1. Introduction

The optical properties of metals depend on coherent excitations of the conduction electrons known as surface plasmon resonances (SPRs) [1,2]. By controlling the nanoscale geometry of the metal, one can tailor its linear and nonlinear optical properties and manipulate optical processes at subwavelength scales. The strong coupling of a free space optical field to the nanoparticle (NP)’s free electrons generates an ultrafast and high third-order optical nonlinearity. This nonlinearity corresponds to the nonlinear refraction and absorption that reflects intensity-dependent variations in the material’s refractive index [3,4]. Taking an advantage of these nonlinear optical properties in metals has enabled all-optical switching and nonlinear propagation functionalities [3,5] in nanophotonics and has the potential to substantially improve numerous plasmonic applications where high energy light excitation are employed, including photothermal therapy to kill cancer cells [6] and strong coupling enabled water splitting [7].

Previously the nonlinear effects of spherical Au NPs were examined in the vicinity of the SPR, and shown to generate a strong wavelength-dependent complex third-order nonlinear optical susceptibility χ⁽³⁾ [8]. This affects both nonlinear absorption and refraction at the SPR, leading to saturable absorption (SA) and reverse saturable absorption (RSA), in addition to self-focusing and -defocusing. Examining the χ⁽³⁾ in non-spherical Au NPs is interesting because they can support numerous plasmon modes in a small form factor and can be tuned to wavelengths far away from the interband electronic transitions of the metal which tend to dominate absorption [9,10]. The nanorod morphology is particularly good in these kinds of measurements because they can support longitudinal (L)- and transverse (T)-modes that can be tuned over broad wavelengths from visible to mid-infrared by changing its length and radius, respectively [9,11]. Thus Au nanorods can support multiple spectral regions of SA/RSA and focusing/defocusing due to their multiple plasmon modes. To our knowledge, almost all experiments analyzing the χ⁽³⁾ nonlinear properties of nanoscale metals use Z-scan technique. These methods can only measure a narrow wavelength range and tend to be less accurate near the SPR due to much weaker nonlinear refraction compared to the nonlinear absorption [12]. Note that the real and imaginary components of χ⁽³⁾ depend on both the nonlinear refraction and absorption coefficients. Hence inaccuracies may occur in the value and even in the sign of the real χ⁽³⁾ and they mostly report the imaginary χ⁽³⁾ [13–16], thus the optical literature has a lot of conflicting χ⁽³⁾ values for nanoscale Au.

In this manuscript we combine pump-probe spectroscopy methods with spectroscopic ellipsometry to study the χ⁽³⁾ properties of Au nanorods over a broad range of wavelengths (370 – 800 nm). Combining these two methods allows us to address the ambiguities of previous investigations and clarify the complex dispersion of the χ⁽³⁾ with several regions of positive and negative nonlinearities and SA and RSA. In addition, our experimental results indicate a significant 40-nm blueshift of the maximum intensity of SA compared to the steady-state longitudinal plasmon mode. Obtaining this result is important because it will allow researchers to implement accurate models for χ⁽³⁾ in electrodynamics models and greatly improve a metamaterial optimization at desired wavelengths. In addition, it could allow the engineering of plasmonic metamaterials that simultaneously function as SA and RSA and/or self-focusing and -defocusing at specific wavelengths. For example, we envision a multifunctional plasmonic NP optimized at specific wavelengths for theranostics. Also, a multiresonant plasmonic NP to simultaneously enhance light absorption and emission of optical gain mediums.

2. Experimental section

The Au nanorods were grown using a seeded growth method. The seed solution was prepared as follows: 5 mL 0.1 M hexadecyltrimethylammonium bromide (CTAB) solution was mixed with 125 μL 10 mM HAuCl₄ in a 20 mL plastic centrifugation tube and stirred at 30 °C for 20 min. Then 0.3 mL of freshly prepared 10 mM NaBH₄ solution (ice cooled) was injected rapidly into the solution mixture. The solution was stirred for 2 min and left to stand at 30 °C for several hours prior to making the nanorods. Seeded growth of nanorods: 40 mL 0.1 M CTAB solution was mixed with 2 mL 10 mM HAuCl₄ solution using a vortex mixer (Eppendorf Thermomixer C). The solution was then put in a water bath at 30 °C for 4 hours. 220 μL 10 mM AgNO₃ solution, 320 μL 0.1 M ascorbic acid and 1.6 mL 1M HCl solution were injected in this sequence while mixing thoroughly. This solution was then left undisturbed at 30 °C water bath for 17 hours. The final product was separated by centrifuging at 8000 rpm for 20 min. All the supernatant was poured out. The product was dispersed in 40 mL water and the 2nd centrifuge with 5500 rpm for 20 min.

To examine the χ⁽³⁾ properties of Au nanorods they were suspended uniformly in a composite film of polyvinyl alcohol (PVA) on a silica glass substrate. First, the PVA solution was prepared by dissolving 100 mg of PVA in 5.0 mL of water under stirring, heated for 5 h at 75 °C, and then cooled at room temperature. Second, 30 μL of the Au nanorod stock solution was added to 100 μL of PVA solution. Finally, the mix was spin-coated on a silica glass substrate. The final loading percentage of Au nanorods of 0.8% in the PVA matrix was controlled by dilution of the Au nanorods stock solution in the PVA solution. The thickness of the PVA/AuNR composite is 710-nm.

