composite nanostructure.

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2.2 Morphology and structure characterization

Morphology and structure of the samples were characterized using field emission scanning electron microscopy (SEM, Carl Zeiss Inc., Oberkochen, Baden-Württemberg, Germany), transmission electron microscopy (TEM, JEOL JEM-2100 operating at 200 kV, JEOL Ltd. Inc., Akishima, Tokyo, Japan) and X-ray diffraction (XRD, Bruker D8 Advance, Bruker Inc., Karlsruhe, Badensko-Wuertembersko, Germany). The XPS spectrum was measured with Thermo ESCALAB 250XI (Thermo Fisher Scientific Inc., USA). UV-Vis spectra were recorded on a PerkinElmer Lambda 35 UV-Vis spectrometer (Agilent Inc., Sacramento, CA,USA).

2.3 Measurement of nonlinear optical properties

Nonlinear optical properties of the samples were investigated by using the Z-scan technique [29]. The transmittance of each sample through a finite aperture in the far field as a function of the sample position z with respect to the focal plane was measured. Nonlinear absorption coefficient and susceptibility were calculated by open aperture (OA) and closed aperture (CA) Z-scan curves respectively. In the Z-san system, a Nd:YAG mode-locked pulse laser (PL2251A, EKSPLA Inc., Vilnius, Lithuania) was used with the wavelength of 532 nm, the pulse width (FWHM) of 30 ps and the pulse repetition of 10 Hz. The laser beam waist was 10.6 µm. The linear transmittance of the aperture in the far field is defined as $S = 1 - \textrm{exp} ( - 2r_a^2/w_a^2)$, where ra is the radius of the aperture and wa is the beam radius at the aperture in the linear regime. In this work, OA Z-scan S=1, CA Z-scan, S was measured to be 36.25%.

3. Results and discussion

3.1 Morphology and structure analysis

Figure 2(A), (B) and (C) are typical SEM images of rGO-Au, Au@CdS and rGO-Au@CdS, respectively. It is seen from Fig. 2(A) that Au nanospheres were decorated on rGO with no apparent aggregation and their average size was estimated to be about 15 nm. Figure 2(B) depicts that CdS was deposited on the surface of Au, Au@CdS core-shells were formed and distributed evenly. For comparison, rGO-Au@CdS samples were prepared with different growth durations of 5 h, 6 h and 7 h. Figure 2(C) is the SEM image of rGO-Au@CdS obtained after 6 h and the average size of Au@CdS core-shells on rGO is about 45 nm. Figure 2(D), (E) and (F) are TEM images of rGO-Au@CdS obtained after 5 h, 6 h and 7 h, respectively. It can be seen that CdS gradually surrounded Au nanospheres and core-shell NCs were completely formed and grown on the surface of rGO. The size of the core-shell NCs increased with the increase of reaction time, and it might be aggregated on the surface of rGO after 6 h.

 figure: Fig. 2.

Fig. 2. SEM images of rGO-Au (A), Au@CdS (B) and rGO-Au@CdS (C); TEM images of rGO-Au@CdS composites S1 (D), S2 (E) and S3 (F).

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XRD was used to determine the phases of rGO-Au, Au@CdS and rGO-Au@CdS in Fig. 3(A). The diffraction peaks of the composite were perfectly indexed to Au (JCPDS no. 65–8601) and CdS (JCPDS no. 65–3414). The stronger peaks at 2θ values of 38°, 44.4°, 64.6° and 77.3° can be attributed to the (200), (220) and (311) crystal planes of Au, respectively. In the phases of Au@CdS and rGO-Au@CdS, the stronger peaks of Au weakens because CdS wraps it around as shell, at the same time, some weaker peak intensities have been recorded at 2θ values of 25.0°, 26.5°, 28.3° and 43.8°, which could be attributed to the (100), (002), (101) and (110) crystal planes of the CdS shell [30]. A weak characteristic band in the phases of Au@CdS from 25° to 35° shows that GO has been reduced. But it has to be noted that all samples are principally composed of a hexagonal CdS phase and Au phase and show almost no diffraction peaks of the rGO. One of the reasons for this phenomenon may be due to the low content of rGO, and the main characteristic band of rGO might be shielded by the main peak of CdS. In the composite nanostructure, the single crystal nature of both Au and CdS ensures a high efficiency of the charge transport in each component as compared to that of their polycrystalline counterparts.

 figure: Fig. 3.

Fig. 3. XRD pattern (A) and XPS spectrum (B) of the samples.

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XPS in Fig. 3(B) was applied to analyze the surface chemical compositions of the rGO-Au@CdS composite. It provides evidence for the formation of C-S between core-shell NCs and rGO, which confirms the successful covalent grafting of Au@CdS onto rGO surface. As observed, the C1s spectrum illustrates a dominant C-C peak (284.8 eV) indicating a high graphitization level in the composite. The 284.24 eV and 284.8 eV peaks in C 1s of rGO can be attributed to sp2 C = C/C-C and sp3 C-C. C = O/C-O peaks at 287.93 eV and 285.78 eV can be attributed to the limitation of reduction method, indicating that there are a few oxygen-containing functional groups exist in the samples. Obviously, the C-S bond located at 285.32 eV confirms the formation of the chemical bond between CdS and rGO. However, the interaction between Au and rGO is not shown, which indicates that Au exists as a core under the protection of the shell in the composite structure, and the thickness of the shell is greater than 10 nm.

3.2 UV-vis absorption spectra

The UV-vis absorption spectra of Au, rGO-Au, Au@CdS and rGO-Au@CdS are illustrated in Fig. 4(A). Taking the absorption peak (517 nm) of Au nanosphere as reference, the absorption peak (550 nm) of rGO-Au is red-shifted because of combination with rGO. The absorption peak (580 nm) of Au@CdS NPs is much red-shifted due to the possible existence of plasmon-exciton coupling. The absorption peak (557 nm) of rGO-Au@CdS is broadened and more red-shifted than that of rGO-Au and less than that of Au@CdS NPs, which is because of the encapsulation effect of rGO on Au@CdS NPs in addition to the possible plasmon coupling. This confirmed the formation of rGO-Au@CdS composite. In order to discuss the charge transfer later, the valence band (Fig. 4(B)) and the energy band (inset Fig. 4(A)) of Au@CdS and rGO were calculated.

 figure: Fig. 4.

Fig. 4. UV-vis absorption spectrum (A) and typical VB spectra (B) of the samples.

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3.3 Nonlinear optical properties

