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The nonlinear absorption in nanostructured Ni-Ti alloys, fabricated by electrochemical deposition, was investigated at 532 and 1064 nm. The type of nonlinear absorption (saturable or reverse saturable absorption) was observed to depend on the laser intensity as well as on the nanoparticle size. The nanostructured Ni-Ti alloys comprising particle mean diameters of 20 and 30 nm exhibited large three-photon absorption (3PA coefficient ~ 106 cm3/GW2) and large two-photon absorption (2PA coefficient ~ 105 cm/GW) at 532 nm, respectively. The observed change over from reverse saturable absorption to saturable absorption at high peak intensities has qualitatively been analyzed by the excited-state theory of conduction electrons.
©2008 Optical Society of America
1. Introduction
Recent years have witnessed a tremendous research on novel nonlinear optical (NLO) metal and semiconductor nanomaterials and their composites for realizing all-optical devices [1–4]. These nanomaterials exhibit remarkable optical nonlinearities and fast optical response due to surface plasmon resonance (SPR), which can be applied for ultrafast optical applications. Measurements of two-photon absorption (2PA) in various metal nanoparticles of different dimensions have already shown that they exhibit very large 2PA coefficients when excited close to their SPR [2]. Currently, titanium (Ti) and nickel (Ni) nanomaterials and their nanocomposites have been very attractive for their substantial third-order nonlinearities [5, 6]. Although bulk Ti and Ni have also been used to produce organometallic complexes with large nonlinear optical responses [7, 8], Ti and Ni nanoparticles are of current interest due to their size-tunable third-order nonlinear responses which enable one to understand the origin of nonlinearities and to optimize their NLO properties desired for nanophotonics [9]. It is also noteworthy that the optical properties of metallic nanocomposite materials can be quite different from those of bulk metals. Hence, it became also important to compare the optical properties of such nanomaterials as a function of particle dimension for future applications.
Additionally, in order to increase the third-order nonlinear susceptibility χ (3) of a NLO material, one approach is to form a nanocomposite from different materials. In this work, we combined Ni and Ti, and fabricated nanostructured Ni-Ti alloys for investigating their NLO responses. There have been reports on the preparation, electronic structures and linear optical properties of bulk martensitic Ni-Ti alloys and their use in micro-actuators and micro-sensing devices [10, 11], but not on their NLO properties. Generally, metallic nanoparticles can be prepared by various methods such as sol-gel, laser deposition, sputtering and electrochemical deposition [5], even though electrochemical technique was preferred in the present work because of its simplicity and cost-effectiveness. Nanostructured Ni-Ti alloys comprised of particle diameters of 20 and 35 nm were prepared. They were found to exhibit giant nonlinear absorption at both 532 and 1064 nm with the nature of nonlinear absorption depending on the intensity of the laser beam as well as on the size of nanoparticles. The saturable absorption was found to occur at intensities higher than those corresponding to the reverse saturable absorption, and this behavior could qualitatively be analyzed based on the rate equation analysis for the excited electrons.
2. Experimental
Ni-Ti alloys with a particle mean diameter of 20 nm (coded as NT1 and NT2) were electrodeposited from the electrolyte prepared by mixing 0.01 M of Ti(SO4), 0.01 M of NiSO4∙6H2O and 0.01 M of trisodium citrate (TSC) with deionized water. TSC was used as a complex agent. For fabricating the alloy with a particle mean diameter of 35 nm (NT3), another electrolyte was prepared by mixing the above chemicals with a concentration of 0.05 M with deionized water. The pH of the citrate containing electrolytes was maintained to be 3. Before deposition of Ni-Ti film, the electrolyte was deaerated by nitrogen gas for 5 min. The electrodeposition was performed using a standard three-electrode cell where a platinum-coated titanium mesh, a saturated Ag/AgCl electrode and an indium titanium oxide (ITO) coated glass plate were used as the counter, the reference, and the working electrode, respectively. The deposition time was maintained to be 10 s for fabricating NT1 and NT3 from the respective electrolytes while for NT2, the deposition was carried out for 30 s. Thus, nanoparticles of different diameters could easily be obtained with NT1 and NT3 just by changing the chemical concentration in the electrolyte, and the film thickness of NT1 and NT2 could be varied by varying the deposition time. The structural and morphological characterizations were carried out by scanning electron microscopy (SEM) and x-ray photoelectron spectroscopy (XPS). The XPS spectra revealed that the samples are in the form of Ni-Ti with a small amount of oxygen as additive. The details to the characterization have been described elsewhere [12]. The absorption spectra of samples fabricated were recorded with a spectrophotometer. The film thickness was measured using an Alpha Step surface profiler (Ambios Tech., XP-1). The SEM images were obtained with a Field Emission scanning electron microscope (FE SEM) (Hitachi, model S-4300SE).
