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Nonlinear optical characterizations were performed on monodispersed silver (Ag) nanoparticles (NPs) of various sizes using a picosecond Z-scan technique with excitation wavelengths of 532 nm and 1064 nm. The Ag NPs were fabricated using a heterogeneous condensation technique in a gas medium. The nonlinear refraction values were higher for the monodispersed Ag NPs whose surface plasmon resonance (SPR) peak is closer to the excitation wavelength. The higher nonlinear optical response is explained in terms of an electric field enhancement near the SPR. Moreover, the fabrication method allows the tailoring of the nonlinear refraction index of the Ag NPs by tuning the SPR peak of the sample. A comparison of the nonlinear refraction index of the monodispersed and polydispersed Ag NPs showed that the nonlinear refractive index of the monodispersed Ag NPs is higher.
© 2014 Optical Society of America
1. Introduction
Metal nanoscale structures, especially those consisting of noble metals, have gained considerable attraction because of their unique optical properties induced by the collective oscillation of free electrons called a surface plasmon (SP). The surface plasmon resonance (SPR) peak is directly related to the nanoparticles (NPs) size, shape, structure and the dielectric constants of the metal and the local environment [1–3]. The bandwidth of the resonance spectrum has been attributed to size distribution, where a narrow size distribution generates a narrow bandwidth, while a wider size distribution generates a wider or broader spectrum [4]. The resulting local field due to the surface plasmons around the nanostructures is known to enhance various optical properties of the material, such as the linear and nonlinear absorptions and the nonlinear refractive index [5–7]. Moreover, a system consisting of monodispersed NPs (nanoparticles with the same parameters such as size, shape, charge etc.) is known to enhance the local field. It has been shown that thin films consisting of monodispersed metal NPs have a sharp SPR peak [8] created in part by the strong and coherent local field around the nanostructures. Hence, it is expected that monodispersed NPs will boost the nonlinear optical response of the metal NPs. It has been suggested that the third-order nonlinear susceptibility χ(3), which is related to the third order nonlinear polarization, of metal NPs is proportional to the local electric field [9–12]. As of present, little attention has been given to the study of the nonlinear optical response of monodisperesd NPs. With the growing interest in materials with special optical properties, it is important to understand how monodispersed NPs influence the nonlinear optical properties of the materials.
In this paper, we present an analysis of the nonlinear optical response of monodispersed silver (Ag) NPs of various sizes. A comparison of the nonlinear refractive index is made between films containing monodispersed NPs and those containing polydispersed NPs (NPs with different parameters such as size, shape, charge etc.). Silver (Ag) nanoparticles are known to exhibit a large third order nonlinear susceptibility χ(3), that is contributed by hot electrons [5,13]. Additionally, their SPR band is far from the interband transition, which makes it easier to study the optical behavior solely due to plasmonic effects [14]. Various works have been done to study the nonlinear optical properties of silver NPs. However it should be noted that all optical investigations were done using polydispersed NPs. The results in this report show that the nonlinear optical response of monodispersed Ag NPs was sensitive to the SPR and that the nonlinearity increased as the SPR approached the excitation wavelength. The significance of this work is that the monodispersed Ag NPs can be fabricated effectively for different sizes. This means that the nonlinear optical properties of Ag NPs can be designed for particular parameters and specifications.
2. Experimental
Monodispersed Ag NPs of different sizes were prepared using a setup as described in an earlier publication [8]. The Ag NPs were deposited on a quartz substrate (Corning 7980 fused silica). Polydisperse Ag NPs were also fabricated but without the use of the size selection process in the fabrication setup and were collected, in a similar fashion, on a quartz substrate [15].