The NLO properties of all samples can be deduced from the Z-scan measurement in Fig. 5. The samples are in anhydrous ethanol solution, the concentration of all samples is 0.5 mg/ml, and the detected NLO signal of anhydrous ethanol is negligible. Figure 5(A) and Fig. 5(B) depict respectively OA z-scan normalized transmittance of rGO, rGO-Au, Au@CdS and rGO-Au@CdS (S1, S2, S3), which reflects the change of NLO absorption properties. In Fig. 5(A), the curves of both rGO and rGO-Au show a symmetry peak at the focus, which means that both rGO and rGO-Au exhibit saturation absorption (SA), and the SA of rGO-Au is reduced compared to that of rGO. The reason for SA is that when the laser intensity is large enough to act on the atom, and the excitation rate of absorption transition increases to be comparable with the relaxation rate, the population of absorption energy levels is significantly reduced, resulting in the reduction of radiation absorption coefficient, the absorption is then saturated. Like graphene, rGO is a direct gap semiconductor and can theoretically absorb any wavelength due to the unique zero-band gap structure of conduction band and valence band crossing. Under the weak irradiation of photons, the electrons in the valence band absorb the energy of photons and jump to the conduction band, and then the hot carrier energy decreases to the equilibrium state. Because electrons are fermions and follow Pauli's incompatibility principle, each electron will occupy an energy state from a low energy state according to the Fermi Dirac distribution. The electrons in the valence band will also redistribute to the low energy state, and the high energy state will be occupied by holes. This process is accompanied by electron hole recombination and phonon scattering. When the light intensity is high enough, electrons are continuously excited to the conduction band. Finally, the photon energy subbands of the valence band and conduction band are completely occupied by electrons and holes, and the interband transition is blocked. Therefore, the interband absorption coefficient approaches zero, the absorption reaches saturation, rGO is bleached. In the case of rGO-Au, there is a wide absorption peak at 550 nm near the excitation wavelength, so the hindrance of interband transition is smaller than that of rGO. Therefore, the SA strength of rGO-Au is less than that of rGO. However, the symmetrical valley of the OA curve of Au@CdS shows the reverse saturation absorption (RSA), indicating that the absorption cross section of its excited state becomes larger than that of its ground state. In Fig. 5(B), all the OA curves of rGO-Au@CdS (S1, S2, S3) mainly show a symmetrical valley, and there are two shoulder peaks of each valley, indicating that the NLO absorption process is the one from SA to RSA and then to SA with the change of irradiance near the focus. This phenomenon may originate from the SA of rGO and RSA of Au@CdS as well as their synergies. It is also observed that with the increase of growth time, the valley gets deeper and the shoulder peak becomes lower, which indicates that the NLO absorption process would experience a final transition from SA to RSA in rGO-Au@CdS composites with the growth time. When the shoulder peak is negligible compared to the valley, the overall performance of NLO absorption can be regarded as RSA effectively. Different NLO absorption characteristics can be used for different practical purposes. The dominant SA characteristic can be used in Q-switching and mode-locking of lasers, while the dominant RSA property can be used in optical switching and optical limiting.

 figure: Fig. 5.

Fig. 5. (A) Open aperture Z-scan curves of rGO, rGO-Au and Au@CdS; (B) Open aperture Z-scan curves of rGO-Au@CdS (sample S1,S2 and S3); (C) Closed-aperture/open-aperture Z-scan curves of rGO, rGO-Au and Au@CdS; (D) Closed-aperture/open-aperture Z-scan curves of rGO-Au@CdS (sample S1,S2 and S3).

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Figure 5(C) and Fig. 5(D) show the CA Z-scan divided by OA Z-scan (CA/OA) curves of all samples, which depicts the change of NLO refraction properties. All the CA/OA Z-scan traces demonstrate the shape of a valley preceding a peak, which indicates that all the samples are self-focusing medium and their nonlinear refractive indexes are positive. Since the peak-valley difference ΔTp-v varies with the sample, it means that the magnitude of NLO refraction has also been regulated.

To quantitatively evaluate the NLO properties rGO, rGO-Au, Au@CdS, rGO-Au@CdS, the experimental data of OA Z-scan are fitted with the equation below [31,32]:

$$T(z) = \sum\limits_{m = 0}^\infty {\frac{{{{[ - {q_0}(z)]}^m}}}{{{{(1 + m)}^{3/2}}}}}$$
where T(z) is the OA Z-scan normalized transmittance, q0(z)=(βI0Leff)/(1+z2/z02), z is the sample position, I0 is the laser intensity at the focus (149 GW/cm2), Leff=[1-exp(αL)]/α, is the effective thickness of the sample, L is the actual thickness of the sample, α is the linear absorption coefficient which can be obtained from the UV-vis spectrum, z0ω02/λ is the length of Rayleigh diffraction, and ω0 is the laser beam waist (10.6 µm). The effective nonlinear absorption coefficient of the sample can be obtained by the fitted curve:β=23/2(1-Tz=0)(1+z2/z02)/I0Leff. From S1 to S3, the effective nonlinear absorption coefficients are obtained to be 107.75 cm/GW, 135.15 cm/GW and 191.98 cm/GW, respectively. The imaginary part of the third order nonlinear susceptibility of the sample is calculated by Imχ(3)=cn02λβ/480π3. As for the nonlinear refraction properties, the normalized CA/OA Z-scan experimental data are fitted by the following equation [31,32]:
$$T(z) = 1\textrm{ - }\frac{{4x\Delta {\Phi _0}}}{{({x^2} + 9)({x^2} + 1)}}$$
where $x = z/{z_0}$, ΔΦ0 is the on-axis phase shift at the focus, defined as $\Delta {\Phi _0} = k\Delta {\textrm{n}_0}{L_{eff}} = k\gamma {I_0}{L_{eff}}$, $k\textrm{ = 2}\pi /\lambda $ is the wave vector, λ is the laser wavelength, γ is the nonlinear refractive index coefficient in m2/W, the nonlinear refraction index in esu is ${n_2}(esu) = (c{n_0}/40\pi )\gamma ({m^2}/W)$. Thus, the real part of the third order nonlinear susceptibility is calculated using $Re {\chi ^{(3)}} = {n_0}{n_2}/3\pi $, and the third-order nonlinear susceptibility is obtained by ${\chi ^{(3)}} = {[{(Re {\chi ^{(3)}})^2} + {({\mathop{\rm Im}\nolimits} {\chi ^{(3)}})^2}]^{{\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}}}}$.The calculated results of all samples are listed in Table 1.

Tables Icon

Table 1. The nonlinear susceptibilities of the samples

These data highlight that the NLO behavior of rGO-Au@CdS was regulated and directly linked to functionalization with Au@CdS. It is observed that the imaginary part Imχ(3) of the susceptibility which is associated with absorption changes from negative to positive, and the values of Imχ(3) in S1,S2 and S3 increases and approaches to the value of Au@CdS, indicating that the nonlinear absorption changes from SA to RSA and is regulable. The real part Reχ(3) which is associated with Kerr effect is also regulated and enhanced with its maximum value occurring in S2, and then decreases in S3 possibly due to the aggregation. The third-order susceptibility χ(3), determined by both Imχ(3) and Reχ(3), is thus regulated and enhanced, the maximum value is about two times as that of rGO. It is also observed that the performances including nonlinear absorption and nonlinear susceptibility of rGO-Au@CdS cannot be explained as a simple direct superposition of the performances of rGO and Au@CdS because there is a difference between the direct addition of the two individual components and the real result of rGO-Au@CdS composite. The additional effect may be due to the interface structure, mainly C-S bonds that has been confirmed by XPS, through which electron charges can be transferred between the two and thus affect the optical nonlinearities.

3.4 Charge transfer effect on the NLO properties

As observed in Fig. 5 and in Table 1, nonlinear absorption and refraction properties of rGO are regulated by Au@CdS NCs. Particularly, the nonlinear absorption switches from SA to RSA with the light intensity increase. To further interpret the charge transfer effect on the regulation of the NLO properties of rGO-Au@CdS composites, a model of charge transfer mechanism is proposed based on the valence band (VB) spectrum and relative energy levels in Fig. 6. Since the Fermi energy EF of Au@CdS is slightly higher than the Dirac cone point of rGO, Au@CdS can be regarded as an electron donor, and rGO as an electron acceptor, so that electrons can not only transit within each of them, but also transfer between them. Upon the illumination of laser pulse with the photon energy of 2.23 eV (532 nm), electrons can be rapidly transited from the valence band to the conduction band, and from an excited state to a higher excited state, in both Au@CdS with the band gap of 1.55 eV and rGO with the gapless band structure [33]. And the electrons at the excited state of Au@CdS can also be transferred to rGO, which may interrupt the carrier relaxation in rGO and favor SA. Therefore, the main cause of SA/RSA switch upon light intensity in the rGO-Au@CdS composites could be attributed to the result of the competition between the transfer of the electrons from the excited state of Au@CdS to rGO and the absorption of the excited state electrons of Au@CdS. Within the regime of intensive light, rGO exhibits SA and pristine Au@CdS exhibits RSA, while rGO-Au@CdS composites exhibit SA followed by RSA, i.e., SA dominates the nonlinear absorption at the relative lower intensity, however, as the light intensity is increased higher, the absorption of the excited state then becomes dominant, RSA occurs following SA. With the increase of growth time of the sample S1, S2 and S3, the size and contact area of Au@CdS on the surface of rGO are increased, which leads to the enhancement of the dominate RSA of the rGO-Au@CdS composites and a tendency to the maximum value of RSA of the pristine Au@CdS NCs.

 figure: Fig. 6.

