1 Introduction

Nonlinear optical properties are of great importance in fields such as telecommunications, data storage, and imaging, as they allow for efficient manipulation and control of light waves. Nonlinear optical materials exhibit a nonlinear response to light intensity, which can lead to effects such as frequency conversion, harmonic generation, and optical limiting [1,2,3]. Graphene and graphene oxide have exhibited unique thermal, and electronic properties [4, 5]. Furthermore, Graphene oxide is a promising candidate for nonlinear optical applications due to its high third-order nonlinear susceptibility and broadband absorption spectrum. [6], Muralidharan et al. [7] studied the nonlinear optical absorption and optical limiting of thermally stable reduced graphene oxide polymeric films at 532 nm. Zhang et al. [8] designed graphene-oxide quantum dots and studied the nonlinear optical properties at different wavelengths using a femtosecond laser. Yan et al. [9] reported enhanced optical nonlinearities of graphene oxide films by carbon dioxide laser direct writing. Furthermore, the nanocomposites based on graphene derivatives improve the nonlinear optical properties such as high-pressure CO single wall carbon nanotube HiPCO-SWCNTs films [10], and reduced graphene oxide/silver nanoparticles [11].

on the other hand, Gold nanorods (AuNRs) have received significant attention due to their high longitudinal surface plasmon resonance (LSPR) in the near infra-red region (NIR). SPR bands can be tailored by adjusting their shape, size, and dielectric medium. Many researchers have an interest in the nonlinear optical properties of rods [12,13,14,15]. Wang et al. [16] studied the nonlinear absorption of gold nanorods (length 46 nm) using an 800 nm femtosecond laser. García-Ramírez et al. [17] prepared gold nanorods with different aspect ratios and studied their nonlinear optical properties using 26 ps at 532 and 1064 nm, Moreover, metallic nanoparticles exhibit advanced nonlinear optical properties due to surface plasmon resonance. optical nonlinearity are enhanced with combining metal nanomaterials in hybrid metal nanostructures such as Ag-CdSe [18], Mn-CdS [19], Au-CdS nanorods [20], Au-CdSe [21, 22]. In addition, nanomaterials incorporation in host polymer provides a novel path for tailoring new nonlinear optical (NLO) materials, where polymeric composites are stable. Polyvinylpyrrolidone k30 PVP is one of the most promising polymers for different applications. it is used to increase the mechanical strength and thermal stability of the hybrid material. [23,24,25]

GO can be merged with metallic nanomaterials to obtain composites with superior nonlinear optical properties through local-field enhancement. For example; Kinastowska et al. [26] have studied plasmonic enhancement of graphene’s nonlinear absorption by preparing gold nanoparticle-decorated graphene dispersion using femtosecond laser pulses. Nancy et al. [27] investigated the nonlinear absorption of silver graphene oxide nanocomposite using a nanosecond laser. Lee et al. [28] recorded an enhancement of the optical properties of Graphene Oxide-Au composites using two-photon excitation emission measurements.

There are reports devoted to the study of third-order NLO properties of gold nanorods in the colloidal form [17], graphene oxide [29, 30], and gold-graphene nanocomposites (at 532 nm) [11], graphene gold nanorods composite [12], while there is no report to show the comparison between the optical nonlinearity for a colloidal and polymeric form of the mentioned nanostructures. In this study, before discussing the nonlinear measurements, sample preparations were introduced, and the characterization of samples via linear optical absorption measurements, Transmission Electron microscope TEM, and Raman Spectroscopy were presented. Then, nonlinear optical absorption was studied for Au nanorods, GO, and GO@AuNRs at a resonant excitation wavelength for colloidal and polymeric forms. This work has a significant impact on the nonlinear absorption behavior of GO@AuNRs and their constituent AuNRs and GO. The optical limiting was achieved at different powers. the composites can be used in photonic applications such as sensor protection, optical limiting devices, plasmon waveguide, and medical therapies.

