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Abstract
It is now well established that the nonlinear optical properties of ZnO nanoparticles can be significantly enhanced by coupling them to metallic nanoparticles. While the nonlinear absorption properties are well reported, there is large variation in the coefficients of nonlinear refraction reported in literature, largely due to simplifications made during the analysis of experimental z-scan data used to determine the coefficients. This work presents closed aperture z-scan theory which incorporates the effects of nonlinear absorption, thus providing a more accurate measure of the coefficient of nonlinear refraction. With this theory, it is shown that the coefficient of nonlinear refraction increases by an order of magnitude when ZnO is coupled to Au nanoparticles.
Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Nonlinear refraction, also known as the nonlinear Kerr effect, is a vital tool in the realization of optical information processing and all optical computing. In particular, optical devices such as waveguides, all optical switches, logic gates, and storage devices, all depend on nonlinear optical processes. In the search for new materials to broaden the application of these devices, it is essential to accurately characterize the relevant nonlinear optical processes. This is a challenging task in bulk materials, which is made even more difficult in nano- and composite- materials.
ZnO nanoparticles are one particular nanomaterial that have attracted significant interest due to their wide 3.4 eV bandgap, negligible visible absorption and strong 60 meV binding energy. This combination of properties has seen them proposed for many applications such as biological imaging and treatment, solar energy harvesting and nanoscale lasing. In addition, ZnO has strong nonlinear optical properties that have potential for high resolution biological imaging and treatment [1] as well as UV-blue nanolasers [2,3].
It is well established that the nonlinear optical properties of semiconductor nanostructures can be enhanced by placing them in close proximity to metallic structures. Previous studies investigating ZnO nanoparticles and ZnO-metal composite nanostructures report enhancements in nonlinear absorption and refraction [4,6, 21]. However, there is large variation in the magnitude of the enhancement reported in these studies and, in particular, the nature of the specific absorption processes occurring. This has largely been due to a lack of consideration of transient effects when determining nonlinear coefficients [5]. In recent work [7], we have accurately determined the nonlinear absorption coefficients of ZnO and ZnO-Au composites which took into account two photon absorption (2PA), three photon absorption (3PA), saturable absorption and excited state absorption (ESA).
In addition to this, there is a three order of magnitude variation in the reported coefficient of nonlinear refraction for ZnO nanostructures in the literature [8,9]. The major source of variation in these studies is the assumed simplification that the closed aperture trace can be divided by the open aperture trace to remove the effects of nonlinear absorption from the closed aperture measurements [10]. This assumption is only valid under certain circumstances [10], which are not satisfied in many of the reports in literature. A likely explanation for the invalid simplifications is the lack of analytic solution describing the transmission in the closed aperture trace when nonlinear absorption processes also occur. Analytic solutions have been provided in the past for the case where only 2PA is present [11], however previous studies have shown this is not the case for ZnO and ZnO-metal nanostructures [5,7].
To overcome the difficulty in the theoretical treatment, in this paper we build upon theory for numerical simulations of the open aperture z-scan trace, presented elsewhere [7], and extend it to the closed aperture z-scan. By incorporating the nonlinear absorption coefficients into the numerical simulations of the closed aperture z-scan, and comparing them to experimental data, more accurate coefficients of nonlinear refraction can be determined. These results are then compared with the simplified approach of dividing the closed aperture trace by the open aperture trace to demonstrate the importance of including significant nonlinear absorption processes into the theoretical treatment.