Fig. 6. (A) The charge transfer mechanism and (B) energy-level diagram of rGO-Au@CdS composites; (C) Normalized transmittance as functions of irradiance intensity.

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The nonlinear absorption properties of rGO-Au@CdS composites can be analyzed by using the following propagation equation and rate equations. The propagation equation in the sample can be expressed as a function of input intensity I:

$$\frac{{\textrm{d}I}}{{\textrm{d}z^{\prime}}} ={-} \alpha (I)I$$
where $\alpha (I )\; \; $ is the intensity-dependent absorption coefficient of rGO-Au@CdS composite and can be obtained from analytical solution of rate equations. z′ is the propagation depth inside the material. For each position along the Z-axis, the expressions of Eq. (3) are integrated over z′ from 0 to L, where L is the sample thickness, and the output intensity Iout (z′=L) from the sample are obtained. So the transmittance of the sample can be obtained as Iout/Iin, where Iin (z′=0) is the center intensity of the input beam spot to the sample and can be obtained as follows:

According to the field distribution function of the basic mode TEM00 of Gaussian beam, the total power of the TEM00 can be calculated theoretically as

$$P = \int_0^\infty {{I_{in}}} {e^{ - 2\frac{{{r^2}}}{{{\omega ^2}(z)}}}}.2\pi r\textrm{d}r = \frac{1}{2}\pi {\omega ^2}(z){I_{in}}$$

From Eq. (4), Iin is obtained as

$${I_{in}} = \frac{{2P}}{{\pi {\omega ^2}(z)}} = \frac{{2E}}{{\tau \pi {\omega ^2}(z)}} = \frac{{2E}}{{\tau \pi \omega _0^2[1 + {{(z/{z_0})}^2}]}}$$
where E is pulse energy, τ pulse width, ω(z) beam radius at the position z of the sample, ω0 beam radius at the focus, and z0 diffraction length of the beam which is equal to z0 = πω02/λ. Rate equations for the charge transfer model of rGO-Au@CdS composites are expressed as
$$\frac{{\textrm{d}{N_2}}}{{\textrm{d}t}} = \frac{{{N_1}{\sigma _1}I}}{{h\nu }} - \frac{{{N_2}}}{{{\tau _2}}}$$
$$\frac{{\textrm{d}{N_1}}}{{\textrm{d}t}} = \frac{{{N_0}{\sigma _0}I}}{{h\nu }} - \frac{{{N_1}}}{{{\tau _1}}} - \frac{{{N_1}}}{{{\tau _3}}} - \frac{{{N_1}{\sigma _1}I}}{{h\nu }} + \frac{{{N_2}}}{{{\tau _2}}}$$
$$\frac{{\textrm{d}{N_\textrm{0}}}}{{\textrm{d}t}} ={-} \frac{{{N_0}{\sigma _0}I}}{{h\nu }} + \frac{{{N_1}}}{{{\tau _1}}} + \frac{{{N_{ - E/2}}}}{{{\tau _4}}}$$
$$\frac{{\textrm{d}{N_{ + E/2}}}}{{\textrm{d}t}} ={-} \frac{{{N_{ + E/2}}}}{{{\tau _5}}} + \frac{{{N_1}}}{{{\tau _3}}} + \frac{{{N_{ - E/2}}{\sigma _2}I}}{{h\nu }}$$
$$\frac{{\textrm{d}{N_{ - E/2}}}}{{\textrm{d}t}} = \frac{{{N_{ + E/2}}}}{{{\tau _5}}} - \frac{{{N_{ - E/2}}{\sigma _2}I}}{{h\nu }} - \frac{{{N_{ - E/2}}}}{{{\tau _4}}}$$
$$N = {N_0} + {N_1} + {N_2} + {N_{ - E/2}} + {N_{ + E/2}}$$
where N0, N1, N2, N-E/2 and N+E/2 stand for the populations densities corresponding to the ground state, first excited state and second excited state of Au@CdS and −E/2 state and + E/2 state of rGO, respectively. E stands for pulse energy. σ0 and σ1 stand for absorption cross-sections of ground state and the first excited state of Au@CdS, σ2 and σ3 for absorption cross-sections of −E/2 state and + E/2 state of rGO. τ1 and τ2 stand for the lifetime of the first excited state and the second excited state of of Au@CdS. τ3 and τ4 are the transition time from Au@CdS to rGO and from rGO back to Au@CdS, respectively. τ5 is the + E/2 state lifetime of rGO. N is the total population density. Thus Eq. (3) can be expressed as
$$\frac{{\textrm{d}I}}{{\textrm{d}z^{\prime}}} ={-} ({\sigma _\textrm{0}}{N_0} + {\sigma _\textrm{1}}{N_1} + {\sigma _2}{N_{ - E/2}} + {\sigma _3}{N_{ + E/2}})I$$
and the intensity dependent absorption coefficient α(I) of rGO-Au@CdS composite can be expressed as
$$\alpha (I) = {\sigma _\textrm{0}}{N_0} + {\sigma _\textrm{1}}{N_1} + {\sigma _2}{N_{ - E/2}} + {\sigma _3}{N_{ + E/2}}$$

For each certain position z of the sample, under the 38 ps pulse excitation, the steady-state approximation, dNi/dt=0 (i=0,1,+E/2,-E/2), can be used to solve the above rate equations. Therefore, the intensity dependent absorption coefficient α(I) is obtained as

$$\alpha (I) = \textrm{ = }\frac{{{R_3}{\tau _4}{I_2}{I^2} + ({R_1}{\tau _3} + {R_2}{\tau _4} + {R_3}{\tau _5}){I_2}{I_3}I + ({\tau _1} + {\tau _3}){I_1}{I_2}{I_3}}}{{({\tau _3}{I_3} + {\tau _4}{I_2}){I^2} + ({\tau _3} + {\tau _4} + {\tau _5}){I_2}{I_3}I + ({\tau _1} + {\tau _3}){I_1}{I_2}{I_3}}}{\sigma _\textrm{0}}N$$
where R1=σ10, R220, R330. I1=/σ0τ1, I2=/σ1τ2 and I3=/σ2τ5 represent the saturation intensities. It can be seen that the expression of absorption coefficient is complicated, which is not only related to the lifetime and the saturation intensity of each energy level, but also related to the irradiation intensity. The physical parameters of the lifetime and the saturation intensity can be fitted experimentally. To analyze the variation of absorption with the irradiation intensity, the inflection point of irradiation intensity theoretically can be found by using mathematical differentiation. When dα(I)/dI<0, the absorption decreases with intensity and SA occurs, and when dα(I)/dI>0, the absorption increases with intensity and RSA occurs, so the value of the intensity obtained from dα(I)/dI=0 is the inflection point from RSA to SA or vice versa.

