Barium titanate (BaTiO3) is a technologically important material because of its nonlinear properties, such as its strong second harmonic generation and high third order susceptibility. While many nonlinear effects have been extensively studied on the bulk scale, there are still questions regarding the strength of nonlinear effects in nanoparticles. The nonlinear properties of BaTiO3 nanoparticles and nanorods have been studied using the closed aperture z-scan technique. Silver was then grown photochemically on the surface of the BaTiO3 nanoparticles, and it was found that the third order susceptibility increases dramatically.
©2012 Optical Society of America
Nonlinear optical materials have been studied for many years and have been utilized in a wide range of applications. With the increasing use of and interest in nanomaterials, it is important that these phenomena be explored in the nanoscale regime in order to better understand the interactions of matter with light on this level. In particular, nonlinear optical nanomaterials have the potential to enhance and extend techniques and devices in the areas of communications [1–3], optical devices [4–6], biosensors [7–9], and imaging [7, 10, 11]. While many nonlinear effects were once thought to only occur on the bulk scale, it has been shown that some nonlinear effects, such as four wave mixing and harmonic generation in nanocrystals, can still occur at the nanoscale [5, 10, 12]. Nanomaterials with large nonlinear responses can be used as contrast agents in nonlinear microscopy [7, 9, 11], as biosensors [7–9], photocatalysts [13, 14], optical limiters [15, 16], and in photonic devices [4–6]. In order to quantify the nonlinear optical properties of nanomaterials, the closed aperture z-scan technique was used on samples of BaTiO3 and silver seeded BaTiO3 (Ag@BaTiO3) nanoparticles in solution. While many nonlinear effects are driven through higher energy density pulses, especially in metal nanomaterials, the nonlinear response of BaTiO3 and Ag@BaTiO3 nanoparticles occurs in both the continuous wave and pulsed regimes. In this work, we focus on the nonlinear properties of BaTiO3 nanoparticles in the continuous wave regime and the enhancement of these properties with the addition of silver seeds. While the nonlinear properties are likely dominated by the thermo-optic nonlinearities under continuous wave and longer pulse illumination [17–19], measuring the properties with the z-scan yields the total effective nonlinear refractive indices and absorption, making it difficult to separate purely optical effects from thermal effects . With the applications for these particles potentially using either type of laser source, the nonlinear response of these particles needs to be investigated.
Barium titanate (BaTiO3) is a perovskite crystal with a high third order susceptibility when in the tetragonal phase, so it is well suited for nonlinear imaging techniques, such as third harmonic generation and optical phase conjugation . BaTiO3 nanoparticles (NPs) were fabricated with average diameters of 200 nm and 500 nm through either the hydrothermal or solvothermal synthesis method (Fig. 1 ) [22–24]. In a typical synthesis, barium chloride or barium hydroxide was used as the barium source. This was mixed with titanium dioxide in an aqueous or water/ethanol solution with sodium and potassium hydroxide, sealed in a steel autoclave, and heated at 190 °C for 12 – 48 hours. All chemicals used were of 99% purity and were purchased from Sigma Aldrich. Also, BaTiO3 NPs were purchased from NanoAmour of Houston, Tx to provide a standard for crystallinity and optical properties. In addition, BaTiO3 nanorods with diameters of 50 nm and average lengths of 250 nm and Ba2YbF7 nanoparticles were also fabricated using the hydrothermal method to provide secondary structures to compare with the nonlinear properties of the larger BaTiO3 particles (Figs. 2 , 3 ).