2. Theory
The time dependent change in transmission through a nonlinear media measured during a z-scan experiment can be determined by considering the time dependent intensity and phase changes of the incident field, in the radial (r), transverse (z) directions. These are given by [12]
where $z^{\prime}$ is the propagation depth through the sample, α[I(r,z,t)] is the intensity dependent absorption, ${n_2}$ is the coefficient of nonlinear refraction arising from the nonlinear Kerr Effect and k = 2π/λ is the wavevector. The form of α[I(r,z,t)] varies depending on the optical properties of the material and the experimental conditions.The numerical determination of the open aperture z-scan for ZnO and ZnO-Au has been presented previously [7]. The technique is extended here to allow it to be applied to the closed aperture traces. The intensity and phase change of the electric field as it propagates through a medium can be determined iteratively throughout the sample volume. These can be calculated numerically for small discrete steps (Δz’) of the sample length (L). At each step n, the intensity and phase of the electric field exiting the slice [ΔΦn(r,z,t), In(r,z,t)] were calculated using the intensity [7] and phase of the field exiting the previous slice [ΔΦn-1(r,z,t), In-1(r,z,t)] by
The validity of the numerical simulations was verified by comparing numerical simulations, in the limit of small phase changes, to the analytic solution presented by Sheik-Bahae et al. [10]. The Sheik-Bahae et al. analytic function for ΔΦ0 = 0.1 cm3/GW2 was compared to numerical simulation with an identical ΔΦ0 value and achieved good agreement, as demonstrated in Fig. 1(a). Further verification of the simulations was undertaken by performing least squares fits of closed aperature z-scan to experimental closed aperature data from a toluene reference sample with a well-established n2 value [15] and negligible nonlinear absorption, and found to be in good agreement, as can be seen in Fig. 1(b).
Fig. 1. (a) Numerical closed aperature z-scan simulations (ΔΦ0 = 0.1) (circles) is compared to analytic solutions [10] (solid line) and (b) closed aperature simulation is compared to experimental closed aperature data on 2 mm toluene sample.
For materials that possess both nonlinear absorption and nonlinear refraction, the closed aperture trace will display a combination of both the change in transmission through the aperture due to refraction and absorption. Examples of the effect that the different nonlinear absorption processes have on the closed aperture z-scan trace are shown in Fig. 2.
Fig. 2. Numerical simulations of closed aperture z-scan trace (ΔΦ0 = 0.1) when nonlinear refraction occurs in conjunction with (a) saturable absorption, (b) two photon absorption and (c) excited state absorption. The coefficients used in the simulations are indicated on the graphs.
All the simulations shown have ΔΦ0 = 0.5 and linear absorption αL = 0.5. The effect of saturable absorption, demonstrated in Fig. 2(a) and calculated for I/Is = 0,0.5,1,2, increases the transmission around the beam waist, reducing the valley of the closed aperture trace and enhancing the peak. The simulations in Fig. 2(b), show the effects of 2PA, calculated for q0 = βI0L = 0,0.1,0.2,0.4, which act to decrease the transmission around the beam waist producing an enhancement of the valley in the closed aperture trace and a decrease of the peak. A similar effect is observed in the closed aperture traces with ESA, shown in Fig. 2(c), for p0 = αESAI02L = 0,0.5,1,2.
3. Experimental investigation of ZnO and ZnO-Au
3.1 Sample preparation and characterisation
The samples used in this study were ZnO nanocones and ZnO-Au composite nanoparticles. Capping agent-free ZnO nanocones were synthesized using a well-established method [16]. Using the same ZnO nanocones, a photochemical deposition technique [17] was used to synthesize the ZnO-Au hybrid nanoparticles. For measurements, ZnO and ZnO-Au samples were diluted in ethanol to a ZnO concentration of 0.1 mg/mL. The corresponding Au concentration in the ZnO-Au sample was 0.005 mg/mL. The prepared samples were characterized by imaging with a JEOL 1400 Transmission Electron Microscope (TEM) and measuring the extinction spectra using a Cary50 UV-Visible spectrophotometer.
TEM images of ZnO and ZnO-Au samples are shown in the right and left inset of Fig. 3, respectively. Due to the absence of the capping agent on the ZnO nanoparticles, the particle shapes vary slightly but maintain a consistent size between 50-100 nm. The ZnO-Au nanoparticles have a near 1:1 ratio of ZnO to Au nanoparticles, with no visible free Au particles in solution. The Au nanoparticles have a consistent diameter of approximately 10 nm.