Figure 6(C) demonstrates the experimental (dots) and fitted (solid line) normalized transmittance of each sample with different intensity. The fitted line is obtained by Iout/Iin expression which is determined from Eqs. (3), (5) and (14) and divided by a measured far field linear transmission. The expression α(I) is implemented to the propagation equation Eq. (3) which is complemented into computational code. It can be seen that rGO exhibits SA, Au@CdS NCs exhibits RSA, yet rGO-Au@CdS composites of sample S1, S2 and S3 exhibit RSA following a smaller SA. Furthermore, the RSA in sample S1, S2 and S3 has the tendency to approach but no exceed that of pristine Au@CdS NCs, which means that the RSA of Au@CdS in the composites would become dominant with the increase of the size of Au@CdS and the contact area with rGO.

A qualitative explanation can be given about the nonlinear absorption in rGO-Au@CdS. At low intensity, most of the populations are in the ground state, the ground state absorption is dominant, and the absorption is linear. At high intensity, on the one hand, the population in the excited state of Au@CdS is increased and its absorption increases, which results in RSA of it. On the other hand, some of the electrons in the excited state of Au@CdS transfer to rGO, and disrupt the relaxation of the electrons in the upper part of the Dirac cone of rGO, which further blocks the transition from the ground state to excited state of rGO and contributes to the SA in rGO. The RSA in Au@CdS is weaker than SA in rGO, which results in SA in rGO-Au@CdS. With the intensity increase, at higher intensity, the RSA of Au@CdS begins to exceed the SA of rGO, so that the RSA dominates the absorption of rGO-Au@CdS. Yet, the total RSA of rGO-Au@CdS could not exceed that of Au@CdS because of the SA role of rGO existed.

4. Conclusions

In conclusion, rGO-Au and rGO-Au@CdS composites were successfully synthesized by the solvothermal method and their NLO properties were investigated by Z-scan technique. The saturation absorption of rGO was reduced by combining Au QDs. When combined with Au@CdS NCs, the nonlinear absorption became a switching characteristic from saturated absorption to reverse saturated absorption as the light intensity increased, and the reverse saturation absorption was enhanced with the size increase of Au@CdS NCs. The third-order nonlinear susceptibility of rGO was also regulated by combining with Au QDs and Au@CdS NCs, and enhanced twice in rGO-Au@CdS composite materials. All the results indicate that the NLO properties of rGO were effectively regulated by Au and Au@CdS, and rGO- Au@CdS composite materials have the potential applications in the area of all-optical switches and optical limiters. The investigations may pave a way to regulate the NLO properties of 2D materials for applications in photonic devices.

Funding

National Natural Science Foundation of China (61875053); Henan Provincial Excellent Youth Project (202300410047).

Disclosures

The authors declare no conflicts of interest.

References

1. B. Guo, Q. L. Xiao, S. H. Wang, and H. Zhang, “2D layered materials: synthesis, nonlinear optical properties, and device applications,” Laser Photonics Rev. 13(12), 1800327 (2019). [CrossRef]  

2. K. S. Novoselov, D. Jiang, F. Schedin, T. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102(30), 10451–10453 (2005). [CrossRef]  

3. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef]  

4. T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. M. Moreno, and F. H. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16(2), 182–194 (2017). [CrossRef]  

5. K. F. Mak, D. Xiao, and J. Shan, “Light–valley interactions in 2D semiconductors,” Nat. Photonics 12(8), 451–460 (2018). [CrossRef]  

6. J. Moore, “The birth of topological insulators,” Nature 464(7286), 194–198 (2010). [CrossRef]  

7. X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83(4), 1057–1110 (2011). [CrossRef]  

8. M. Luo, T. Fan, Y. Zhou, H. Zhang, and L. Mei, “2D black phosphorus-based biomedical applications,” Adv. Funct. Mater. 29(13), 1808306 (2019). [CrossRef]  

9. S. Dhanabalan, J. Ponraj, Z. Guo, S. Li, Q. Bao, and H. Zhang, “Emerging trends inphosphorene fabrication towards next generation devices,” Adv. Sci. 4(6), 1600305 (2017). [CrossRef]  

10. B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on black phosphorus photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018). [CrossRef]  

11. C. Tan, Z. Lai, and H. Zhang, “Ultrathin two-dimensional multinary layered metal chalcogenide nanomaterials,” Adv. Mater. 29(37), 1701392 (2017). [CrossRef]  

12. J. Zhou, J. Lin, X. Huang, Y. Zhou, Y. Chen, J. Xia, H. Wang, Y. Xie, H. Yu, J. Lei, D. Wu, F. Liu, Q. Fu, Q. Zeng, C. H. Hsu, C. Yang, L. Lu, T. Yu, Z. Shen, H. Lin, B. I. Yakobson, Q. Liu, K. Suenaga, G. Liu, and Z. Liu, “A library of atomically thin metal chalcogenides,” Nature 556(7701), 355–359 (2018). [CrossRef]  

13. C. Yan, C. Gong, P. Wangyang, J. Chu, K. Hu, C. Li, X. Wang, X. Du, T. Zhai, and J. Xiong, “2D group IVB transition metal dichalcogenides,” Adv. Funct. Mater. 28(39), 1803305 (2018). [CrossRef]  

14. K. J. Koski and Y. Cui, “The new skinny in two-dimensional nanomaterials,” ACS Nano 7(5), 3739–3743 (2013). [CrossRef]  

15. A. Gupta, T. Sakthivel, and S. Seal, “Recent development in 2D materials beyond graphene,” Prog. Mater. Sci. 73, 44–126 (2015). [CrossRef]  

16. X. Kong, Q. Liu, C. Zhang, Z. Peng, and Q. Chen, “Elemental two-dimensional nanosheets beyond graphene,” Chem. Soc. Rev. 46(8), 2127–2157 (2017). [CrossRef]  

17. X. Wang, Y. Cui, T. Li, M. Lei, J. Li, and Z. Wei, “Recent advances in the functional 2D photonic and optoelectronic devices,” Adv. Opt. Mater. 7(3), 1801274 (2019). [CrossRef]  

18. Y. J. Kim, Y. Kim, K. Novoselov, and B. H. Hong, “Engineering electrical properties of graphene: chemical approaches,” 2D Mater. 2(4), 042001 (2015). [CrossRef]  

19. V. B. Mohan, K. Lau, D. Hui, and D. Bhattacharyya, “Graphene-based materials and their composites: A review on production, applications and product limitations,” Composites, Part B 142, 200–220 (2018). [CrossRef]  

20. V.M. Mikoushkin, S. Y. Nikonov, A. T. Dideykin, A. Y. Vul, D. A. Sakseev, M. V. Baidakova, O. Yu. Vilkov, and A. V. Nelyubov, “Graphene hydrogenation by molecular hydrogen in the process of graphene oxide thermal reduction,” Appl. Phys. Lett. 102(7), 071910 (2013). [CrossRef]  

21. G. Liu, S. Dai, F. Cao, B. Zhu, P. Li, and Y. Z. Gu, “Preparation and enhanced nonlinear optical properties of Bi2S3/RGO composite materials,” Opt. Mater. 89, 112–117 (2019). [CrossRef]  

22. Z. Zhang, P. Li, P. C. Li, and Y. Z. Gu, “Facile one-step synthesis and enhanced optical nonlinearity of graphene-γMnS,” Nanomaterials 9(12), 1654 (2019). [CrossRef]  

23. M. Khanzadeh, M. Dehghanipour, M. Karimipour, and M. Molaei, “Improvement of nonlinear optical properties of graphene oxide in mixed with Ag2S@ZnS core-shells,” Opt. Mater. 66, 664–670 (2017). [CrossRef]  

