1. Introduction

In recent years, the optical nonlinear properties of nanoparticles have attracted many interests, which have many potential applications in optical limiter [1], multiphoton imaging [2] and all-optical switching [3–9]. Due to the unique optical properties called surface plasmon resonance (SPR), noble metal nanoparticles such as Au, Ag and Cu have been of particular interest for a long time [10,11]. Because of the large nonlinear optical effects and fast response time, noble metal nanoparticles have great potential application in all-optical switching [9], which require a nonlinear material with large nonlinear refraction and small linear and nonlinear absorption. To evaluate the figures of merit (FOM) of the optical nonlinear materials, two parameters are defined, the one-photon FOM, W = (|n₂|I_s)/(α₀ λ) and the two-photon FOM, T = (βλ/|n₂|) where I_s is the saturable intensity at which the nonlinear refractive index change saturates, α₀ is the linear absorption coefficient, β is the two-photon absorption (TPA) coefficient, n₂ is the nonlinear refraction and λ is the central wavelength. A suitable candidate for all-optical switching requires W ≫ 1 and T ≪ 1.

Many previous works [12-17] indicate the nonlinearities of small particles of are quite sensitive to the particle size, it becomes important to compare the optical properties of nanoparticles as a function of particle size, which enables one to understand the origins of nonlinearity and to optimize nonlinear properties desired for applications. There are many ways to fabricate particles of different sizes, such as chemical methods [12-15] and sputtering method [17], which make particles are comprised of spheres of various sizes or random distributed. Nanosphere Lithography (NSL) developed from Natural Lithography by Van Duyne in 1995, has been proved to be a powerful tool to fabricate periodic particle array (PPA) with tunable shape and size, making it possible to quantitatively study the optical properties of nanoparticles [18].

In this paper, we report a systematical study on size-related nonlinearities in triangular Au nanoparticle arrays of four sizes of fabricated by NSL method and the perpendicular bisector of the particles are 37 nm, 70 nm, 140 nm and 190 nm. The Z-Scan results showed a different nonlinear process from previous work [8,13]. As the size increased, the nonlinear absorption changed from TPA to saturated absorption (SA), while the nonlinear refraction changed from self-defocusing to self-focusing. By tuning the particle size, the high quality of FOMs, W~5, T~0.05 were obtained.

2. Experiment

In the NSL processing step, the monodisperse polystyrene (PS) nanosphere suspensions were purchased from Duke Scientific Corp., and the diameters of the spheres, D used in the experiment were 160±5 nm, 300±5 nm, 600±5 nm and 820±5 nm. The details of the NSL are described elsewhere [19]. For the pulsed laser deposition (PLD) processing step, a KrF (Lambda Physik, 248 nm) laser beam was used as the laser source with the laser energy density at the target of 2 J/cm² and the laser repetition frequency of 6 Hz. The deposition time was set to be 30 min. After the deposition, the NSL mask was removed by sonicating in ethanol for 2-4 minutes to obtain the Au PPAs. The surface morphology of the NSL mask and the Au PPAs were observed by SEM (FEI QUANTA 200). The SPR spectra were measured by UV-visible absorption spectroscopy (U-3310 UV Solutions) in a wavelength range from 340 nm to 900 nm. The incident light was perpendicular to samples through a small aperture with diameter of 2 mm to measure the absorption properties of small area.

The third-order nonlinear optical properties were determined by the Z-scan method [20]. In our experiments, a femtosecond laser system, which consisted of a mode-locked Ti: Sapphire oscillator and a regenerative amplifier (Spitfire, Spectra-Physics, 800 nm, 50 fs, 1 kHz) was used as the light source, which focused by a lens with a focal length of 200 mm. The radius of the beam waist (ω₀) was 33 µm, calculated from the equation, ω(z)² = ω²₀ (1+z²/z²₀), where z₀ = πω²₀/λ is the Rayleigh length. The value of z₀ was calculated to be 3.5 mm, much larger than the thickness of either the 0.2 mm-thickness substrate or the sample. Under these conditions, as the shape of the Z-scan result for the substrate is flat, the substrates have a very small nonlinear optical effect that can be neglected and the large nonlinear absorption observed here results from the Au PPAs. The transmitted beam energy through OA or CA is received by silicon diodes (PC20-6, Silicon Sensor GmbH) and double-phase lock-in amplifier (SR830, Stanford Research System). The reversibility of the results has been checked to confirm that no reshaping or damage has occurred.

3. Results and discussion

Figure 1 show SEM images of the Au nanoparticle arrays for the four different sizes. The size of the nanoparticle can be defined with two parameters: the in-plane perpendicular bisector a and the out-of-plane particle height b. By a geometrical calculation, D=0.233a, the value of a is calculated to be 37 nm, 70 nm, 140 nm and 190 nm, which are in good agreement with the experimental results shown in Fig. 1. The value of b is to be a constant for the same deposition time.

 

Fig. 1. show SEM images of triangluar nanoparticles arrays of four sizes of (a) 37 nm, (b) 70 nm, (c) 140 nm and (d) 190 nm.