The third-order NLO characteristics of the nanostructured Ni-Ti alloys were investigated by employing the single beam z-scan technique [13] using a Q-switched Nd:YAG laser delivering nanosecond pulses at a repetition rate of 10 Hz at 532 and 1064 nm. The laser beam was focused to a spot size of 20 μm by a convex lens whereas the Rayleigh length was 2.3 mm. The nonlinear transmission measurement was performed when the sample was at focus by varying the incident pulse energy.
3. Results and discussion
The SEM images of NT1, NT2 and NT3 are shown in Fig. 1. NT1 and NT2 possess particles of diameter of 20 nm, while the diameter of NT3 was 35 nm. The film thicknesses (L) of NT1, NT2 and NT3 were approximately 40, 82 and 46 nm, respectively. As shown in Fig. 2, the SPR absorption peak of the samples NT1 and NT2 was located at 435 nm. A slight red-shift of the SPR from 435 to 448 nm as a result of the increasing particle size was observed in NT3.
Fig. 1. SEM images of NT1 (a), NT2 (b) and NT3 (c). NT1 and NT2 have particles of mean diameter of 20 nm with different film thicknesses. NT1 and NT3 have comparable film thicknesses, but different particle mean diameters of 20 and 35 nm, respectively.
Fig. 2. Linear absorption spectra for NT1, NT2, and NT3. The surface plasmon resonance absorption peaks are denoted.
The nonlinear absorption measurements were made at wavelengths away from the SPR absorption band. The open aperture z-scan results obtained for three samples at 532 nm are depicted in Figs. 3–5. Figure 3 shows the nonlinear absorption curves for NT1 obtained at different input laser intensities. Initially, at a lower intensity, reverse saturable absorption (RSA) was observed, and the absorption depth increased with increasing input intensities. Above 0.2 GW/cm2, a transition to saturable absorption (SA) appeared and only SA was observed at higher intensities.
Fig. 3. Open aperture z-scan curves for NT1 at 532 nm. Saturable absorption occurred at higher intensities than those corresponding to reverse saturable absorption. Solid lines are fit of data to Eqs. (1) and (2). Dotted line indicates theoretical fit of data with Eq. (1) assuming only 2PA.
An identical nonlinear absorption trend in the same intensity range, as shown in Fig. 4, was observed in NT2. The open aperture results obtained for NT3 are shown in Fig. 5. Contrary to the results of experiments on NTI and NT2, only RSA was observed in NT3 in the similar intensity range. The substrate, ITO-coated glass plate, alone did not show any nonlinear response within the intensity range used for this experiment at 532 nm.
Fig. 4. Open aperture z-scan curves for NT2. Change of RSA to SA was observed with increasing intensity.
Fig. 5. Open aperture z-scan curves for NT3 at different input intensities. Solid line is a fit of data to Eq. (1) assuming 2PA. Saturable absorption was not observed in NT3 in the same intensity range used for the other two samples.
The nonlinear absorption curves in Figs. 3–5 were theoretically fitted with Eqs. (1) and (2) obtained from the derivation for 2PA and three-photon absorption (3PA) coefficients [4, 14], which are given by
where Leff = (1−e −α0L)/α 0 is the effective sample thickness of NT3 and L′eff = (1−e −2α0L)/2α 0 that of NT1 and NT2 in the present case. α 0 is the linear absorption coefficient and α 2 and α 3 are the effective 2PA and 3PA coefficients, respectively. By fitting the experimental data with these equations, we found that NT3 exhibits large 2PA while NT1 and NT2 having smaller nanoparticles exhibit large 3PA. Additionally, the increasing nonlinear absorption coefficient values of samples with increasing intensities suggested the role of an excited-state absorption in the nonlinear absorption. The magnitudes of 3PA coefficients of NT1 and NT2 are nearly same indicating no significant thickness dependence of nonlinear absorption in these samples. Generally, parameters such as particle shape and sizes and their distribution have significant influences on the nonlinear response of nanomaterials, and the processes involved in nonlinear absorption are free carrier absorption, multi-photon absorption, and saturable absorption. It is evident as we compare the nonlinear absorption property of NT 1 with that of NT3 that the size of nanoparticles apparently has caused changes to the order of multi-photon absorption. We note that a similar observation of multi-photon absorption with reducing particle size has been previously reported for CdSe nanoparticles [4].
