**3.1. Nonlinear optical studies of Au nanoparticles**

**3. Nonlinear optical properties of metal nanoparticles**

metal nanoparticles synthesized by ion implantation.

nonlinear spectroscopy.

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The stability combined with a large third-order susceptibility and ultrafast response means that metal nanoparticles are very promising materials for the creation of photonic devices. SPR is the main characteristics of metal nanoparticles, which strongly depend on the size, shape, and type of metal nanoparticles and the dielectric parameter of surrounding environments [14]. A huge enhancement of the nonlinear optical response in random media with metal nanoparticles is often associated with optical excitation of the SPR. Typical three metals having plasmon band in visible range are Au, Ag, and Cu. In contrast, metals such as Pt, Pd, and Cr show SPR in the wavelengths shorter than 300 nm. Therefore, large transparency and low propagation losses in the visible and infrared range are expected in Pt, Pd, and Cr nanoparticles. In many studies, composite materials with metal nanoparticles were fabricated by various methods and then generally studied using lasers operating at frequencies corresponding to the spectral range of the SPR, as listed in Ref. [15]. The review [15] has summarized the development of nonlinear optical random metal-dielectric composites based on

**Figure 5.** Normalized transmission curves of Z-scan data with an aperture divided by those without an aperture.

Among the nanoparticles of noble metals, Au and Ag nanoparticles have attracted more interest and initiated more theoretical and experimental studies [1, 2, 16–31], as they both show a strong SPR band in the visible region. Moreover, their SPR absorption band can be tuned across the entire visible spectra by changing the size and shape of nanoparticles. The SPR of metal nanoparticles can lead to many interesting optical properties. For example, ultrafast nonlinear optical absorption is important since it can considerably alter the propagation of intense light in the medium, which can make metal nanoparticles be applied in optoelectronics, optical limiters and switchers, as well as in optical memories, optical computing, and The first experimental results on the nonlinear optical effects of Au nanoparticle were obtained by Ricard et al. in 1985 [32]. They prepared the Au nanoparticle with an average diameter of 10 nm and measured the third-order nonlinear susceptibility using phase conjugation to be 1.5 × 10<sup>−</sup><sup>9</sup> esu at 530 nm. They traced the enhancement to the nonlinearities of the electrons in Au particles.

Among all composite materials, those made out of gold NPs embedded in a dielectric matrix are more important, because of their strong SPR absorption band in the visible region [33]. The coexistence of unique linear and nonlinear (especially third-order) optical properties makes the material be well suited for the potential applications ranging from optical limiter [20, 34], quantum information processing [35, 36], cancer treatment [37–39], on to all-optical switching [33, 40, 41]. In this direction, Au NPs embedded in dielectric media have been widely put more attention for their SPR, which depends strongly on the NPs environment and geometry [42].

Many investigations were performed in Au nanoparticles to study the nonlinear refractive index and nonlinear absorption [2, 16–22]. Moreover, the optical limiting of Au nanoparticles has also been studied widely for protection of human eyes and optical devices from laser damage. The contents studied mainly include the effects of sizes, matrices, and shapes on the nonlinear optical properties in Au nanoparticles [43].

Sánchezdena O et al. studied the size dependence of nonlinear optical response in Au metallic nanoparticles with diameters of 5.1, 13.4, and 14.2 nm synthesized and embedded in sapphire by using ion implantation [43]. Under 532-nm, 26-ps pulses, they found that the Au NPs exhibited a negative nonlinear absorption, which increases with size and size-independent positive nonlinear refraction.

For larger Au nanoparticles than those above, a systematic study of the size-related nonlinear optical properties of triangular Au particles was performed by S.H. Yoon et al. who fabricated the triangular Au nanoparticle arrays with four larger sizes of 37, 70, 140, and 190 nm on SiO2 substrates using nanosphere lithography [44]. **Figure 6** shows the absorption spectra of the Au nanoparticles of different sizes. It can be seen that the SPR absorption peaks lie at 552, 566, 580, and 606 nm for the 37, 70, 140, and 190 nm Au nanoparticles, respectively. With the increasing particle size, the absorption peak shifts to longer wavelength.

