We report a new approach that uses the single beam Z-scan technique, to discriminate between excited state absorption (ESA) and two and three photon nonlinear absorption. By measuring the apparent delay or advance of the pulse in reaching the detector, the nonlinear absorption can be unambiguously identified as either instantaneous or transient. The simple method does not require a large range of input fluences or sophisticated pulse-probe experimental apparatus. The technique is easily extended to any absorption process dependent on pulse width and to nonlinear refraction measurements. We demonstrate in particular, that the large nonlinear absorption in ZnO nanocones when exposed to nanosecond 532 nm pulses, is due mostly to ESA, not pure two-photon absorption.
© 2014 Optical Society of America
Nonlinear optical effects in nanomaterials have gained much interest in recent years due to the numerous potential applications in biomedical imaging  and as compact light emitters in photonic devices [2,3]. Unlike linear optical processes, the nonlinear response of a medium allows the incident light frequency to be upconverted through harmonic generation and many other processes, making it possible to fabricate UV emitters that are pumped by visible light. In order to optimize the performance of these devices, characterization of the medium's nonlinear response is essential. The single beam Z-scan technique, developed by Sheik-Bahae et al. , has become a standard method used for quantifying the nonlinear absorption properties of a medium. However, by simply measuring variations in light transmission through a sample, it is difficult to determine which of the numerous multi-photon nonlinear processes is responsible. Evidence for this is the variation observed between Z-scan measurements performed with pulse durations at the femtosecond to those at the nanosecond , which occurs because the longer pulses can excite additional transient nonlinear absorption processes. To overcome this, extensions to the original Z-scan technique are required to differentiate between instantaneous and transient nonlinearities. For semiconductor materials, when femtosecond laser pulses with photon energies less than the materials band-gap are used, only the instantaneous nonlinearities such as ground state two- and three-photon absorption (2PA and 3PA respectively) are responsible for the nonlinear absorption . However, for longer pulse durations, excited state nonlinearities such as 2PA induced excited state absorption (ESA) can also take place. While complicated pump-probe techniques  can be used, Gu et al.  developed a single beam method that involved performing Z-scans at various fluences. However, this technique cannot differentiate between ground state 3PA and ESA, as both are three photon processes, and has limited application in many materials because of nonlinear absorption induced optical damage which limits the possible range of laser pulse input fluences.
ZnO has received significant interest in nonlinear applications due to its intrinsically high 2PA as a bulk medium, which becomes many orders of magnitude higher in its nanoparticle form . However, often it is simply assumed that the 2PA is the dominant nonlinear absorption mechanism regardless of the experimental parameters used such as pulse duration, etc. Observations of an intensity dependent 2PA coefficient in ZnO  provides further evidence that unaccounted for higher order nonlinearities are also present. Understanding the nature and identifying the underlying mechanism for the observed enhanced nonlinear absorption is vital for the design and optimization of nonlinear devices. For example, ESA is not desirable in UV light emitters that are pumped by visible or infrared radiation, since this process does not generate additional UV light. Similarly, too much ESA in optical limiting applications can cause optical damage of the nanomaterial from overheating .
In this paper we demonstrate that it is possible to use nanosecond pulsed laser excitation to separate instantaneous and transient nonlinearities in ZnO. We show how variations in the pulse transit time to the detector can be used in the single beam Z-scan arrangement to measure the nonlinear response of ZnO nanocones and to identify the dominant nonlinear absorption mechanism.
In the thin sample approximation, the intensity () change over a propagation length () within a sample with linear (), 2PA (), and 3PA () absorption coefficients is given by :7]:7]:Fig. 1(a) where we combine Eqs. (1)–(3) and solve for the specific cases of 2PA, 3PA and ESA. Each curve in Fig. 1(a) shows the theoretically predicted transmitted pulse when a Gaussian shaped temporal pulse is incident on a sample that possesses 20% nonlinear absorption. An instantaneous nonlinearity such as pure 2PA or 3PA flattens the temporal Gaussian beam without affecting symmetry. Conversely, in ESA more of the tail of the pulse is absorbed since the leading edge of the pulse excites the medium into an excited state. As a result, the asymmetry in the output pulse makes it appear to be shifted forward in time. Traditionally, the appearance of pulse distortion has been used to determine the presence of ESA . However, if the input pulse shape is not ideal, as shown in Fig. 1(b) for a forward skewed pulse; the resultant pulse deformation can be even more complicated making it difficult to clearly identify ESA from the temporal pulse shape itself. Quantification would then require complicated pump-probe experiments . However, the pulse deformation caused by transient nonlinear absorption also results in a variation in the transit time from pulse emission to arrival at the detector. Therefore, pulses transmitted through ESA dominated nonlinear absorbing media will arrive earlier at the detector than pulses transmitted through 2PA or 3PA media. This means that a simple metric such as the normalized pulse delay defined in Eq. (4), which determines the temporal shift in the pulse peak, can be used to identify the dominant nonlinear absorption mechanism.Fig. 1(a)) and forward skewed (Fig. 1(b)) input pulses are given in Figs. 1(c) and 1(d) respectively. It is clear that the 2PA and 3PA instantaneous nonlinearities result in either no variation, or a positive delay time for the Gaussian and forward skewed input pulses. However, the 2PA induced ESA results in a negative pulse delay time (i.e. apparent pulse advancement). The pulses emitted by the laser used in our experiments are forward skewed so we expect some positive pulse delay if 2PA or 3PA is dominant or some pulse advancement if ESA is dominant.