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The linear absorption spectra of the Au PPAs were measured in the wavelength range from 340 nm to 900 nm. Figure 2 shows the absorption spectra of Au PPAs of different sizes. It can be seen that the absorption peaks due to SPR of Au particles are located at 552 nm, 566 nm, 580 nm and 606 nm for the 37 nm, 70 nm, 140 nm and 190 nm sizes. The absorption peak shifts to the longer wavelength as the particle size increases, giving a significant increase in the linear absorption coefficient at 800 nm. This size-related linear absorption properties lead to the competition between the two nonlinear mechanisms: The interband transition through the dominant TPA process and the intraband contribution ascribed to the SA process with excitation at the edge of the SPR band λ = 800 nm.

 

Fig. 2. Absorption spectra of Au PPAs with SPR peak at 552 nm, 566 nm, 580 nm and 606 nm. As the sizes increase, the SPR peaks shift to the longer wavelength.

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Fig. 3. The OA Z-scan results of 4 samples at exciting intensities at the focal point I₀= 55 GW/cm². The solid lines show the theoretical best fit.

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Figure 3 shows typical OA results for four samples. The black dots indicate the experimental data and the solid curves represent the theoretical fits. The laser intensities at the focal point, I₀ = E₀/πω² τ, were calculated to 55 GW/cm². At the repetition rate of 1 kHz, the accumulative thermal effects can be neglected. The curve of 37 nm shows a TPA process with an additional SA component, as manifested by a peak (increased transmittance) at the beam waist flanked by two valleys (decreased transmittance). For the curves of 70 nm and 140 nm, the TPA component turns weaker and the SA become dominant. The curve of 190 nm shows only the SA process. The interpretation of this difference is that the absorption at the excitation region is much weaker than that at 400 nm for Au PPA of 37 nm, and the interband contribution ascribed to the TPA process plays a dominant role, while the absorption at 800 nm is larger than that at 400 nm for the Au PPA of 190 nm and the intraband contribution ascribed to the SA process becomes dominant. The curves of 70 nm and 140 nm show the transition in this variation of two nonlinear mechanisms.

 

Fig. 4. The CA Z-scan results of 4 samples at exciting intensities at the focal point of I₀=55 GW/cm². The solid lines show the theoretical best fit.

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Figure 4 shows the CA Z-scan data for Au PPAs at I₀ = 55 GW/cm². The ratio of closed-aperture transmittance to the corresponding open-aperture data was taken as an approximation to the nonlinear refraction value. The distance between the peak and the valley (ΔZ_p−v) is about 6 mm as compared to 1.71z₀, which indicates that the observed nonlinear effect is the third-order response. For the Au PPAs of 37 nm and 70 nm, the self-defocusing effect occurs, the sign of nonlinear refraction is negative. For the Au PPAs of 140 nm and 190 nm, the self-focusing effect occurs, with positive nonlinear refraction. For the Au PPAs of 37 nm and 70 nm, the dominant interband transition due to the TPA process decreases the nonlinear refraction index. As the particle size increases, the SA process becomes dominant. The excited electrons give rise to an increase in the refractive index, resulting in self-focusing. It is worth noting that there are two clear deviations from the theoretical values of data of the 70 nm, indicating a transition process from self-defocusing to self-focusing.

Both the OA and CA data shown in Fig. 3 and Fig. 4 are fitted well using the modified equation [8]:

where α₀ is the linear absorption coefficient at a wavelength of 800 nm, β = β⁰/[1+(I/I′_s)²] is the TPA coefficient, β⁰ is the TPA coefficient at low intensity and I_s and I′_s are the saturation intensity for the SA and TPA processes respectively. The results are listed in the table below:

Figures 5(a) and (b) show the size-related nonlinear absorption and refraction at the same intensity of I₀= 55 GW/cm². It exhibits a saturated TPA process in Fig. 5(a). In Fig. 5 (b), as the size increases, the sign of nonlinear refraction changes from negative to positive, while the absolute value decreases. Fig. 5 (c) and (d) show the size-related one- and two-photon FOMs, W and T for all-optical switching. As the size increases, W decreases from 7.5 to 4.1, T decreases from 0.12 to 0. The largest W value of 7.5 is obtained in the Au PPA of 37 nm, which gains from the small linear absorption α₀ at this size. Because of the low TPA coefficient, the lowest T value of 0 occurs with the 190 nm PPA.

Table 1. Dependence of α₀, β, n₂, T and W for Au PPAs with different sizes in the intensity of 55 GW/cm².

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Fig. 5. (a) and (b) Nonlinear absorption coefficient and refraction index at the same intensity of I₀= 55 GW/cm² as a function of particle sizes. (c) and (d) show the values of FOMs as a function of particle sizes.

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Previous works report many materials such as p-polyenevinylene (W≫ 1, T~0.6) [4], RO₂-B₂O₃-SiO₂ (R=Li, Na, and K) polarizing glass containing silver nanorods (W~1.6, T~0.1) [5], double walled carbon nanotubes (DWNT) (W~1.3, T~0.4) [6,7], have been the candidate for all-optical switching near 800 nm. In this paper, the high quality FOMs, W~5, T~0.05 can be obtained in Au PPAs of the size around 100 nm, which is good enough to become a prime candidate for all-optical switching in infrared region.

4. Conclusion

In summary, triangular Au nanoparticle arrays 37 nm, 70 nm, 140 nm and 190 nm were fabricated by NSL and PLD techniques. The nonlinear optical properties of the sample were investigated by the Z-scan method at a wavelength of 800 nm with pulse duration of 50 fs. The results showed a size-related variation between the two mechanisms of groundstate bleaching and two-photon absorption. The high quality of FOMs indicate the Au PPA is a prime candidate for all-optical switching in infrared region.