24. T. He, W. Wei, L. Ma, R. Chen, S. Wu, H. Zhang, Y. Yang, J. Ma, L. Huang, G. G. Gurzadyan, and H. Sun, “Mechanism studies on the superior optical limiting observed in graphene oxide covalentlyfunctionalized with upconversion NaYF4:Yb3+/Er3+ Nanoparticles,” Small 8(14), 2163–2168 (2012). [CrossRef]  

25. W. Zhou, J. Zhu, C. Cheng, J. Liu, H. Yang, C. Cong, C. Guan, X. Jia, H. Fan, Q. Yan, C. Li, and T. Yu, “A general strategy toward graphene@metal oxide core–shell nanostructures for high-performance lithium storage,” Energy Environ. Sci. 4(12), 4954–4961 (2011). [CrossRef]  

26. J. Cao, M. Safdar, Z. Wang, and J. He, “High-performance flexible supercapacitor electrodes based on Te nanowire arrays,” J. Mater. Chem. A 1(34), 10024–10029 (2013). [CrossRef]  

27. W. Chen, Y. Lin, T. Yang, Y. Pu, and Y. Hsu, “Au/ZnS core/shell nanocrystals as an efficient anode photocatalyst in direct methanol fuel cells,” Chem. Commun. 49(76), 8486 (2013). [CrossRef]  

28. W. Chen, T. Yang, and Y. Hsu, “Au-CdS core−shell nanocrystals with controllable shell thickness and photoinduced charge separation property,” Chem. Mater. 20(23), 7204–7206 (2008). [CrossRef]  

29. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryl, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]  

30. L. Cheng, J. Liu, T. Chen, M. Xu, M. Ji, B. Zhang, X. Zhang, and J. Zhang, “Ternary cooperative Au-CdS-RGO hetero-nanostructures: synthesis with multi-interface control and their photoelectrochemical sensor applications,” RSC Adv. 6(37), 30785–30790 (2016). [CrossRef]  

31. Y. Cao, C. Wang, B. Zhu, and Y. Gu, “A facile method to synthesis high-quality CdSe quantum dots for large and tunable nonlinear absorption,” Opt. Mater. 66, 59–64 (2017). [CrossRef]  

32. H. Zeng, J. Han, D. Qian, and Y. Gu, “Third-order nonlinear optical properties of multiwalled carbon nanotubes modified by CdS nanoparticles,” Optik 125(21), 6558–6561 (2014). [CrossRef]  

33. A. E. Nikolaenko, N. Papasimakis, E. Atmatzakis, Z. Luo, Z. X. Shen, F. D. Angelis, S. A. Boden, E. D. Fabrizio, and N. I. Zheludev, “Nonlinear graphene metamaterial,” Appl. Phys. Lett. 100(18), 181109 (2012). [CrossRef]  

References

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    [Crossref]
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    [Crossref]
  5. K. F. Mak, D. Xiao, and J. Shan, “Light–valley interactions in 2D semiconductors,” Nat. Photonics 12(8), 451–460 (2018).
    [Crossref]
  6. J. Moore, “The birth of topological insulators,” Nature 464(7286), 194–198 (2010).
    [Crossref]
  7. X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83(4), 1057–1110 (2011).
    [Crossref]
  8. M. Luo, T. Fan, Y. Zhou, H. Zhang, and L. Mei, “2D black phosphorus-based biomedical applications,” Adv. Funct. Mater. 29(13), 1808306 (2019).
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    [Crossref]
  10. B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on black phosphorus photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018).
    [Crossref]
  11. C. Tan, Z. Lai, and H. Zhang, “Ultrathin two-dimensional multinary layered metal chalcogenide nanomaterials,” Adv. Mater. 29(37), 1701392 (2017).
    [Crossref]
  12. J. Zhou, J. Lin, X. Huang, Y. Zhou, Y. Chen, J. Xia, H. Wang, Y. Xie, H. Yu, J. Lei, D. Wu, F. Liu, Q. Fu, Q. Zeng, C. H. Hsu, C. Yang, L. Lu, T. Yu, Z. Shen, H. Lin, B. I. Yakobson, Q. Liu, K. Suenaga, G. Liu, and Z. Liu, “A library of atomically thin metal chalcogenides,” Nature 556(7701), 355–359 (2018).
    [Crossref]
  13. C. Yan, C. Gong, P. Wangyang, J. Chu, K. Hu, C. Li, X. Wang, X. Du, T. Zhai, and J. Xiong, “2D group IVB transition metal dichalcogenides,” Adv. Funct. Mater. 28(39), 1803305 (2018).
    [Crossref]
  14. K. J. Koski and Y. Cui, “The new skinny in two-dimensional nanomaterials,” ACS Nano 7(5), 3739–3743 (2013).
    [Crossref]
  15. A. Gupta, T. Sakthivel, and S. Seal, “Recent development in 2D materials beyond graphene,” Prog. Mater. Sci. 73, 44–126 (2015).
    [Crossref]
  16. X. Kong, Q. Liu, C. Zhang, Z. Peng, and Q. Chen, “Elemental two-dimensional nanosheets beyond graphene,” Chem. Soc. Rev. 46(8), 2127–2157 (2017).
    [Crossref]
  17. X. Wang, Y. Cui, T. Li, M. Lei, J. Li, and Z. Wei, “Recent advances in the functional 2D photonic and optoelectronic devices,” Adv. Opt. Mater. 7(3), 1801274 (2019).
    [Crossref]
  18. Y. J. Kim, Y. Kim, K. Novoselov, and B. H. Hong, “Engineering electrical properties of graphene: chemical approaches,” 2D Mater. 2(4), 042001 (2015).
    [Crossref]
  19. V. B. Mohan, K. Lau, D. Hui, and D. Bhattacharyya, “Graphene-based materials and their composites: A review on production, applications and product limitations,” Composites, Part B 142, 200–220 (2018).
    [Crossref]
  20. V.M. Mikoushkin, S. Y. Nikonov, A. T. Dideykin, A. Y. Vul, D. A. Sakseev, M. V. Baidakova, O. Yu. Vilkov, and A. V. Nelyubov, “Graphene hydrogenation by molecular hydrogen in the process of graphene oxide thermal reduction,” Appl. Phys. Lett. 102(7), 071910 (2013).
    [Crossref]
  21. G. Liu, S. Dai, F. Cao, B. Zhu, P. Li, and Y. Z. Gu, “Preparation and enhanced nonlinear optical properties of Bi2S3/RGO composite materials,” Opt. Mater. 89, 112–117 (2019).
    [Crossref]
  22. Z. Zhang, P. Li, P. C. Li, and Y. Z. Gu, “Facile one-step synthesis and enhanced optical nonlinearity of graphene-γMnS,” Nanomaterials 9(12), 1654 (2019).
    [Crossref]
  23. M. Khanzadeh, M. Dehghanipour, M. Karimipour, and M. Molaei, “Improvement of nonlinear optical properties of graphene oxide in mixed with Ag2S@ZnS core-shells,” Opt. Mater. 66, 664–670 (2017).
    [Crossref]
  24. T. He, W. Wei, L. Ma, R. Chen, S. Wu, H. Zhang, Y. Yang, J. Ma, L. Huang, G. G. Gurzadyan, and H. Sun, “Mechanism studies on the superior optical limiting observed in graphene oxide covalentlyfunctionalized with upconversion NaYF4:Yb3+/Er3+ Nanoparticles,” Small 8(14), 2163–2168 (2012).
    [Crossref]
  25. W. Zhou, J. Zhu, C. Cheng, J. Liu, H. Yang, C. Cong, C. Guan, X. Jia, H. Fan, Q. Yan, C. Li, and T. Yu, “A general strategy toward graphene@metal oxide core–shell nanostructures for high-performance lithium storage,” Energy Environ. Sci. 4(12), 4954–4961 (2011).
    [Crossref]
  26. J. Cao, M. Safdar, Z. Wang, and J. He, “High-performance flexible supercapacitor electrodes based on Te nanowire arrays,” J. Mater. Chem. A 1(34), 10024–10029 (2013).
    [Crossref]
  27. W. Chen, Y. Lin, T. Yang, Y. Pu, and Y. Hsu, “Au/ZnS core/shell nanocrystals as an efficient anode photocatalyst in direct methanol fuel cells,” Chem. Commun. 49(76), 8486 (2013).
    [Crossref]
  28. W. Chen, T. Yang, and Y. Hsu, “Au-CdS core−shell nanocrystals with controllable shell thickness and photoinduced charge separation property,” Chem. Mater. 20(23), 7204–7206 (2008).
    [Crossref]
  29. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryl, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
    [Crossref]
  30. L. Cheng, J. Liu, T. Chen, M. Xu, M. Ji, B. Zhang, X. Zhang, and J. Zhang, “Ternary cooperative Au-CdS-RGO hetero-nanostructures: synthesis with multi-interface control and their photoelectrochemical sensor applications,” RSC Adv. 6(37), 30785–30790 (2016).
    [Crossref]
  31. Y. Cao, C. Wang, B. Zhu, and Y. Gu, “A facile method to synthesis high-quality CdSe quantum dots for large and tunable nonlinear absorption,” Opt. Mater. 66, 59–64 (2017).
    [Crossref]
  32. H. Zeng, J. Han, D. Qian, and Y. Gu, “Third-order nonlinear optical properties of multiwalled carbon nanotubes modified by CdS nanoparticles,” Optik 125(21), 6558–6561 (2014).
    [Crossref]
  33. A. E. Nikolaenko, N. Papasimakis, E. Atmatzakis, Z. Luo, Z. X. Shen, F. D. Angelis, S. A. Boden, E. D. Fabrizio, and N. I. Zheludev, “Nonlinear graphene metamaterial,” Appl. Phys. Lett. 100(18), 181109 (2012).
    [Crossref]