Silver was seeded onto the 200 nm and 500 nm BaTiO3 nanoparticles by photoreduction of silver nitrate in solution with BaTiO3 and polyvinylpyrrolidone (PVP) which mediated the growth of silver seeds on the surface as opposed to forming silver particles separately in the solution. In a typical silver deposition, 0.3 g of BaTiO3 nanoparticles were suspended in a half ethanol, half water solution with 0.3 g of PVP and 0.6 g of AgNO3. This solution was exposed to visible illumination from a tungsten-halogen lamp at 200 W for 1.5 hours while under vigorous stirring. The size of the silver seeds on the surface is directly related to the time of exposure during photochemical reduction, and 1.5 hours was chosen so that the silver seeds growing on the NPs did not become so large that they began to detach from the BaTiO3. Figures 4 and 5 illustrate the Ag seeds grown by photochemical deposition on the facets of BaTiO3. Those facets with the positive ends of the polarization vector directed toward the surface preferentially grow the Ag seeds, as was found in a previous study of BaTiO3 bulk samples .
3. Experimental setup
The nonlinear properties of nanoparticles were investigated using the well known closed aperture z-scan technique . In this setup, a Spectraphysics DPSS laser (λ = 532 nm) was focused through a lens with f = 7.3 cm with a detector in the far field with a small aperture (S << 1) aligned to the center of the beam (Fig. 1). A translational stage was placed such that solutions containing the nanoparticles, placed within a quartz microcuvette (L = 2 mm), traversed the focal point (Fig. 6 ).
Although the nonlinear effects were observed with a continuous wave source, both visually and by measurement, a chopping blade (200 Hz) was placed in the beam pathway, and a lock-in amplifier was added to the setup to increase the signal to noise ratio and stability of the signal. As described in previous work, the nonlinear optical properties can be extracted through fitting plots of the transmittance with the Eq. (1) [21, 26]:Eq. (2) [27, 28]:29]:
Under the condition of cw laser illumination, it has been noted that the Sheik-Bahae formalism is not the most accurate description since it does not take into account heat diffusion within the samples and nonlocal interaction of the laser beam with the nanoparticles [30–32]. As such, the formalism developed by Cuppo, et al. which is based on a thermal lens model is also considered, where the transmittance can be described by Eq. (5) [31, 32]:Eq. (6) :Eqs. (5) and (6), the nonlinear index of refraction due to thermal effects can be calculated using the same relation found in the definition of the phase change. Although the measurements were made under cw illumination, and thermo-optical effects are expected to dominate, the measurements were treated with each of the four formalisms in order to obtain a clearer picture of the properties of Ag@BaTiO3 under these conditions.
The z-scan technique was performed multiple times on each of the nanoparticle types separately prepared in an aqueous solution; examples of the results for each type of nanoparticle are given in Figs. 7 , 8 , 9 , 10 . The error bars represent the standard deviation between the high and low values obtained for each point along the z-scan. Nonlinear fitting of the previously described Eq. (1) was conducted using the phase changes due to the nonlinear refractive index and nonlinear absorption as the fitting parameters. The distinctive peak-to-valley shape of the closed aperture z-scan is a clear indication of third order nonlinear processes, which was present in each of the samples. The nonlinear refractive index and absorption was calculated for each of the as prepared samples and can be found in Table 1 .
The z-scan results for each nanoparticle solution clearly show the peak-to-valley shape which indicates third order nonlinear properties. The nonlinear response from the nanoparticle solution was clearly visible in the far-field during measurement in the laboratory, demonstrated by a self-focused intense disk when the sample was on the side closer to the lens and laser source and as a self-defocused optical vortex when the sample was on the opposite side of the focal point. As was expected, the tetragonal 500 nm and 200 nm BaTiO3 nanoparticles exhibited higher nonlinear indices of refraction than the smaller, cubic BaTiO3 nanorods. The Ba2YbF7 nanoparticles exhibited the lowest third order susceptibility which is likely due to their extremely small size and crystalline structure. Comparing the silver seeded BaTiO3 nanoparticles to those without silver seeds, there is a clear and dramatic increase in the third order susceptibility. Not surprisingly, the 500 nm Ag@ BaTiO3 samples exhibited the largest susceptibility, but it is important to note that even the 200 nm Ag@ BaTiO3 samples had a larger susceptibility than the 500 nm and 200 nm BaTiO3. This enhancement of the nonlinear response is likely due to the silver seeds creating either localized heating around the nanoparticles, increasing the thermo-optical nonlinearities, or by localized electromagnetic field enhancements which allow a polarization to be more easily induced in the nanocrystalline BaTiO3. The results calculated from the Sheik-Bahae formalism were slightly lower than those from the peak-to-valley calculation, although they were still in good agreement. Since it depends on the whole range of values rather than just the maximum and minimum, the nonlinear curve fitting tends to be more accurate which is why it has smaller standard deviations. The results obtained using the thermal lens and aberrant thermal lens formalisms are slightly lower than those obtained using the Sheik-Bahae equations, yet are still in good agreement. It is important to note that within each mathematical treatment, the Ag@BaTiO3 samples continually showed a significant increase in the nonlinear response over the bare BaTiO3 nanoparticles.