2 Materials and methods

2.1 Preparation of GO, AuNRs, and GO@AuNRs in colloidal and polymer form

2.1.1 Chemicals and reagents

Tetra chloroauric acid (HAuCl43H2O), silver nitrate (AgNO3), cetyltrimethylammonium- bromide (CTAB) (99% purity), L-Ascorbic acid, NaNO3 (99% purity), H2SO4 (95–98% purity), Graphite powder (99% purity), Sodium borohydride (NaBH4) (96% purity), H2O2 36% and potassium permanganate (KMnO4) (99% purity), Polyvinylpyrrolidone polymer (PVP) (99% purity), were purchased from Sigma Aldrich. Deionized distilled water (DD water) was used in all procedures and all solvents were used without further purification.

2.1.2 Synthesis of graphene oxide nanosheets (GO)

GO was prepared as in Fig. 1a using a modified Hummer’s method by oxidation of graphite powder, potassium permanganate, and sulfuric acid producing diamanganese heptoxide (Mn2O7) which oxidizes the double bonds of graphite forming GO [31,32,33]. This procedure involved dissolving 1 g of graphite powder in 50 ml of sulfuric acid H2SO4, then adding 1 g of sodium nitrate NaNO3 and stirring the mixture for 30 min. The reaction vessel was placed in an ice bath with the temperature set at approximately 3 °C. 6 g of potassium permanganate (KMnO4) was gradually added. After stirring the reaction mixture at 35 °C for a whole night, 50 ml of water was added, and after 1 h of stirring, the reaction temperature was raised to about 90 °C. After that, 280 ml of warm water and 10 ml of hydrogen peroxide H2O2 were added. The appearance of a brownish-yellow colour indicated the formation of GO. A GO sample is washed, centrifuged, and dried at 60 °C.

Fig. 1
figure 1

Scheme on preparations of a GO, b AuNRs with different aspect ratios, c GO@AuNRs

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2.1.3 Synthesis of AuNRs with different aspect ratios

AuNRs were synthesized as in Fig. 1b by the seed-mediated growth method [34] in two steps. First, the seed solution is prepared by adding iced NaBH4 (0.6 ml, 0.01 M) to 7.5 ml of 0.2 M CTAB and 2.5 ml of 0.001M HAuCl4, a brownish-yellow solution is formed. After stirring, the seed was kept at room temperature. Then, using the growth solution of AuNRs prepared by CTAB (50 ml, 0.2 M), by adjusting the concentration of AgNO3 in the growth solution, two different samples with two aspect ratios of AuNRs can be obtained. So, 2 ml of AgNO3 (0.004 M for preparation of AuNRs1 and 0.002 M for preparation of AuNRs2), and HAuCl4 (50 ml of 0.001 M) were added after that in each sample and stirred at room temperature, also L-ascorbic acid (0.1 M) was then added, and that solution became colourless immediately.. Finally, add 0.8 ml of the seed solution. The growth solution was kept at room temperature. The colour of the solution gradually changed to amaranth within about 10 min. AuNRs1 and AuNRs2 started to grow for 24 h until the growth was complete. After that, the AuNRs were purified by centrifugation at 12,000 rpm for 10 min to remove excess CTAB. [35]

2.1.4 Synthesis of GO@AuNRs with different ratios

GO is prepared by acid/base treatments [36]. It has surface functional groups such as carbonyl, hydroxyl, and carboxyl, which are responsible for its solubility in different solvents, which makes GO a good host for the formation of nanohybrids with different nanomaterials [37, 38]. GO@AuNRs were prepared as in Fig. 1c by adding AuNRs into GO solution in a dropwise manner; this method has been reported by many authors, usually by using cross linkers to stimulate electrostatic interaction of GO with AuNRs [38, 39]. In this method, AuNRs were synthesized separately and interacted with GO. 500 µg/ml of GO was dispersed in water by sonication for 3 h, then changing the feeding volume ratios of 1 µ moles of AuNRs to GO (GO: AuNRs = 1:1, 1:3, and 1:5) volume to volume ratio (v/v) with a continuous stirring for 30 min [40] to obtain three different, very stable samples of GO@AuNRs.