**Figure 7** shows the typical OA Z-scan experiment results of the four samples. The curve of the 37-nm sample showed a TPA with an additional SA component. For the samples with size of 70 and 140 nm, TPA component turned weaker and SA became dominant. The curve of the 190-nm sample showed only the SA component. These differences occur because the absorption in the excitation region is much weaker than that at 400 nm for the Au nanoparticles sized 37 nm, and herein, the interband transition to the TPA process plays a key role. However, the absorption at 800 nm is larger than that at 400 nm for the 190-nm Au nanoparticles; this is because the SA process becomes dominant. The curves of the samples of 70 and 140 nm showed a transition in this variation of the two nonlinear mechanism contributions.

**Figure 8** shows the CA Z-scan data for four Au nanoparticles of 37, 70, 140, and 190 nm. For the 37 and 70 nm Au nanoparticles, a self-defocusing occurs, and the nonlinear refraction index

**Figure 6.** Absorption spectra of Au periodic particle arrays with sizes of 37, 70, 140, and 190 nm.

decreases due to the dominant interband transition caused by the TPA process. However, for the 140 and 190 nm Au nanoparticles, self-defocusing occurs. With the increase of particle size, the SA becomes dominant. The increase of refractive index is due to the excited electrons, resulting in the self-focusing.

But we believe that the increasing trend of optical limiting capability with size will terminate somewhere, and there should be an optimal size for optical limiting. To testify the hypothesis, we synthesized the gold nanoparticles with even larger radii of 15, 25, 50, and 70 nm and studied the optical limiting performance of the nanoparticles with different size at 532 nm for

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**Figure 8.** The CA Z-scan results of the four samples at exciting intensity *I* 0 = 55 GW/cm 2.

**Figure 9.** Optical limiting curves of gold nanoparticles with the radii of 15, 25, 50, and 70 nm.

As shown in **Figures 9** and **10**, the optical limiting effect is found to be size-dependent. Compared with what Francois et al. have found [8], however, the results in our experiments are more complicated. When the size of gold nanoparticles increases from 15 to 25 nm, optical limiting capability increases. But when particle size increases further, optical limiting capability decreases instead. Visual description for the comparison of optical limiting ability is shown in **Figure 10**.

8-ns laser pulses [45].

It is obvious that the size of Au nanoparticles influences the nonlinear optical properties of Au nanoparticles. Hence, the optical limiting of Au nanoparticles should be size-dependent. Mostafavi et al. prepared gold nanoparticles with 2.5, 9, and 15 nm radii and studied the nonlinear optical response of resulting nanoparticles [8]. They found that the optical limiting threshold and the amplitude depend strongly on size. The 2.5-nm clusters do not limit light even at very high fluence, while the larger clusters do at 530 nm.

**Figure 7.** The OA Z-scan results of four samples with sizes of 37, 70, 140, and 190 nm.

**Figure 8.** The CA Z-scan results of the four samples at exciting intensity *I* 0 = 55 GW/cm 2.

But we believe that the increasing trend of optical limiting capability with size will terminate somewhere, and there should be an optimal size for optical limiting. To testify the hypothesis, we synthesized the gold nanoparticles with even larger radii of 15, 25, 50, and 70 nm and studied the optical limiting performance of the nanoparticles with different size at 532 nm for 8-ns laser pulses [45].

As shown in **Figures 9** and **10**, the optical limiting effect is found to be size-dependent. Compared with what Francois et al. have found [8], however, the results in our experiments are more complicated. When the size of gold nanoparticles increases from 15 to 25 nm, optical limiting capability increases. But when particle size increases further, optical limiting capability decreases instead. Visual description for the comparison of optical limiting ability is shown in **Figure 10**.

**Figure 9.** Optical limiting curves of gold nanoparticles with the radii of 15, 25, 50, and 70 nm.

**Figure 7.** The OA Z-scan results of four samples with sizes of 37, 70, 140, and 190 nm.

even at very high fluence, while the larger clusters do at 530 nm.

decreases due to the dominant interband transition caused by the TPA process. However, for the 140 and 190 nm Au nanoparticles, self-defocusing occurs. With the increase of particle size, the SA becomes dominant. The increase of refractive index is due to the excited electrons,

**Figure 6.** Absorption spectra of Au periodic particle arrays with sizes of 37, 70, 140, and 190 nm.

It is obvious that the size of Au nanoparticles influences the nonlinear optical properties of Au nanoparticles. Hence, the optical limiting of Au nanoparticles should be size-dependent. Mostafavi et al. prepared gold nanoparticles with 2.5, 9, and 15 nm radii and studied the nonlinear optical response of resulting nanoparticles [8]. They found that the optical limiting threshold and the amplitude depend strongly on size. The 2.5-nm clusters do not limit light

resulting in the self-focusing.