2019 (5)

B. Guo, Q. L. Xiao, S. H. Wang, and H. Zhang, “2D layered materials: synthesis, nonlinear optical properties, and device applications,” Laser Photonics Rev. 13(12), 1800327 (2019).
[Crossref]

M. Luo, T. Fan, Y. Zhou, H. Zhang, and L. Mei, “2D black phosphorus-based biomedical applications,” Adv. Funct. Mater. 29(13), 1808306 (2019).
[Crossref]

X. Wang, Y. Cui, T. Li, M. Lei, J. Li, and Z. Wei, “Recent advances in the functional 2D photonic and optoelectronic devices,” Adv. Opt. Mater. 7(3), 1801274 (2019).
[Crossref]

G. Liu, S. Dai, F. Cao, B. Zhu, P. Li, and Y. Z. Gu, “Preparation and enhanced nonlinear optical properties of Bi2S3/RGO composite materials,” Opt. Mater. 89, 112–117 (2019).
[Crossref]

Z. Zhang, P. Li, P. C. Li, and Y. Z. Gu, “Facile one-step synthesis and enhanced optical nonlinearity of graphene-γMnS,” Nanomaterials 9(12), 1654 (2019).
[Crossref]

2018 (5)

V. B. Mohan, K. Lau, D. Hui, and D. Bhattacharyya, “Graphene-based materials and their composites: A review on production, applications and product limitations,” Composites, Part B 142, 200–220 (2018).
[Crossref]

B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on black phosphorus photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018).
[Crossref]

J. Zhou, J. Lin, X. Huang, Y. Zhou, Y. Chen, J. Xia, H. Wang, Y. Xie, H. Yu, J. Lei, D. Wu, F. Liu, Q. Fu, Q. Zeng, C. H. Hsu, C. Yang, L. Lu, T. Yu, Z. Shen, H. Lin, B. I. Yakobson, Q. Liu, K. Suenaga, G. Liu, and Z. Liu, “A library of atomically thin metal chalcogenides,” Nature 556(7701), 355–359 (2018).
[Crossref]

C. Yan, C. Gong, P. Wangyang, J. Chu, K. Hu, C. Li, X. Wang, X. Du, T. Zhai, and J. Xiong, “2D group IVB transition metal dichalcogenides,” Adv. Funct. Mater. 28(39), 1803305 (2018).
[Crossref]

K. F. Mak, D. Xiao, and J. Shan, “Light–valley interactions in 2D semiconductors,” Nat. Photonics 12(8), 451–460 (2018).
[Crossref]

2017 (6)

S. Dhanabalan, J. Ponraj, Z. Guo, S. Li, Q. Bao, and H. Zhang, “Emerging trends inphosphorene fabrication towards next generation devices,” Adv. Sci. 4(6), 1600305 (2017).
[Crossref]

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. M. Moreno, and F. H. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16(2), 182–194 (2017).
[Crossref]

C. Tan, Z. Lai, and H. Zhang, “Ultrathin two-dimensional multinary layered metal chalcogenide nanomaterials,” Adv. Mater. 29(37), 1701392 (2017).
[Crossref]

X. Kong, Q. Liu, C. Zhang, Z. Peng, and Q. Chen, “Elemental two-dimensional nanosheets beyond graphene,” Chem. Soc. Rev. 46(8), 2127–2157 (2017).
[Crossref]

Y. Cao, C. Wang, B. Zhu, and Y. Gu, “A facile method to synthesis high-quality CdSe quantum dots for large and tunable nonlinear absorption,” Opt. Mater. 66, 59–64 (2017).
[Crossref]

M. Khanzadeh, M. Dehghanipour, M. Karimipour, and M. Molaei, “Improvement of nonlinear optical properties of graphene oxide in mixed with Ag2S@ZnS core-shells,” Opt. Mater. 66, 664–670 (2017).
[Crossref]

2016 (1)

L. Cheng, J. Liu, T. Chen, M. Xu, M. Ji, B. Zhang, X. Zhang, and J. Zhang, “Ternary cooperative Au-CdS-RGO hetero-nanostructures: synthesis with multi-interface control and their photoelectrochemical sensor applications,” RSC Adv. 6(37), 30785–30790 (2016).
[Crossref]

2015 (2)

Y. J. Kim, Y. Kim, K. Novoselov, and B. H. Hong, “Engineering electrical properties of graphene: chemical approaches,” 2D Mater. 2(4), 042001 (2015).
[Crossref]

A. Gupta, T. Sakthivel, and S. Seal, “Recent development in 2D materials beyond graphene,” Prog. Mater. Sci. 73, 44–126 (2015).
[Crossref]

2014 (1)

H. Zeng, J. Han, D. Qian, and Y. Gu, “Third-order nonlinear optical properties of multiwalled carbon nanotubes modified by CdS nanoparticles,” Optik 125(21), 6558–6561 (2014).
[Crossref]

2013 (4)

V.M. Mikoushkin, S. Y. Nikonov, A. T. Dideykin, A. Y. Vul, D. A. Sakseev, M. V. Baidakova, O. Yu. Vilkov, and A. V. Nelyubov, “Graphene hydrogenation by molecular hydrogen in the process of graphene oxide thermal reduction,” Appl. Phys. Lett. 102(7), 071910 (2013).
[Crossref]