Fig. 3. UV-Visible extinction spectra of ZnO and ZnO-Au samples. Inset: TEM images of ZnO (left, solid border), and ZnO-Au hybrid nanoparticles (right, dashed border).
The extinction spectra of ZnO and ZnO-Au samples are presented in Fig. 3. Both spectra show a strong extinction peak around 370 nm, corresponding to the ZnO bandgap. As expected, the magnitude of the UV extinction is similar for the two samples, confirming their similar ZnO concentrations. The long tail, for wavelengths >400 nm in both samples, is due to scattering of the incident light by the particles. The ZnO-Au has an additional peak at approximately 550 nm corresponding to localized surface plasmon resonance (LSPR) of Au nanoparticles.
The linear extinction coefficient used for nonlinear absorption fits is determined from the extinction spectra at the incident wavelength of 532 nm. For ZnO, the extinction for all wavelengths above the bandgap is assumed to be entirely due to scatter and the absorption is negligible αZnO = 0 cm-1. For ZnO-Au, although there are methods to separate absorption from scatter [18], it is difficult for the particles of interest here due to their geometry. Therefore, it was assumed that the entire extinction is due to absorption αZnO-Au = 0.37 cm-1.
3.2 Nonlinear optical measurement methodology
The nonlinear optical properties of the samples were measured using the z-scan technique in the open aperture and closed aperture arrangements as shown in Fig. 4. The incident light was produced by a Vibrant 355 Optical Parametric Oscillator operating at 532 nm with a pulse full width half maximum duration of 5 ns and a repetition rate of 10 Hz. The energy was adjusted using a polarizer and a half waveplate. The output beam was focused using a 500 mm lens to a radius of w0 = 41 $\mu $m at the beam waist (z0) producing a Rayleigh range of zR = 9.9 mm. These values were determined by performing closed aperture z-scan measurements on a 2 mm toluene reference sample, which has a well-established coefficient of nonlinear refraction [15].
The light transmitted through the sample was split using a beam splitter so both open aperture and closed aperture measurements could be measured simultaneously using Si photodiodes with a 0.35 ns rise time. During measurements, samples were circulated using a 4 mm quartz flow cell and a peristaltic pump to minimize thermal effects.
3.3 Open aperture z-scan measurements
Nonlinear absorption measurements of ZnO and ZnO-Au, performed using the open aperture z-scan technique with an incident energy of 300 µJ, are presented in Fig. 5(a) and 5(d), respectively. Here, the transmission, normalized to the low intensity transmission, is presented centered on the beam waist with the translation normalized to the Rayleigh range.
Fig. 5. Open Aperture measurements of (a) ZnO nanoparticles and (d) ZnO-Au composite nanostructures; Closed aperture measurements on (b) ZnO nanoparticles and (e) ZnO-Au composite nanostructures; and the closed Aperture trace divided by the open aperture trace of (c) ZnO nanoparticles and (f) ZnO-Au composite nanostructures; Solid lines in (a,b,d,e) show least squares fits to numerical simulations, solid lines in (c,f) show least squares fit to analytic functions.
The ZnO-Au sample exhibits a much stronger change in transmission at higher intensities than ZnO. The increase in transmission above unity for the ZnO-Au sample (Fig. 5(d)) is due to saturable absorption in the Au nanoparticles [19,20]. The coefficients of nonlinear absorption were determined by performing least squares fits of experimental data to numerical simulations of the transmission given in Eq. (7). The best fit simulation for ZnO irradiated with 300 µJ is shown as a solid line in Fig. 5(a). The average 2PA coefficient was found to be β = 0.11 ± 0.08 cm/GW and the ESA coefficient was found to be αESA = 1.1 ± 0.2 cm3/GW2.