2.1.5 Polymerization of GO, AuNRs, and GO@AuNRs films using PVP

PVP is used to form a thin, transparent nanocomposite film. In this method, as in Fig. 1 10 g of PVP (30,000–40000 MW) was gradually mixed in 100 ml of DD water, and the temperature was slowly raised to 40 °C with stirring until a clear 10% PVP solution was obtained. Finally, 5 ml of the prepared PVP solution was poured into a beaker, and 5 ml of each prepared sample (GO, AuNRs, and GO@AuNRs with different ratios) were added, stirred for 15 min, and sonicated for about 15 min. The solutions were poured into a flat frame and allowed to solidify at room temperature for 48 h. The prepared film was kept in the oven at about 40 °C for 24 h to complete drying. After that, the film was cut into small strips [41]. The film thickness of the polymeric films of GO, AuNR1, GO@AuNR1(ratio1-3), and GO@AuNR1(ratio1-5) are 0.45, 0.5, 0.45, and 0.25 mm, respectively.

2.2 Characterization techniques

2.2.1 Apparatus and characterization

Absorption spectra of the prepared samples of GO, AuNRs, and GO@AuNRs were recorded using a spectrophotometer (a Perkin–Elmer Lambda 950). The morphology of the prepared samples was imaged by High-Resolution Transmission Electron Microscope (Tecnai, G20, FEI, Netherlands), with an accelerating voltage of 200 kV. Raman spectroscopy was performed using (Raman Senterra II, Germany) and the Raman scattering was excited with 532 nm excitation wavelength. Using energy-dispersive X-ray spectroscopy (EDX), some details regarding a particular sample composition were gleaned. An integrated EDX detector was installed with the scanning electron microscope Qunta 250 FEG.

2.2.2 Nonlinear optical absorption measurements.

The nonlinear absorption is measured using Nd: YAG laser with parameters (1Hz, 6 ns, 50 µJ at 532 nm) via Open aperture Z scan setup (OA). Samples are scanned around the focal point of a lens using a motorized stage (LTS 150 M THORLABS). The far-field transmittance of the samples was measured by photodetectors (S142C Thorlabs- PM 320 E Thorlabs). The optical limiting measurements were performed by placing the sample at the focal point of the lens as a function of laser power.

In an open aperture Z scan, The normalized transmittance is presented with: [34]

$${\text{T}}\,\left( {\text{z}} \right)\, = \,\mathop \sum \limits_{m = 0}^{\infty } \frac{{q_{0} }}{{(m\, + \,1)^{{{\raise0.7ex\hbox{$3$} \!\mathord{\left/ {\vphantom {3 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} .(1\, + \,{\raise0.7ex\hbox{${z^{2} }$} \!\mathord{\left/ {\vphantom {{z^{2} } {z_{o}^{2} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${z_{o}^{2} }$}})^{m} }}$$
(1)

where q0 = βI0Leff,\(\beta\) is the nonlinear absorption coefficient, the effective interaction length is Leff=\(\frac{1-{e}^{-{\alpha }_{o}L}}{{\alpha }_{o}}\) is with the sample thickness L, and \({\alpha }_{o}\) is the linear absorption coefficient, thus by fitting the experimental data to Eq. (1), we can determine β. z is the displacement along the z direction, zo is the diffraction length equals \({\raise0.7ex\hbox{${\pi \omega_{o}^{2} }$} \!\mathord{\left/ {\vphantom {{\pi \omega_{o}^{2} } \lambda }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\lambda $}}\) where \(\omega_{o}\) is the beam waist at the focal point = 20 µm, and λ is the laser wavelength. The intensity of the laser beam at 532 nm = 0.79 GW/cm2 at 50µJ.

3 Results and discussions

3.1 Optical characterization of GO, AuNRs, and GO@AuNRs in colloidal form

3.1.1 Characterization of colloidal GO, and AuNRs

Regarding the preparation of gold nanorods, a small amount of gold seed solution is added to the growth solution in the presence of the action of surfactants, then the seed grows into AuNRs. The solution of this experiment is containing different materials as follows HAuCl4 as a precursor of gold; CTAB as a surfactant; silver nitrate which induces anisotropic growth of AuNRs [35]; and ascorbic acid which promotes the reduction of gold from Au+3 to Au+1. Gold precursor and the solution changed from yellow color to transparent solution. Au seed was added to the growth solution to make the Au atoms grow along the one-dimensional direction on the surface of the seeds under the action of CTAB and grow into a one-dimensional rod shape [29].