The optical absorption spectra were measured with a double beam UV-Vis (Perkin Elmer lambda 19) spectrometer. The size characterizations were done using a SEM (Zeiss Supra 55VP). The nonlinear response of the thin films containing monodispersed Ag NPs were investigated by employing a Z-scan technique [16]. The experiment was performed at excitation wavelengths of 532 nm (second harmonic generation) and 1064 nm (fundamental wavelength) using a Nd:YAG laser which generates a Gaussian beam at a repetition rate of 20 Hz, and a pulse duration of 25 ps. The beam was focused by a 20 cm focal length lens. The transmittance of the samples at different position along the direction of the propagation of the beam, through an aperture, placed at far field was measured. Open and closed aperture Z-scan measurements were carried out. In the open aperture Z-scan measurement, the aperture was kept fully open which corresponds to, linear transmittance, S = 1 [16]. In the open aperture measurement, all the transmitted light through the sample is collected by a detector. The measurement is insensitive to any nonlinear beam distortion due to nonlinear refraction [16]. In the closed aperture Z-scan, the transmittance of the samples through an aperture having a 1.57 mm diameter (S = 0.1) was measured. The closed aperture Z-scan determines the nonlinear refraction of the samples, however, to obtain the information due to only nonlinear refraction, the closed aperture normalized transmittance should be divided by the open aperture normalized transmittance.
3. Results and discussion
The SEM images in Figs. 1(a)-1(c) show that the NPs’ sizes are uniform for the thin films containing monodispersed Ag NPs. The sizes (diameter) for samples a, b, and c are 40 nm, 80 nm and 170 nm respectively. In these samples, the size distribution is narrow with standard deviation, σ, of 12%, 8% and 9% for samples a, b, and c respectively. Nanoparticles with standard deviation σ ≤ 5-15% are considered monodispersed particles [17]. Whereas it is noticeable that the size distribution is wide for the film containing the polydispersed Ag NPs in Fig. 1(d). The particles sizes range from 30 nm to 200 nm. The Ag NPs in all four samples were spherical in shape. The concentrations of all these samples were within a magnitude of ~1011 per sq. cm. and were similar to each other.
The absorption spectra of the monodispersed samples are shown in Fig. 2(a). In Fig. 2(b), the absorption curve of the polydispersed Ag NPs is plotted together with the absorption curve of the monodispersed Ag NP sample a. It can be seen that the spectral width of the monodispersed Ag NPs sample is narrower than the spectral width of the polydispersed Ag NPs. For monodispersed Ag NPs, the SPR has a sharper peak and the bandwidth of the absorption spectrum is much narrower. The surface plasmon peaks of the samples a, b and c are very distinguishable with peaks at 440 nm, 460 nm and 490 nm respectively as shown in Fig. 2(a) and the plasmon bandwidths are 100 nm, 103 nm and 198 nm respectively. The sharp SPR is due to the coherent local field around the monodispersed NPs. The red shift and the decrease in absorbance of the larger size nanoparticles can be attributed to the dephasing of the plasmon oscillations and radiation damping [18,19]. When size of the nanoparticles becomes larger, light cannot polarize the nanoparticles homogeneously but instead multi polar charge distributions are created. The accelerating electrons lose energy because of the additional polarization field. This results in radiation damping, and the reduction of the absorption magnitude and as well as the broadening of the absorption bandwidth. The wider spectral width (270 nm) for the polydispersed Ag NPs is likely due to the wide size distribution of the Ag NPs; a superposition of all the SPR peaks, from the different sizes [8].
Fig. 2 Absorption spectra of Ag NPs: (a) Monodispersed Ag NPs (sample a, 40 nm; sample b, 80 nm; and sample c, 170 nm). (b) Polydispersed Ag NPs plotted with monodispersed Ag NPs (sample a).