The result of an additional single-beam transmittance measurement made for NT1 at different fluences is shown in Fig. 6. The laser used was operated in a single-shot mode to record transmission at each fluence, in order to avoid unwanted thermal effects in the sample. Figure 6 clearly demonstrates the subsequent change of RSA in to SA with increasing fluence. Such dependence of nature of NLA on the fluence can be explained with a standard rate-equation analysis for the conduction electrons in nanoparticles.
Fig. 6. Single-beam transmission versus incident fluence for NT1. Reverse saturable absorption appeared for lower input fluences and saturable absorption for higher fluences.
From the recent investigations on nanomaterials, it is well understood that the nature of nonlinear absorption depends on whether the measurement is made inside or outside the SP absorption band. The SP absorption arises from the transition of the free electrons in the conduction band of metal nanoparticles when excited by laser pulses. Once the electrons in the ground-state are excited by a pulse close to absorption peak, they cannot oscillate at the same frequency as that of the unexcited electrons. The excited electrons are free carriers possessing a whole spectrum of energies, thus causing the ground-state plasmon band to bleach or reduce in intensity, which is almost synchronous with the primary photon absorption. A part of the excited electrons will be pumped to the even higher energy levels, causing excited-state absorption. Therefore, if the measurements are made near the SPR peak, one would observe SA at lower fluences and RSA due to excited state absorption at higher fluences. In the present work, however, the exciting wavelength was outside the SP absorption band and SA was observed in NT1 and NT2 for fluences higher than those corresponding to RSA. Note that it has been observed in several organic materials and in a few nanomaterials that once RSA action has set in, it need not necessarily continue to all higher fluences [15, 16]. The detailed behavior depends on the cross-sections and lifetimes of a series of excited states of the material. Hughes et al. reported the first observation of RSA to SA transfer in an organic dye such as HITCI and the novel effect was explained based on the three-level excited state theoretical model [17]. A similar model was successfully applied to the case of Au/glass nanocomposite system by Qu et al., although they explained the usual nature of SA leading to RSA at higher intensities of nanosecond pulses [18]. In the present case, we applied the excited-state theory of electrons to explain the fluence-dependent RSA to SA change over in the nanostructured Ni-Ti alloys. The electronic transitions in these systems consisting of four energy levels S 0, S 1, S 2 and S 3 corresponding to the population densities N 0, N 1, N 2 and N 3, respectively, are shown in Fig. 7.
The rate equations for a four-energy-level model can be written as
where N = N 0 + N 1 + N 2 + N 3 is the total population, σ’s are the microscopic absorption cross sections, h is the Planck’s constant, ν is the laser frequency used, and τ 10,τ 21 and τ 32 are the life times of S 1, S 2 and S 3, respectively. The change in intensity I of the laser beam as it propagates along the z-direction is given by
If the pulse width is much longer than the lifetimes, the steady-state approximation can be taken into account for the above rate equations, that is ∂Ni/∂t = 0 for i =0, 1, 2 and 3. Additionally, the population N 3 is assumed to be negligible since τ 32 ~ 0. Subsequently, by solving the rate equations in the steady-state regime, the nonlinear absorption coefficient can be obtained, as reported in Ref [18], as
where I s1 = hν/σ 01 τ 10, I s2= hν/σ 12 τ 21, K 1 = σ 12/σ 01, and K 2 = σ 23/σ12. The monotonic change of absorption coefficient α with the incident intensity determines the type of nonlinear absorption that occurs in our samples. If dα/dI < 0, the absorption decreases with increasing laser intensity and a SA takes place, on the other hand if dα/dI > 0, RSA appears. However, when dα/dI = 0, the change over from RSA to SA or SA to RSA will be observed. Using the condition dα/dI = 0, one can derive a quadratic equation in I as
whose roots are
Now, the intensity at which the RSA turns over to the SA is designated as the threshold intensity (Ic) given by,