As seen in Fig. 2; the linear absorption of GO solution showed a characteristic absorption band at about 230 nm. Figure 3a shows the TEM image of GO, which reveals a smooth surface and wrinkled edge of GO nanosheets. In addition, AuNRs have two absorption bands: a transverse surface plasmon resonance (TSPR) in short wavelength region and a longitudinal surface plasmon resonance (LSPR) in long-wavelength region. The TSPR peaks at a visible region were detected at 533, and 541 nm for AuNRs1, and AuNRs2 respectively. TSPR band has less dependence on the length of diameter ratio of the nanorods. However, LSPR has a great dependence on the morphology, size, and surrounding medium environment of AuNRs. As shown in Fig. 2 LSPR were observed at about 689, 650 nm for AuNRs1, and AuNRs2, respectively.

Fig. 2
figure 2

Linear absorption of GO, AuNRs1, and AuNRs2 in colloidal form

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Fig. 3
figure 3

TEM of a GO, b, c AuNR1, d, e AuNR2

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The increase of the length-diameter ratio of the AuNRs is due to the significant redshift of LSPR. so the enhancement of LSPR conveys the optimization of the optical and thermal properties of AuNRs and it can be used in many sensing applications by changing the rod aspect ratio[36]. The average aspect ratios of AuNRs1, and AuNRs2 are 3.4, and 2.7, respectively.

In Fig. 3, the TEM images of the prepared AuNRs1 and AuNRs2 show that they have a nanorod-shaped morphology. The AuNRs2 had a shorter length and width when 0.002M AgNO3 was employed as seen in Table 1. This sample has an aspect ratio of roughly 2.7, but as the amount of AgNO3 in the growth solution is increased to 0.004M for AuNRs1, the length and width of gold nanorods rises to 44, 13 nm respectively. As a result, the aspect ratios for AuNRs1 becomes roughly 3.4 (the detailed data are shown in Table 1) [36].

Table 1 AuNRs specifications: length, width, aspect ratio, and λ max
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3.1.2 Characterization of colloidal GO@AuNRs composite

The CTAB-capped AuNRs interacted with the negatively charged GO through electrostatic attraction, resulting in the preparation of GO@AuNRs. High dispersion and stability were supplied by repulsion from the negative charges on the surface of GO@AuNRs. By using UV–visible spectroscopy, GO@AuNRs were identified as presented in Fig. 4a, In this sample AuNRs1 coated with positively charged bilayers. The LSPR peak of GO@AuNRs is located about 700 nm, whereas the TSPR peak is located at 545 nm. Additionally, a typical GO band was seen at around 230 nm, proving that AuNRs and GO were successfully interacting.The stability of the prepared GO@AuNRs was obtained when AuNRs solution was added slowly into GO solution with continuous stirring at room temperature. As a result, by electrostatic interaction, AuNRs were firmly bonded to the surface of the thin layer of GO. Due to the wide surface areas of graphene oxide, as the concentration of AuNRs to GO increase the peak position and intensity change.The peaks heigh increase correspond to transitions in the molecule scale pi to pi and sigma to pi, as shown obviously in Fig. 4b, c, d. the absorption properties based on the principles of pi-electron conjugation and plasmonic behavior. The pi-electron system of GO can interact with the pi electrons of the surface of AuNRs in the composite. This interaction can facilitate charge transfer between GO and AuNRs, leading to enhanced absorption in the composite. This can result in increased absorption peak intensity and position of the absorption spectrum. Also sigma electrons of the ligands on AuNRs can interact with the pi electrons of GO through sigma to pi interactions. These interactions can also affect the absorption properties of the composite.

Fig. 4
figure 4

a absorption spectra of GO@AuNRs with different ratios, b, c, d TEM images of GO/GNRs nanocomposites with different ratios (1:1; 1:3; 1:5), e Raman spectra of colloidal solutions of GO and GO@AuNRs

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As shown in the Appendix, the optical absorption measurements were examined after one and 6 months of preparation. The spectra reveal that the prepared samples still exhibit the same absorption bands six months later, demonstrating the solution's long-term stability.