The complex third-order nonlinear optical susceptibility χ(3) of the samples were quantitatively analyzed by performing open and closed aperture Z-scan measurements [16]. The nonlinear absorption, which is related to the imaginary part of χ3 [Imχ3], was measured using the open aperture Z-scan technique [16]. The normalized transmittance of the open aperture measurement can be expressed as [16]:
Where β is the nonlinear absorption coefficient, I0 is the intensity of laser radiation, Leff = (1-e-α0L)/α0 is the effective interaction length with the sample thickness L, α0 is the linear absorption coefficient, z0 = πω02/λ is the Rayleigh diffraction length, and ω0 is a waist radius of the focused laser beam. The sample thicknesses were ~50 nm, 100 nm and 180 nm for samples a, b, and c respectively. For polydispersed Ag NPs, the L was ~200 nm. The linear absorption coefficients for samples a, b, c and the polydispersed Ag NPs were 21.7 x 103 cm−1, 25.4 x 103 cm−1, 15.0 x 103 cm−1 and 24.5 x 103 cm−1 respectively. If | β I0 Leff | < 1, only the first few terms are needed. The theoretical curve fitting was done using Eq. (1) to obtain the β values from the experimental curves. The open aperture Z-scan measurements for the monodispersed samples (a and b) and the polydispersed Ag NPs are shown in Fig. 3(a).Fig. 3 Normalized transmittance obtained from the open aperture Z-scan at the excitation wavelength of 532 nm. (a) Monodispersed Ag NPs (samples a and b). (b) Polydispersed Ag NPs. The dotted lines are experimental data and the solid lines are theoretical fitting.
In Fig. 3, it can be seen that bleaching (or saturable absorption) occurs for both the monodispersed and polydispersed Ag NPs. This low irradiance response is typical for NPs excited near the SPR peak [9,13,20]. The β values of all of the samples are given in Table 1. When bleaching occurs the value of β is negative, while for two-photon absorption the value of β is positive [16].
Table 1. Nonlinear Refraction Values and Absorption Coefficients of Monodispersed and Polydispersed Ag NPs with Different SPR Peaks
To determine the nonlinear refractive index of the sample, which is related to the real part of χ3 [Reχ3], the normalized transmittance from the closed aperture measurement was divided by the normalized transmittance data obtained from the open aperture measurement. The closed aperture measurement is a combination of both the nonlinear absorption and the nonlinear refraction of the sample. The division operation effectively subtracts the nonlinear absorption component from the closed aperture (S < 1) measurement, leaving only the component related to the nonlinear refractive index of the sample. The experimental and theoretical Z-scan curves for the monodispersed and polydispersed Ag NPs samples are shown in Fig. 4.
Fig. 4 Experimental curves derived from closed and open aperture measurement when excited at 532 nm. (a) Monodispersed Ag NPs (samples a, b and c). (b) Polydispersed Ag NPs. The dotted lines are experimental data and the solid lines are theoretical fitting.
To evaluate the nonlinear refractive index γ values, the experimental curves were fitted with the theoretical expression given by [16]:
where ∆ Ф is the nonlinear phase change at the exit surface of the sample due to the nonlinear refraction. ∆ Ф is related to nonlinear refraction index γ by:Using Eqs. (2) and (3), and with ω0 = 25 μm and 60 μm for 532 nm and 1064 nm respectively, the nonlinear refractive index γ was determined for the monodispersed Ag NPs. It should be noted Eq. (2) is derived for a small aperture (S ≈0). For S = 0.1, the curve fitting using Eq. (2) has an error of less than 10% [21]. For larger values of S and for the samples that have higher relative nonlinear absorption compared to nonlinear refraction, the error may increase [21]. The values for monodispersed and polydispersed Ag NPs are shown in Table 1. The sign of γ is negative for the samples as indicated by the peak-valley sequence of the experimental curve (shown in Fig. 4), which is contrary to the valley-peak sequence of the reference sample CS2 (not shown) which has a positive nonlinear refractive index [16]. The negative nonlinear refraction for Ag NPs and Ag composites have been reported by other groups [9,10].The γ value increases as the SPR peak of the monodispersed Ag NPs approaches the excitation wavelength. As mentioned earlier, χ(3) is directly proportional to the local field around the nanostructure and increases resonantly with the SPR band [9]. When the excitation is in resonance with the plasmon oscillation, the strong local field generated around the nanoparticles contributes to the higher polarizability of the molecules and thereby enhancing the nonlinear optical properties of the nanoparticles. The sharp SPR peak of the monodispersed samples in the experiment affords a clear opportunity to see how the SPR peak influences the nonlinear refraction of Ag NPs. Such effect would not be easy to notice if the SPR bandwidth is very large. Another interesting result is, the value of the nonlinear refractive index γ for all three monodispersed Ag NPs samples are larger than that of the polydispersed Ag NPs sample. The enhancement in nonlinear refraction in the monodispersed Ag NPs can be attributed to the coherent and thus higher local electric field due to the monodispersity of the NPs, which is evident from the sharp SPR peak.