In the case of nanostructured Ni-Ti alloys with a particle diameter of 20 nm, RSA was observed initially at low intensities. It leads to σ 12 > σ 01 and hence K 1 > 1 . However, at sufficiently high intensities, as the S 2 level becomes significantly populated, absorption from the second excited state becomes an important factor in determining the high-fluence response. In particular, this transition will have a key influence on whether the saturation of the second-excited-state absorption occurs. At higher intensities, the build-up of population in an excited-state may lead to a reduction of the corresponding absorption coefficient (saturation or bleaching). Consequently, as observed in NT1 and NT2, RSA action will cease when an accumulation of population in the second excited state S 2 depletes the number of electrons contributing to absorption processes. Therefore, as the intensity increases beyond Ic, the change over of RSA to SA happens. This requires that K 2 < K 1, leading to a condition that σ 23 < σ 12 > σ 01. By substituting these conditions in Eq. (6), one can readily obtain a positive real value for the threshold intensity Ic. Thus, in NT1 and NT2, when the absorption cross-section of the first excited state σ 12 is greater than those of the ground state σ 01 and the second-excited-state σ 23 while the incident intensity approaches Ic, the transfer from RSA to SA occurs. Experimentally, we observed a saturation of absorption in NT1 (Fig. 6) for fluence values above 0.42 J/cm2. Laser-induced damage was observed in the sample above 0.85 J/cm2. Note that a similar observation of RSA leading to SA at higher fluences in the case of Au nanosol was speculated to be the saturation of the induced absorption [16]. Experimentally determined values of effective 2PA and 3PA coefficients for the nanostructured Ni-Ti alloys at 532 nm are summarized in Table 1.
Table 1. Nonlinear absorption coefficients of NT1, NT2 and NT3 at 532 nm.
Results of the nonlinear absorption measurements performed at 1064 nm for NT1 and NT3 are presented in Fig. 8. NT1 showed RSA while NT3 exhibited SA at the same intensity of 0.9 GW/cm2. The effective 2PA parameter for NT1 was found to be 0.68×105 cm/GW and the nonlinear absorption coefficient of NT3 was −0.65×105 cm/GW. The intensity-dependent absorption studies could not be systematically carried out at 1064 nm, because the ITO-coated glass itself showed significant SA above 1.0 GW/cm2, making it difficult to discriminate the contribution of substrate from that of Ni-Ti alloys.
Fig. 8. Nonlinear absorption curves for NT1 and NT3 at 1064 nm. The data can be fitted well with 2PA process using Eq. (1).
Although the z-scan technique enables to measure nonlinear refraction, the thermal effects were found to be dominant in its measurement of the samples using nanosecond pulses. A single 7-ns pulse might be long enough to induce thermal accumulation that affects the nonlinear refraction originating from electronic polarization. In addition, large nonlinear absorption also contributes to the thermal effect. Nevertheless, the present study indicates that nanostructured Ni-Ti alloys show potential for nonlinear optical applications. In the case of RSA dyes [15], the power limiting performance was influenced by a range of molecular parameters and dynamics of excited states, and hence certain general figures of merit (ratio of absorption cross sections and life times of different energy levels) were predicted to enhance the dynamic range of induced absorption. In the case of nanostructured Ni-Ti samples, we observed that the dynamic range of induced absorption can be extended only by particle size selection. Thus, such Ni-Ti alloys allow one to employ them for low power optical limiting devices by suitably tailoring the particle size. A direct comparison of Ni-Ti nanoalloys with similar samples under identical experimental condition is presently not possible. However, the magnitudes of nonlinear absorption coefficients of NT 1–3 are comparable with those of recently reported Ag-Ti cosputtered composite films [5] and 5-nm-thick Au films [19]. The 3PA coefficients of NT1 and NT2 are one order of magnitude larger than those of CdSe nanoparticles (~105 cm3/GW2) [4].
4. Conclusions
Nonlinear absorption measurements, performed at 532 and 1064 nm on nanostructured Ni-Ti alloys with different particle diameters, revealed very large nonlinear absorption coefficients. The nature of nonlinear absorption was found to depend on the laser intensity as well as on the particle size. The intensity-dependent behavior, particularly RSA to SA change over at higher intensities, has qualitatively been discussed based on the rate equation analysis of excited elections. Because of the huge effective 2PA coefficient and the RSA behavior of NT3, we expect that the NLO response of nanostructured Ni-Ti alloys can selectively be tuned by particle-size control for suitable photonic applications including optical limiting.
Acknowledgments
This work was supported by the Korea Science and Engineering Foundation grant (No. R0A-2007-000-20113-0) and by the Korea Research Foundation grant (MOEHRD, KRF-2007-412-J04002), funded by the Korean government.
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