Figure 4e shows the Raman spectra of GO and GO@AuNRs. Characteristic peaks for GO and GO/AuNRs nanocomposites were discovered at 1350, 1328 (D band), 1604, and 1607. 5 cm-1 (G band), as appropriate. The D band position is blue-shifted as a result of the loading of AuNRs. The D-band reveals the intrinsic defects in the graphitic plane, while the G-band corresponds to the optical vibrations of GO atoms. The intensity of the D-band decreased with AuNR loading. The broadening of the D band is found to be 93, and 134 cm−1 for GO, and GO@AuNRs respectively. This broadening is explained as a result of the increased defects and interactions between the AuNRs and GO [37, 38]. The ID/IG ratio, which compares the D and G bands was 0.8, and 1.38 for GO and GO@AuNRs, respectively. This ratio reveals the level of disorder, and the effectiveness of the oxidization process [39, 40].

3.2 Nonlinear optical absorption of GO, AuNRs, and GO@AuNRs in colloidal form

An open-aperture Z scan is a technique used to measure the nonlinear optical absorption of a sample. In this setup, the sample is exposed to laser pulses with a wavelength of 532 nm and a duration of nanoseconds. To perform the Z scan, the sample is moved along the optical axis (Z-axis) of a lens using a translation stage. The sample is scanned across the lens’s focal point, creating a gradient of laser intensities in the focus plane. As the sample is moved through the focus plane, the intensity of the laser pulses varies at each point. This variation in laser intensity leads to changes in the sample’s transmittance. Nonlinear absorption can be quantified by examining the variations in transmittance as a function of the sample position along the Z-axis.

We measured the nonlinear absorption of GO, AuNRs, and GO@AuNRs Composites at 532 nm. We present in Fig. 5a, the measured nonlinear optical absorption of GO at 50, 80 µJ optical energy per pulse. GO shows reverse saturable absorption (RSA) at different powers. What stands out Fig. 5a is the general trend of the transmission where a valley with 2 humps around the focal point. Here, saturable absorption SA (peak around the focal point) and reverse saturable absorption RSA (valley around the focal point) are competing. It is seen that this valley depth is improved as the laser intensity increases; this means GO exhibits RSA as the laser energy intensity increases. By fitting this data to Z scan theory using Eq. (1), the NLA coefficient β is calculated to be 0.95*10–10 m/W.

Fig. 5
figure 5

a GO nonlinear absorption at 50, 80 µJ at 532 nm, b Nonlinear absorption of colloidal gold nanoparticles of different aspect ratios

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Saturable absorption SA happens when the excited state's cross-section is smaller than that of the ground state. The transmittance of the system will rise as it is pumped with a high-intensity laser beam. Meanwhile, the transmittance decreases as the excited states’ absorption cross-section increases relative to the ground state, and reverse saturable absorption develops (RSA) [18, 21, 41].

As shown in Fig. 5b, AuNRs1 and AuNRs2 exhibit a valley around the focal point, respectively, so β for AuNRs1 and AuNRs2 are found to be 0.45*10–10 and 0.35*10–10 m/W respectively. This is an indication that AuNRs with a higher aspect ratio have a higher β. Furthermore, an enhancement for β is achieved in the colloidal composite GO@AuNRs1 with different ratios of GO to AuNRs1 as shown in Fig. 6. For the composites GO@AuNRs1 (ratio 1:3) and GO@AuNRs1 (ratio 1:5), It was found that an improvement for β was discovered to be 0.595*10–10 and 0.8*10–10 m/W, respectively. In comparison to AuNR1, there is an improvement of 13.2 percent and 17 percent for GO@AuNRs1 (ratio 1:3) and GO@AuNRs1 (ratio 1:5), respectively.

Fig. 6
figure 6

Nonlinear absorption of colloidal composites of GO@Goldnanorods of GO to gold nanorod ratio (1:3) and (1:5) at 50 µJ

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3.3 Optical characterization of GO, AuNRs, and GO@AuNRs in polymeric form

To enhance the stability and performance of composite materials. We prepared the materials doped in PVP. This usually brings the materials to be stable for a long time relative to the case for colloidal solution which may aggregate after 12 months. PVP is a non-toxic, non-ionic amorphous polymer with high solubility in polar solvents. A mixture of completely dissolved PVP aqueous solution with well-dispersed AuNRs was allowed to dry and form a film.