The nonlinear optical responses of the samples were measured at 1064 nm, far from the SPR peaks. The normalized transmittance through an open aperture for the monodispersed Ag NPs (sample c) showed a reversal in the sign of β, changing from negative for 532 nm to positive for an excitation at 1064nm (Fig. 5(a)). The theoretical fitting of the experimental curve using Eq. (1) yielded a value of β = (4.4 ± 0.4) x 10−9 m/W. The curve suggested that there is two-photon absorption when the samples are excited at a very high intensity (19.09 GW/cm2). At low intensities two-photon absorption was undetectable.
Fig. 5 Normalized transmittance obtained from (a) the open aperture Z-scan at the excitation wavelength of 1064 nm for the monodispersed Ag NPs (sample c) and (b) the closed aperture measurement obtained from monodispersed Ag NPs samples when excited at 1064 nm. The dotted lines are experimental data and the solid lines are theoretical fitting.
The closed aperture Z-scan measurement of all three monodispersed Ag NPs (samples a,b, and c) at the excitation wavelength of 1064 nm and at the intensity of 2.97 GW/cm2 is shown in Fig. 5(b). In order to verify that the samples were not damaged at this intensity, we checked the repeatability of our measurements by increasing and lowering the intensity across the range of the measurement. Here, the subtraction of an open aperture measurement was not needed since the contribution of nonlinear absorption was negligible. The Z-scan profiles showed a negative nonlinearity (n2 < 0), similar to the closed aperture curves when excited at 532 nm. The nonlinear refraction values are shown in Table 1. The values show that the samples whose SPR is closer to 532 nm show higher nonlinearity near two photon excitation (1064 nm) as well. The nonlinear refraction values at 532 nm and 1064 nm were plotted as a function of size (see Fig. 6).
Fig. 6 Nonlinear refraction, γ, for both 532 nm and 1064 nm plotted with respect to different sizes of monodispersed Ag NPs.
Comparing the larger value of the nonlinear refraction for 1064 nm with that for the 532 nm excitation, it appears that two photon excitation (for 1064 nm) is the dominant resonant effect producing a greater enhancement.
From Table 1, it can be seen that the shift in the SPR peak, which can be tuned by changing the parameters (e.g. size) of the NPs, causes a change in the nonlinear properties of the monodispersed Ag NPs samples. We note that as the SPR peak approaches the excitation wavelength the nonlinear refractive index increases for both 532 nm and 1064 nm.
4. Conclusion
The nonlinear optical properties of the monodispersed Ag NPs of different SPR peaks were investigated and the comparison was made with the polydispered Ag NPs. The narrow and sharp optical extinction for monodispersed Ag NPs suggests that the sample has an enhanced local field. The nonlinear refraction increased as the SPR peak approached the excitation wavelength of 532 nm. The sample with SPR peak closer to 532 nm also showed higher nonlinearity at two-photon excitation (1064 nm). Saturable absorption and two-photon absorption were observed at 532 nm and 1064 nm excitation wavelengths respectively. A higher nonlinear refraction was also observed in the monodispersed Ag NPs when compared to that of the polydispersed Ag NPs. The fabrication method has the ability to generate thin films with enhanced nonlinear optical properties. It is possible to tune the optical nonlinearity of nanoparticle thin films; tailoring the film to produce a pre-defined χ(3).
Acknowledgments
One of the authors (Pemba Lama) acknowledges the financial support provided by Corning Incorporated. The authors also acknowledge the science department of The City College of New York for the SEM facility.
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