We demonstrate this method by investigating the nonlinear absorption of ZnO nanocones dispersed in ethanol using the single beam Z-scan technique  as shown in Fig. 2. The Z-scan experiments were performed using a Brilliant EaZy Q-Switched Nd:YAG laser at wavelength of 532 nm. The temporal profile of the laser pulse from the laser was forward skewed with a FWHM ~5 ns. The spatial profile was not an ideal Gaussian so the Z-scan was performed using a top hat beam tightly focused to a 35 µm airy spot. The aperture after the sample was used to obtain reference closed aperture Z-scans of toluene to find the Rayleigh range () of the focused beam. This aperture is removed for non-linear absorption measurements (i.e. open aperture measurements). The temporal distributions of the incident and the transmitted pulses in the Z-scans were measured using a fast silicon detector connected to a high bandwidth digital oscilloscope.
The ZnO nanocones sample consisted of ~100 nm nanoparticles synthesized as described elsewhere . Powders of ZnO nanocones were dispersed in ethanol with the aid of ultrasonic agitation and transferred to quartz cuvettes (2 mm pathlength) for absorption measurements. The pathlength of the sample was chosen to be less than the Rayleigh range of the Z-scan set-up so that the thin sample approximation (Eq. (1)) could be implemented. The optical extinction spectra of a 0.1 mg/ml sample and a representative SEM image is shown in Figs. 3(a) and 3(b) respectively. Since ZnO is a wide band gap material () the extinction in the visible and infrared can be attributed to scattering, while the extinction in the UV has contributions from both absorption and scattering. Since the laser photon energy is less than the bandgap (), there is negligible linear absorption of the incident light in the Z-scan measurements and therefore, any excited state absorption is induced by 2PA. Open aperture Z-scans of 0.1 and 0.2 mg/ml samples were performed at three different pulse fluences (). The laser fluence range was limited at lower fluences by noise and at higher fluences by optical damage of the samples.
4. Experimental results
Typical normalized transmission Z-scan traces of a 0.2 mg/ml ZnO nanocones sample at 1.32 and 0.87 GW/cm2 are given in Figs. 4(a) and 4(b) respectively. The least squares single parameter fits to 2PA and 3PA are also shown. Since the Z-scan measurements themselves do not reveal temporal information, it is not possible to differentiate between the two different three photon processes of instantaneous 3PA and transient ESA. Furthermore, Fig. 4 demonstrates that it is difficult to determine consistently and unambiguously whether two or three photon absorption is the dominant process with Fig. 4(a) suggesting it is 3PA, while Fig. 4(b) inferring it is 2PA.
The single parameter fits for 2PA and ESA normalized by the sample concentration are given in Fig. 5 with different input maximum intensities, I0. The results show that the fitted is of the same order of magnitude as bulk ZnO (4.2 cm/GW)  despite the low volume fraction of the nanoparticles in the solvent (~10−5). This is in good agreement with other published data on nano sized ZnO . However, the fitted values are monotonically increasing with pulse intensity indicating the nonlinear absorption is not solely 2PA, consistent with the Z-scan traces. There is less variation in the fitted values of but it is difficult to discern a clear trend. Typically, the relative contributions of 2PA and ESA would be determined by fitting trend lines to plots like those shown in Fig. 5. However, due to the large uncertainties inherent in nonlinear measurements of this type and the small range of intensity inputs available due to noise and optical damage concerns, this was not possible for our sample. This highlights the problem in using transmission data alone to determine the cause of nonlinear absorption in a sample.
However, measuring the pulse delay at each of the Z-scan locations readily highlights the difference between instantaneous and non-instantaneous nonlinearities as shown in Fig. 6. Here, the single parameter fit values from Fig. 4 are used to calculate the theoretical pulse delays which are shown along with the measured pulse delay time in reaching the detector. Clearly, there is a strong correlation between the ESA fit and the experimental results indicating the majority of the nonlinear absorption is due to ESA.
Figure 6 demonstrates that ESA is the dominant nonlinear absorption mechanism for those specific experimental conditions in ZnO. Figure 7 shows the pulse delay as a function of transmission for all six Z-scan sets of measured data. Thus, for all three fluences at both concentrations and at all sample locations that were used, the agreement with the theoretically predicted pulse delay due to ESA is significantly better than that for the two instantaneous processes, 2PA and 3PA. This suggests that for ZnO nanocones that ESA is the dominant nonlinearity when exposed to nanosecond duration 532 nm pulses.
This modified Z-scan analysis could be applied to investigate other multi-photon excited state absorption and will only be limited by the lifetimes of the excited states. If the excited state lifetime is much shorter than the pulse duration, the delay time would approach zero. If the excited state lifetime and the pulse duration are approximately the same, then the ESA could still be significant but the pulse delay would be reduced and ESA underestimated.
Identification of 2PA induced ESA in ZnO nanocones using the pulse delay analysis in the single beam Z-scan technique has been demonstrated. Non-linear absorption in ZnO nanocones exposed to nanosecond duration 532 nm pulses has been identified as resulting predominantly from ESA. This simple method allows easier identification of ESA compared to existing techniques utilizing single beam Z-scan apparatus. By isolating the principal nonlinear absorption mechanism, this new technique could help guide materials fabrication in nonlinear optical applications. Future work will be devoted to developing simpler empirical relations between pulse delay and transmission measurements for different excited state absorption and refraction nonlinearities. Input pulses with a Gaussian spatial beam profile would simplify this approach.
This material is based on research sponsored by the Air Force Research Laboratory, under agreement number FA2386-13-114016. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Research Laboratory or the U.S. Government. Microscopy was carried out at the Central Analytical Research Facility, IFE. M.P.S gratefully acknowledges Monique Tourell for her assistance in manuscript preparation.
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