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**3.2. Nonlinear optical studies of Ag nanoparticles**

532 and 1064 nm [23, 24] by using Z-scan.

For Au nanoparticles, there is significant overlap between the interband absorption and the plasmon resonance absorption, which decreases substantially the efficiency of plasmon excitation. In the case of Ag, however, the interband transition absorption at about 320 nm is far from its SPR wavelength of about 400 nm. This makes the plasmon excitation in Ag nanoparticles more efficient than that in Au nanoparticles. Moreover, the separation of two kinds of absorption facilitates the separate investigation of the nonlinear optical effects arising from interband transitions and those due to SPR. Hence, many groups conducted research on the

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For example, Gurudas et al. studied the picoseconds optical nonlinearity in silver nanodots prepared by pulsed laser deposition at 532 nm [22]. The nonlinear refraction and nonlinear absorption of these nanoparticle films were measured by using the Z-scan technique. The broad SPR absorption indicates that there are different-sized and different-shaped nanoparticles in the samples. At 532 nm, the SA and RSA are found to be dependent on sample properties. So by designing properly nanoparticles with different sizes and shapes, it may be possible to use these materials for various applications such as mode locking and optical limiter to protect sensors or eyes from the damage of high-power laser. Zheng et al. have investigated the shape-dependent NLO behaviors of nanostructured Ag nanoplates, nanowires, and nanoparticles suspensions (as shown in **Figure 12**) and their silica gel glass composites at both

NLO abilities of the nanostructured suspensions are found to be shape-dependent at 532 and 1064 nm. **Figure 13** shows the OA Z-scan experiment results of the nanostructured Ag in aqueous suspensions. All the samples exhibit typical RSA, but the deepness of the valleys differs from one to another, indicating different RSA abilities. As shown in **Figure 14**, they also investigated the NLO properties of the Ag/silica gel glass nanocomposites. In contrast to corresponding suspensions, the composites show more complicated OA Z-scan curves and the curves are insensitive to the nanostructured shapes. To a different extent, all the traces show

**Figure 12.** SEM images of the investigated Ag (a) nanoplates, (b) nanowires, and (c) nanoparticles.

nonlinear absorption and optical limiting in silver nanoparticles [1, 22–31].

**Figure 10.** Optical limiting capability changing with particle size.

We analyzed the results in terms of the surface layer of nanoparticles. We assume that only surface layer of the particle can respond to outside light. We think of the thickness of the surface layer to be *ds*. The absorption region of gold nanoparticles with different sizes is shown in **Figure 11**. When gold nanoparticle has the radius less than *ds*, light energy can be absorbed by whole particle. Then, the absorbed energy transfers to surrounding solvent and leads to solvent bubbles. Moreover, the larger the size is, the stronger the nonlinear scattering is, and gold nanoparticles exhibit size-enhanced optical limiting. This is in consistent with the results in 15- and 25-nm gold nanoparticles. But when the radius of gold nanoparticle increases to be larger than *ds*, only outer layer *ds* can absorb light energy. The energy will first transfer to the core (black part in **Figure 11**) of gold nanoparticles. The transferring energy from gold nanoparticle to solvent decreases, which will obstruct the surrounding solvent to form bubbles. The obstruction makes the optical limiting weaker in larger particle.

Based on the analysis above, we found that, when the radius of nanoparticle is equal to the surface layer *ds*, the absorption-induced scattering is the strongest, correspondingly the optical limiting is most effective. That means, the optical limiting optimal size of metal nanoparticles equals to surface layer thickness *ds*. For gold nanoparticles, it is 25 nm. The investigation may be helpful for the synthesis of metal nanoparticles for optical limiting. Undoubtedly, more studies are required to find out the exact reasons for this behavior.

**Figure 11.** Absorption regions in gold nanoparticles with different sizes.