J. Cao, M. Safdar, Z. Wang, and J. He, “High-performance flexible supercapacitor electrodes based on Te nanowire arrays,” J. Mater. Chem. A 1(34), 10024–10029 (2013).
[Crossref]

W. Chen, Y. Lin, T. Yang, Y. Pu, and Y. Hsu, “Au/ZnS core/shell nanocrystals as an efficient anode photocatalyst in direct methanol fuel cells,” Chem. Commun. 49(76), 8486 (2013).
[Crossref]

K. J. Koski and Y. Cui, “The new skinny in two-dimensional nanomaterials,” ACS Nano 7(5), 3739–3743 (2013).
[Crossref]

2012 (2)

T. He, W. Wei, L. Ma, R. Chen, S. Wu, H. Zhang, Y. Yang, J. Ma, L. Huang, G. G. Gurzadyan, and H. Sun, “Mechanism studies on the superior optical limiting observed in graphene oxide covalentlyfunctionalized with upconversion NaYF4:Yb3+/Er3+ Nanoparticles,” Small 8(14), 2163–2168 (2012).
[Crossref]

A. E. Nikolaenko, N. Papasimakis, E. Atmatzakis, Z. Luo, Z. X. Shen, F. D. Angelis, S. A. Boden, E. D. Fabrizio, and N. I. Zheludev, “Nonlinear graphene metamaterial,” Appl. Phys. Lett. 100(18), 181109 (2012).
[Crossref]

2011 (2)

W. Zhou, J. Zhu, C. Cheng, J. Liu, H. Yang, C. Cong, C. Guan, X. Jia, H. Fan, Q. Yan, C. Li, and T. Yu, “A general strategy toward graphene@metal oxide core–shell nanostructures for high-performance lithium storage,” Energy Environ. Sci. 4(12), 4954–4961 (2011).
[Crossref]

X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83(4), 1057–1110 (2011).
[Crossref]

2010 (1)

J. Moore, “The birth of topological insulators,” Nature 464(7286), 194–198 (2010).
[Crossref]

2008 (1)

W. Chen, T. Yang, and Y. Hsu, “Au-CdS core−shell nanocrystals with controllable shell thickness and photoinduced charge separation property,” Chem. Mater. 20(23), 7204–7206 (2008).
[Crossref]

2007 (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref]

2005 (1)

K. S. Novoselov, D. Jiang, F. Schedin, T. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102(30), 10451–10453 (2005).
[Crossref]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryl, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

Angelis, F. D.

A. E. Nikolaenko, N. Papasimakis, E. Atmatzakis, Z. Luo, Z. X. Shen, F. D. Angelis, S. A. Boden, E. D. Fabrizio, and N. I. Zheludev, “Nonlinear graphene metamaterial,” Appl. Phys. Lett. 100(18), 181109 (2012).
[Crossref]

Atmatzakis, E.

A. E. Nikolaenko, N. Papasimakis, E. Atmatzakis, Z. Luo, Z. X. Shen, F. D. Angelis, S. A. Boden, E. D. Fabrizio, and N. I. Zheludev, “Nonlinear graphene metamaterial,” Appl. Phys. Lett. 100(18), 181109 (2012).
[Crossref]

Avouris, P.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. M. Moreno, and F. H. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16(2), 182–194 (2017).
[Crossref]

Baidakova, M. V.

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G. Liu, S. Dai, F. Cao, B. Zhu, P. Li, and Y. Z. Gu, “Preparation and enhanced nonlinear optical properties of Bi2S3/RGO composite materials,” Opt. Mater. 89, 112–117 (2019).
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G. Liu, S. Dai, F. Cao, B. Zhu, P. Li, and Y. Z. Gu, “Preparation and enhanced nonlinear optical properties of Bi2S3/RGO composite materials,” Opt. Mater. 89, 112–117 (2019).
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W. Zhou, J. Zhu, C. Cheng, J. Liu, H. Yang, C. Cong, C. Guan, X. Jia, H. Fan, Q. Yan, C. Li, and T. Yu, “A general strategy toward graphene@metal oxide core–shell nanostructures for high-performance lithium storage,” Energy Environ. Sci. 4(12), 4954–4961 (2011).
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J. Cao, M. Safdar, Z. Wang, and J. He, “High-performance flexible supercapacitor electrodes based on Te nanowire arrays,” J. Mater. Chem. A 1(34), 10024–10029 (2013).
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W. Chen, Y. Lin, T. Yang, Y. Pu, and Y. Hsu, “Au/ZnS core/shell nanocrystals as an efficient anode photocatalyst in direct methanol fuel cells,” Chem. Commun. 49(76), 8486 (2013).
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C. Yan, C. Gong, P. Wangyang, J. Chu, K. Hu, C. Li, X. Wang, X. Du, T. Zhai, and J. Xiong, “2D group IVB transition metal dichalcogenides,” Adv. Funct. Mater. 28(39), 1803305 (2018).
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V. B. Mohan, K. Lau, D. Hui, and D. Bhattacharyya, “Graphene-based materials and their composites: A review on production, applications and product limitations,” Composites, Part B 142, 200–220 (2018).
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L. Cheng, J. Liu, T. Chen, M. Xu, M. Ji, B. Zhang, X. Zhang, and J. Zhang, “Ternary cooperative Au-CdS-RGO hetero-nanostructures: synthesis with multi-interface control and their photoelectrochemical sensor applications,” RSC Adv. 6(37), 30785–30790 (2016).
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W. Zhou, J. Zhu, C. Cheng, J. Liu, H. Yang, C. Cong, C. Guan, X. Jia, H. Fan, Q. Yan, C. Li, and T. Yu, “A general strategy toward graphene@metal oxide core–shell nanostructures for high-performance lithium storage,” Energy Environ. Sci. 4(12), 4954–4961 (2011).
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M. Khanzadeh, M. Dehghanipour, M. Karimipour, and M. Molaei, “Improvement of nonlinear optical properties of graphene oxide in mixed with Ag2S@ZnS core-shells,” Opt. Mater. 66, 664–670 (2017).
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M. Khanzadeh, M. Dehghanipour, M. Karimipour, and M. Molaei, “Improvement of nonlinear optical properties of graphene oxide in mixed with Ag2S@ZnS core-shells,” Opt. Mater. 66, 664–670 (2017).
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Y. J. Kim, Y. Kim, K. Novoselov, and B. H. Hong, “Engineering electrical properties of graphene: chemical approaches,” 2D Mater. 2(4), 042001 (2015).
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Y. J. Kim, Y. Kim, K. Novoselov, and B. H. Hong, “Engineering electrical properties of graphene: chemical approaches,” 2D Mater. 2(4), 042001 (2015).
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X. Kong, Q. Liu, C. Zhang, Z. Peng, and Q. Chen, “Elemental two-dimensional nanosheets beyond graphene,” Chem. Soc. Rev. 46(8), 2127–2157 (2017).
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T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. M. Moreno, and F. H. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16(2), 182–194 (2017).
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K. J. Koski and Y. Cui, “The new skinny in two-dimensional nanomaterials,” ACS Nano 7(5), 3739–3743 (2013).
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T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. M. Moreno, and F. H. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16(2), 182–194 (2017).
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J. Zhou, J. Lin, X. Huang, Y. Zhou, Y. Chen, J. Xia, H. Wang, Y. Xie, H. Yu, J. Lei, D. Wu, F. Liu, Q. Fu, Q. Zeng, C. H. Hsu, C. Yang, L. Lu, T. Yu, Z. Shen, H. Lin, B. I. Yakobson, Q. Liu, K. Suenaga, G. Liu, and Z. Liu, “A library of atomically thin metal chalcogenides,” Nature 556(7701), 355–359 (2018).
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Lei, M.