The results obtained for the Ag@BaTiO3 samples compare well with those available in the literature with our results being slightly higher than one reference for silver deposited on BaTiO3 thin films, Re χ3 = −2.56*10−7 esu and Im χ3 = −1.45*10−8 esu , and slightly lower than one for Ag/BaTiO3 nanocomposite thin films, Re χ3 = 8.567*10−6 esu and Im χ3 = 4.151*10−7 esu . While these reported results were obtained using nanosecond laser pulses, the role which thermal nonlinearities play in z-scan measurements with different laser sources has been the subject of many papers, such as those by Ganeev and de Nalda, and thermal nonlinearities were determined to be non-negligible even down to nanosecond pulses, especially with a high repetition rate [18, 19]. Given that the mechanisms for the nonlinear properties of our samples and those previously mentioned are very similar, they provide a reasonable measure to compare with our results. In similar nanocomposites of BaTiO3 nanoparticles surrounded by a Au shell, it was shown by Pu, et al., that there was an increase in the second harmonic generation by a factor of 500 when excited near the plasmon resonance of the nanocavity ; we expect to see similar results in our own samples when excited near the plasmon resonance of the Ag seeds, and it will be interesting to study these enhancements as a function of the size and plasmon resonance of the Ag seeds.
It should be noted that purely silver nanoparticles were also tested with our z-scan setup; however, accurate measurements could not be obtained since the particles began to fuse and aggregate on the surface of the cuvette as soon as they neared the focal point of the system. Also, the z-scan measurements with particularly large error bars, such as the one near the focal point in Fig. 10, showed an anomalously high point in one of the measurements which therefore skewed the deviation. However, all other measurements at these points were very close to each other, and the anomalous point was likely due to extra particles moving through the focus of the beam at the exact moment.
The nonlinear properties of different types of nanoparticles were investigated using the z-scan technique. It was found that BaTiO3 nanoparticles with the tetragonal crystalline phase still exhibit high third order susceptibilities even down to 200 nm scales, making it a good nanomaterial for use in nanophotonics applications such as nonlinear microscopy and optical phase conjugation. It was then subsequently shown that the addition of silver seeds on the surface greatly enhances the third order nonlinear properties for these nanoparticles. More importantly, it has been shown for the first time that the nonlinear susceptibilities for these nanomaterials are on the same order as thin films with similar composition. These highly nonlinear nanomaterials may prove most useful as contrast agents, biosensors, and phase conjugate nanomirrors. As such, under the right conditions, such as in counter-propagating four wave mixing, they could produce phase conjugate waves which will retrace their way back to the originating source and could effectively undo scattering effects of turbid media where they are present. This will have profound implications for their use as imaging contrast agents as well as in nanophotonic and biophotonic devices or sensors. Current work is underway to test the biocompatibility of these materials and utilize them as contrast agents, biosensors, and phase conjugate nanomirrors.
This research was supported by the National Science Foundation Partnership for Research and Education in Materials (NSF-PREM) Grant No. DMR – 0934218 and by a grant from the National Institute on Minority Health and Health Disparities (G12MD007591) from the National Institutes of Health. The authors would also like to acknowledge the support from NIH-RCMI Grant No. 5G12RR013646-12.
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