As illustrated in Fig. 7, the linear absorption of GO-PVP is displaced to 240 nm. AuNRs-PVP exhibits the transverse and longitudinal bands, with the longitudinal peak being red-shifted to 746 nm from that of colloidal AuNRs.

Fig. 7
figure 7

Absorption spectra of GO@AuNRs with different ratios

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Three peaks are seen in the case of the GO@AuNRs1-PVP film, as shown in Fig. 7; the distinctive peak of the GO nanosheets is at about 234 nm, and the transverse peak of the AuNRs is at around 527 nm. Comparing the longitudinal peak to the same peak in the colloidal form of the GO@AuNRs, the longitudinal peak is wider. The presence of PVP is what causes this impact. The higher coupling between plasmons in the nearby GO, AuNRs, and GO@AuNRs is to account for this. Since they are significantly dense in films than in solutions, and maybe also as a result of the interaction of the AuNRs with the PVP [42].

The energy gap of a material can be determined from its absorption spectrum using the Tauc's plot approach by (αhν)m = B(hν-Eg) [43], where Eg is the material's bandgap, B is a constant, and h is Plank's constant. For direct and indirect transitions that are permitted, m = 2 or 0.5. Plots of (αhν)2 Vs h were used to estimate the direct band gap, as shown in Fig. 8. By extending the linear sections of the curves to zero absorption, the permitted direct transition energies were found.

Fig. 8
figure 8

Tauc’s plot for a the GO colloidal, b GO@AuNRs 1:1, GO@AuNRs1:3, GO@AuNRs 1: 5 colloidal c polymeric film of GO-PVP, and GO@AuNRs.-PVP

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The determined direct bandgap values for the GO colloidal solution, GO@AuNRs 1:1, GO@AuNRs1:3, GO@AuNRs 1: 5 colloidal samples were determined to be 3.91, 4.63, 4.76, 4.84 eV, respectively. In comparison to the polymeric films of GO, and GO@AuNRs; the direct band gap was found to be 4.66, 4.19 eV as seen in Fig. 8c.

In addition; Junaid et al. [44] reported that the direct optical bandgap of born-doped reduced graphene oxide was reduced with the increment of boron doping concentration, they attributed the optical bandgap reduction of the oxygen-related functional groups in the reduced graphene oxide nanosheets rGO carbon network. Aslam et al. [43] mentioned that the direct/indirect band gap decreased with increasing rGO-doped PVA. Yahia et al. [45] reported a decrease in the band gap with increasing GO contents due to the production of new levels within the band gap. This promotes the flow of electrons from the valence bands to these local levels of conduction. This may indicate the increase in the structural disorder of the polymer films with increasing GO concentrations.

The polymerized GO's Raman spectrum is shown in Fig. 9a presenting discrete Raman peaks at about 1345 cm−1 and 1602 cm− 1, which correspond to the GO D and G bands, respectively, as well as the significantly enhanced Raman peaks at 1605 cm− 1, which are attributed to the stretching vibration of the C=O, show that PVP molecules primarily interact with GO nanosheets through the oxygen of the C=O bond and interfere with the D band of GO. Their increased Raman spectra will be more prominent the closer the distance is between the functional group of the molecule and the GO. The CH2 chain is also near to the surface of GO, as seen by the considerable amplification of the signal at 2925 cm−1 [46]. Furthermore, the same peaks could be seen in the polymerized GO@AuNRs’ Raman spectra, but they were blue-shifted to have the respective values of 1330, 1595, and 2922 cm− 1. the ID/IG rise from 1.2 in GO to 1.34 in GO@AuNRs upon loading AuNRs and PVP. (ID/IG) is indicating the disorder in GO due to the defects associated with the disruption of the lattice symmetry in GO sheet during the polymerization process and the formation of GO@AuNRs.