For the ZnO-Au composite nanostructures, the 2PA coefficient, ESA coefficient and saturation intensity were determined by least squares fits to numerical simulations. The best fit simulation for 300 µJ is shown as a solid line in Fig. 5(d). The average 2PA coefficient was found to be β = 0.4 ± 0.5 cm/GW, the ESA coefficient was determined as αESA = 52 ± 5 cm3/GW2 and the saturation intensity was Is = 20 ± 4 MW/cm2. For both ZnO and ZnO-Au samples, there is little two photon absorption occurring compared to other nonlinear processes. When one nonlinear process is orders of magnitude weaker than others in a given measurement it can’t be calculated reliably and is often ignored in fitting to open aperture z-scan traces. However, as it is a necessary process for ESA in these samples, it is included for consistency. The inaccuracy of the calculation of β will have an insignificant effect on the measurement of n2, when it is used as an input to numerical simulations of the closed aperture z-scan trace, since it is so weak.
3.4 Closed aperture z-scan measurements
With the nonlinear absorption coefficients characterized, it is now possible to determine the coefficients of nonlinear refraction. The closed aperture z-scan traces of ZnO and ZnO-Au are presented in Fig. 5(b) and 5(e), respectively, for an incident energy of 300 $\mu $J. These results are presented with the transmission normalized to the low intensity transmission and centered on the beam waist with the translation normalized to the Rayleigh range. Despite the relatively high level of noise in the z-scan traces, an obvious valley followed by a peak can be identified in all traces, which indicates that the particles exhibit self-focusing properties. The enhancement of the valley, and suppression of the peak, resembles the simulations presented in Fig. 2(b) and 2(c) and indicate strong nonlinear absorption is also present.
Numerical simulations of the closed aperture z-scan traces were performed using the process outlined in Section 2 with the absorption coefficients determined in Section 3.3. The least squares fit to the numeric simulations are presented as solid lines in Fig. 5(b) and 5(e). The average value of nonlinear refraction for ZnO was determined from the three highest energies tested only, due to the weak change in transmission at the lowest energies, and was found to be n2 = (6 ± 2) ×10−6 cm2/GW. The average value of nonlinear refraction determined for ZnO-Au was n2 = (6 ± 1) ×10−5 cm2/GW, an order of magnitude larger than the average coefficient for ZnO. The coefficient on nonlinear refraction determined here for the ZnO nanocones is within the three orders of magnitude range of values previously published, but importantly, does not make any invalid or unnecessary assumptions.
3.5 Closed aperture/open aperture fit comparisons
To demonstrate the importance of including the nonlinear absorption coefficients into the numerical simulations of the closed aperture z-scan we present a direct comparison between the simulation fits and the results determined by simply dividing the closed aperture trace by the open aperture trace. In this case, the effects of nonlinear absorption are theoretically removed from the closed aperture z-scan trace, which can then be fit to the analytic solution [10]
4. Conclusion
This paper compared the nonlinear refraction properties of ZnO and ZnO-Au composite nanostructures using numerically simulated closed aperture z-scan traces which incorporates the effects of nonlinear absorption. The nonlinear absorption coefficients first had to be determined from the open aperture z-scan trace. The known nonlinear absorption coefficients were then used to generate numerical simulations of the closed aperture z-scan trace. These were then employed to determine the coefficient of nonlinear refraction. Using this method, it was found that the coefficient of nonlinear refraction increased by an order of magnitude when ZnO was coupled to Au nanoparticles. By incorporating the nonlinear absorption coefficients in the theoretical fits for the closed aperture trace, this study has avoided the need for making unnecessary simplifications and therefore, presents a more accurate estimation of the coefficient of nonlinear refraction.
Funding
Air Force Research Laboratory (FA2386-14-1-4056).
Acknowledgments
Microscopy was carried out at the Central Analytical Research Facility (CARF) operated by the Institute for Future Environments (IFE). Access to CARF is supported by generous funding from the Science and Engineering Faculty (SEF).
Disclosures
The authors declare no conflicts of interest.
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