X. Wang, Y. Cui, T. Li, M. Lei, J. Li, and Z. Wei, “Recent advances in the functional 2D photonic and optoelectronic devices,” Adv. Opt. Mater. 7(3), 1801274 (2019).
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Li, C.

C. Yan, C. Gong, P. Wangyang, J. Chu, K. Hu, C. Li, X. Wang, X. Du, T. Zhai, and J. Xiong, “2D group IVB transition metal dichalcogenides,” Adv. Funct. Mater. 28(39), 1803305 (2018).
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[Crossref]

W. Zhou, J. Zhu, C. Cheng, J. Liu, H. Yang, C. Cong, C. Guan, X. Jia, H. Fan, Q. Yan, C. Li, and T. Yu, “A general strategy toward graphene@metal oxide core–shell nanostructures for high-performance lithium storage,” Energy Environ. Sci. 4(12), 4954–4961 (2011).
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X. Wang, Y. Cui, T. Li, M. Lei, J. Li, and Z. Wei, “Recent advances in the functional 2D photonic and optoelectronic devices,” Adv. Opt. Mater. 7(3), 1801274 (2019).
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Z. Zhang, P. Li, P. C. Li, and Y. Z. Gu, “Facile one-step synthesis and enhanced optical nonlinearity of graphene-γMnS,” Nanomaterials 9(12), 1654 (2019).
[Crossref]

G. Liu, S. Dai, F. Cao, B. Zhu, P. Li, and Y. Z. Gu, “Preparation and enhanced nonlinear optical properties of Bi2S3/RGO composite materials,” Opt. Mater. 89, 112–117 (2019).
[Crossref]

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Z. Zhang, P. Li, P. C. Li, and Y. Z. Gu, “Facile one-step synthesis and enhanced optical nonlinearity of graphene-γMnS,” Nanomaterials 9(12), 1654 (2019).
[Crossref]

Li, S.

S. Dhanabalan, J. Ponraj, Z. Guo, S. Li, Q. Bao, and H. Zhang, “Emerging trends inphosphorene fabrication towards next generation devices,” Adv. Sci. 4(6), 1600305 (2017).
[Crossref]

Li, T.

X. Wang, Y. Cui, T. Li, M. Lei, J. Li, and Z. Wei, “Recent advances in the functional 2D photonic and optoelectronic devices,” Adv. Opt. Mater. 7(3), 1801274 (2019).
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J. Zhou, J. Lin, X. Huang, Y. Zhou, Y. Chen, J. Xia, H. Wang, Y. Xie, H. Yu, J. Lei, D. Wu, F. Liu, Q. Fu, Q. Zeng, C. H. Hsu, C. Yang, L. Lu, T. Yu, Z. Shen, H. Lin, B. I. Yakobson, Q. Liu, K. Suenaga, G. Liu, and Z. Liu, “A library of atomically thin metal chalcogenides,” Nature 556(7701), 355–359 (2018).
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J. Zhou, J. Lin, X. Huang, Y. Zhou, Y. Chen, J. Xia, H. Wang, Y. Xie, H. Yu, J. Lei, D. Wu, F. Liu, Q. Fu, Q. Zeng, C. H. Hsu, C. Yang, L. Lu, T. Yu, Z. Shen, H. Lin, B. I. Yakobson, Q. Liu, K. Suenaga, G. Liu, and Z. Liu, “A library of atomically thin metal chalcogenides,” Nature 556(7701), 355–359 (2018).
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Lin, Y.

W. Chen, Y. Lin, T. Yang, Y. Pu, and Y. Hsu, “Au/ZnS core/shell nanocrystals as an efficient anode photocatalyst in direct methanol fuel cells,” Chem. Commun. 49(76), 8486 (2013).
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J. Zhou, J. Lin, X. Huang, Y. Zhou, Y. Chen, J. Xia, H. Wang, Y. Xie, H. Yu, J. Lei, D. Wu, F. Liu, Q. Fu, Q. Zeng, C. H. Hsu, C. Yang, L. Lu, T. Yu, Z. Shen, H. Lin, B. I. Yakobson, Q. Liu, K. Suenaga, G. Liu, and Z. Liu, “A library of atomically thin metal chalcogenides,” Nature 556(7701), 355–359 (2018).
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Liu, G.

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of rGO-Au@CdS composite nanostructure.
Fig. 2.
Fig. 2. SEM images of rGO-Au (A), Au@CdS (B) and rGO-Au@CdS (C); TEM images of rGO-Au@CdS composites S1 (D), S2 (E) and S3 (F).
Fig. 3.
Fig. 3. XRD pattern (A) and XPS spectrum (B) of the samples.
Fig. 4.
Fig. 4. UV-vis absorption spectrum (A) and typical VB spectra (B) of the samples.
Fig. 5.
Fig. 5. (A) Open aperture Z-scan curves of rGO, rGO-Au and Au@CdS; (B) Open aperture Z-scan curves of rGO-Au@CdS (sample S1,S2 and S3); (C) Closed-aperture/open-aperture Z-scan curves of rGO, rGO-Au and Au@CdS; (D) Closed-aperture/open-aperture Z-scan curves of rGO-Au@CdS (sample S1,S2 and S3).
Fig. 6.
Fig. 6. (A) The charge transfer mechanism and (B) energy-level diagram of rGO-Au@CdS composites; (C) Normalized transmittance as functions of irradiance intensity.

Tables (1)

Tables Icon

Table 1. The nonlinear susceptibilities of the samples

Equations (14)

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T ( z ) = m = 0 [ q 0 ( z ) ] m ( 1 + m ) 3 / 2
T ( z ) = 1  -  4 x Δ Φ 0 ( x 2 + 9 ) ( x 2 + 1 )
d I d z = α ( I ) I
P = 0 I i n e 2 r 2 ω 2 ( z ) .2 π r d r = 1 2 π ω 2 ( z ) I i n
I i n = 2 P π ω 2 ( z ) = 2 E τ π ω 2 ( z ) = 2 E τ π ω 0 2 [ 1 + ( z / z 0 ) 2 ]
d N 2 d t = N 1 σ 1 I h ν N 2 τ 2
d N 1 d t = N 0 σ 0 I h ν N 1 τ 1 N 1 τ 3 N 1 σ 1 I h ν + N 2 τ 2
d N 0 d t = N 0 σ 0 I h ν + N 1 τ 1 + N E / 2 τ 4
d N + E / 2 d t = N + E / 2 τ 5 + N 1 τ 3 + N E / 2 σ 2 I h ν
d N E / 2 d t = N + E / 2 τ 5 N E / 2 σ 2 I h ν N E / 2 τ 4
N = N 0 + N 1 + N 2 + N E / 2 + N + E / 2
d I d z = ( σ 0 N 0 + σ 1 N 1 + σ 2 N E / 2 + σ 3 N + E / 2 ) I
α ( I ) = σ 0 N 0 + σ 1 N 1 + σ 2 N E / 2 + σ 3 N + E / 2
α ( I ) =  =  R 3 τ 4 I 2 I 2 + ( R 1 τ 3 + R 2 τ 4 + R 3 τ 5 ) I 2 I 3 I + ( τ 1 + τ 3 ) I 1 I 2 I 3 ( τ 3 I 3 + τ 4 I 2 ) I 2 + ( τ 3 + τ 4 + τ 5 ) I 2 I 3 I + ( τ 1 + τ 3 ) I 1 I 2 I 3 σ 0 N

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