Fig. 9
figure 9

a Raman Spectra of GO@AuNRs-PVP, GO-PVP. b Average inter-defect distance LD, Defect density nD for GO, GO-PVP, GO@AuNRs, GO@AuNRs-PVP. c EDX spectra of Go-PVP, AuNRs-PVP, and GO@AuNRs-PVP

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According to Yadav et al.’s discussion of the graphene oxide gold nanoparticles hybrid [47], the higher ID/IG ratios of GO@AuNRs hybrids point to the nucleation of Au NP on the surfaces of (GO), which introduces flaws in the structure. In addition, Kumar et al. [48] found that ID/IG were 0.059, 0.17 for graphene and graphene-loaded carbon nanotube hybrid. They indicated the low value of ID/IG due to the minimum defects by the existence of carbon nanotube in the hybrid composite.

The quality of the prepared materials was verified by evaluating the inter-defect distance between neighboring defects LD. using \({L}_{D}^{2}\left(nm\right)=\frac{1.8X{10}^{-9}}{{\lambda }_{L}^{4}(nm)} [\frac{{I}_{G}}{{I}_{D}}]\) where λL is the laser excitation wavelength [49]. In addition, The defect density can be calculated in terms of LD; nD \(\left({cm}^{-2}\right)=\frac{{10}^{14}}{\pi {L}_{D}^{2}}\) [50]

The computed values of LD were found to be 13.4,10.9,10.2, and 10.3 nm for GO, GO-PVP, GO@AuNRs, and GO@AuNRs-PVP, respectively. This means that the distance between neighboring defects reduces for the hybrid composites of GO@AuNRs, GO@AuNRs-PVP, and the polymeric films of GO. Consequently, the defect density rises in the hybrid composites. This is confirmed by calculating the defect density nD. Figure 9b illustrates the relation of LD (left y-axis); nD(right y-axis) for the prepared samples. It was found that nD were 1.78*1011, 2.66*1011, 3.05*1011, 2.98*1011 \({cm}^{-2}\) for GO, GO-PVP, GO@AuNRs, GO@AuNRs-PVP, respectively.

Fig. 10
figure 10

Nonlinear absorption of a AuNRs-PVP and GO-PVP at 50 µJ. b GO@AuNRs-PVP of different AuNRs ratio at 50 µJ

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By using EDX analysis, the C and Au concentrations on the surface of the samples were determined quantitatively as illustrated in Fig. 9c. Due to the influence of PVP, with formula (C6H9NO)n, we observe C, N, and O are present in all samples while Au is observed in AuNRS-PVP and GO@AuNRs-PVP. The synthesized GO-PVP and GO@AuNRs-PVP samples include graphene oxide and PVP, which is confirmed by the presence of a carbon peak. Table 2 lists the elements that make up the prepared polymer composite. These weight percentages show that the composite of GO@AuNRs-PVP was successfully absorbed into the blend and that the weight percentage is nearly in line with the predecessors.

Table 2 EDX results for AuNRs-PVP, GO-PVP, GO@AuNRs-PVP
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3.4 Nonlinear optical absorption of GO, AuNRs, and GO@AuNRs in polymer form

AuNRs-PVP exhibits RSA behavior leading to a negative nonlinear absorption coefficient as can be seen in Fig. 10, While GO-PVP shows a superior enhanced NLA compared to colloidal GO (3*10–10 m/W). On the other hand, adding GO to the different percentages of AuNRs in the polymer form Fig. 10b enhance AuNRs' nonlinearity, as seen in Table 3. The nonlinear absorption of AuNRs-PVP has also been enhanced by GO, which offers the possibility to optimize the NLA characteristics of AuNRs [51].

Table 3 Nonlinear absorption coefficient for GO, AuNRs1, AuNRs2, and GO@AuNRs in colloidal and polymer forms at 532nm
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The produced nanomaterials’ nonlinear absorption coefficients are listed in Table 3. In hybrid composites, an improvement was seen due to charge transfer and a rise in GO defect density. Additionally, boosting β for GO@AuNRs-PVP is a combination of the above-mentioned reasons and the reduced optical bandgap of the polymeric form of hybrid GO@AuNRS. where it has long-term stability without particle aggregation.

To depict the charge transfer, Yadaf et al. [47] created the five-level rate-equation model seen in Fig. 11 where D1 and D2 stand for the ground and excited levels, respectively, for the donor (Au). Similarly, A1, A2, and A3 stand for the ground, first excited, and second excited levels of the acceptor (GO), respectively. after laser excitation. One-photon absorption occurs in the donor Au NP, which moves the excited electron to the acceptor's first excited state, A2 (GO). The acceptor absorbs a second photon from its first excited state to reach its second excited state. The improvement of excited state absorption ESA is the outcome of such a charge transfer.

Fig. 11
figure 11

Schematic diagram of charge transfer. the ground and excited levels denote D1, D2 for gold nanorods as a donor, representing the ground, first excited, and second excited levels of graphene oxide denote A1, A2, and A3 as acceptors

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Furthermore, we compared our results with previous work as listed in Table 4 where the material, preparation method, and laser parameters are listed. The primary nonlinear absorption processes are multiphoton (two-photon absorption 2PA, three-photon absorption) and excited-state absorptions (ESA). ESA and 2PA are similar in that they both involve the absorption of multiple photons. However, there are differences between them that are important to understand. In two-photon absorption, the material simultaneously absorbs two photons and causes it to absorb energy since there is no real resonant single-photon absorption state. As a result, the process has become extremely intensity-sensitive. On the other hand, ESA is a two-step two-photon absorption process in which the material first absorbs a photon and makes the transition to the allowed resonant single-photon state and in the second step, another photon is absorbed to make the transition to the next allowed single-photon state. This step-by-step absorption of two photons through real states occurs in materials only when the excited-state absorption cross-section is more than the ground state. This process typically occurs in a broadband manner, with a large number of possible transitions to higher energy levels. ESA is a nonlinear absorption process, which means that the absorption rate depends on the intensity of the incident light [47, 52]. It is evident from Table 2 that 2PA is observed with femtosecond laser pulses while RSA is observed with nanosecond pulses. It is obvious that at the resonant wavelength of 532 nm, the nonlinear absorption coefficients were higher. Thermal nonlinearities appear using nanosecond laser excitation, but an electronic contribution appears with ultrashort laser excitation. Overall, nonlinearity caused by nanosecond lasers is always higher than picosecond and femtosecond lasers, and this discrepancy may be caused by the effects of pulse duration as seen in Table 4.

Table 4 Nonlinear absorption coefficients of gold nanoparticles and graphene nanocomposites with their Z scan experimental parameters
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Figure 12 shows the transmission as the laser energy is varied when the samples were fixed at the focal point. The optical limiting threshold, which is clearly discovered at 45 µJ for GO-PVP and AuNR1-PVP and 36 µJ for GO@AuNR1-PVP Composites, respectively, is the incident energy level at which optical limiting activity begins. The most obvious finding from this study is GO@AuNRs exhibit better optical limiting compared to its constituents of AuNRs and GO alone

Fig. 12
figure 12

Optical-limiting of GO-PVP, AuNRs, and GO@AuNRs at 532nm

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4 Conclusions

The goal of this work is to compare the nonlinear absorption of GO, AuNRs, and GO@AuNRs in colloidal and polymeric forms. We have reported the synthesis, structure, and nonlinear optical absorption properties of GO, gold nanorods, and graphene oxide- gold nanorods hybrid composite. The outcomes of optical linear absorption and TEM support the accuracy of the materials’ manufacture. Additionally, the Raman spectra were used to calculate the defect density and the inter-defect distance. For GO@AuNRs and GO@AuNRs-PVP, a greater defect density was discovered and the ID/IG ratio between the D and G bands was 1.38 and 1.34, respectively. This ratio provides information about the degree of disorder, and the effectiveness of the oxidation process. Moreover, EDX data shows that GO-PVP has the highest carbon percentage.

The open-aperture Z-scan experiment's findings demonstrate a notable improvement in the nonlinear absorption coefficient values of GO@AuNRs and GO@AuNRs-PVP. the enhancement of the ESA of GO@ AuNRs is due to ESA by the synergistic charge transfer between Au NP and GO domains, which can be consistently described by a five-level charge-transfer model. In addition, boosting of the nonlinear absorption coefficient was achieved in the hybrid polymeric form due to the reduced optical bandgap and the higher defect density. The most obvious finding from this study is the stability of the polymeric forms and the optical limiting trend at resonant wavelength. A great focus on the fabrication of hybrid nanocomposites in polymeric form could produce interesting findings that account more for photonic applications.