The UV-visible extinction spectrum –ln(T/T₀), where T is the transmittance of the substrate SiO₂ with TiN/PVA film and T₀ is the transmittance of the bare substrate, was measured by a spectrometer (Jasco, V670). Transmission electron microscope (TEM) images (JEOL, JEM-2100F) were obtained using accelerating voltage of 200 kV. Linear optical properties and thickness of the composite film were investigated by a variable angle spectroscopic ellipsometry (J. A. Woollam, VASE). Parameters Ψ(ω) and Δ(ω) were measured at angles of incidence from 50° to 70° by 10° steps. The nonlinear transmission changes ΔT/T, defined as the difference between the transmitted light with and without excitation, were measured by a femtosecond pump-probe spectroscopy. The fundamental laser beam at 800 nm was generated using a Spectra Physics Ti:sapphire oscillator and divided into two portions, pump and probe beams. To avoid laser-induced damage, the repetition rate and pulse width of the frequency-doubled pump beam at 400 nm were kept at 0.5 kHz and 130 fs, respectively. The white-light continuum probe beam was generated by a CaF₂ crystal and the chirping effect was corrected by using the Kerr gate technique [17].

3. Results and discussions

Figure 1 shows the TEM image of Au nanorods with average length/width of 47/15-nm, respectively. Figure 2(a) shows a UV-visible extinction spectrum of the Au nanorods after they were embedded in PVA. PVA is highly transparent in the visible spectrum, thus extinction is due almost exclusively to absorption and scattering of the Au nanorods. The spectrum is composed of a well-defined absorption band at 770 nm corresponding to the longitudinal plasmon mode of the Au nanorods. The smaller absorption band at 545 corresponds to the transverse mode [10]. The longitudinal mode is narrow, and its amplitude is much larger than that of the transverse mode as expected due to its larger absorption cross-section. These features indicate that the Au nanorods are well dispersed and the Au/PVA composite film and behave as an ensemble of single Au nanorods with minimal impurities (e.g. spherical particles) or aggregates [18]. The additional small absorption band at 617 nm can be assigned to a higher-order quadrupole plasmon mode, as has been reported previously [19,20]. The complex dielectric function (or relative permittivity) of the Au/PVA composite film is shown in Fig. 2(b). In addition to the contribution of interband and intraband transitions observed in bulk Au, the imaginary component of the dielectric function of Au nanorods exhibits a strong peak at longer wavelength and a weaker peak at shorter wavelength due to the longitudinal and transverse plasmon modes, respectively. Absorbing materials such as metal composites have both real and imaginary optical constants, and use oscillatory theory to describe these properties. Our ellipsometric model uses gaussian oscillators, and the quality of the fitting is described by the mean squared error (MSE) [21]. This type of model provides a good fit with the experimentally-obtained ellipsometric parameters with an MSE of 13.5. Furthermore, various literature values match our ellipsometric results [11,22]. Thus the dielectric functions obtained in these experiments could reasonably be employed to extract the nonlinear optical parameters.

 

Fig. 1 (a) A TEM image of the Au nanorods with a scale bar of 40 nm. Histograms of the (b) length and (c) width of the Au nanorods.

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Fig. 2 (a) Experimental and calculated extinction spectra and the (b) dielectric function of the Au nanorods embedded in PVA film.

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Ultrafast pump-probe spectroscopy was used to measure ΔT/T and compared directly to the extinction spectrum in Fig. 3(a). In the low photoexcitation regime, the sample was illuminated with a peak intensity of 3.4 GW/cm² (0.7 μJ energy per pulse). This pump intensity did not alter the shape of the absorbance spectrum of the Au nanorods so we concluded that no beam-induced damage had occurred. The ΔT/T of a pure PVA film was measured to qualify the contribution of the PVA on the observed nonlinearity of the composite film, but no significant nonlinearity was observed (data not shown). This transient response allowed us to determine the modulation of the optical properties followed by absorption of an ultrashort light pulse. This optical modulation reflects a nonthermal electron distribution inside the nanorod which evolves to a transient equilibrium by electron-electron scattering [4]. Note that the subsequent energy transfer from the hot electron gas to the lattice by electron-phonon interactions after a few picoseconds is out of the scope of this work. SA and RSA are represented as positive and negative ΔT/T values, respectively, and can be observed throughout the visible spectral region of the Au nanorod data.

 

Fig. 3 (a) Comparison of the steady-state extinction of Au nanorods versus the transient transmission changes at peak power of 3.4 GW/cm². (b) The pump power dependence in the vicinity of the L mode and T mode. Inset: Pump power dependence at 770 nm up to 8 GW/cm².

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To examine the spectral location of the maximum photo-induced SA (729 nm) compared to the steady-state longitudinal mode absorption (770 nm), ΔT/T of the SA regions near the longitudinal and transverse plasmon modes with increasing peak excitation intensities up to 27 GW/cm² are shown in Fig. 3(b). This intensity range showed no evidence of laser-induced damage because the absorbance spectra of the particles did not change before and after the experiments. As can be seen at the maximum intensities of ΔT/T near the plasmon modes (545 and 729 nm), ΔT/T increases linearly up to 12 GW/cm² and then saturates. The sign inversion of ΔT/T at 770 nm with varying excitation intensity from negative to positive can be seen in the inset of Fig. 3(b). This sign inversion implies a transition from RSA to SA. Several reports have attributed this phenomenon to a change in the competition between saturable absorption, two- and three-photon absorption [23,24]. However, our group experimentally demonstrated that the transition from RSA to SA is due to local-field enhancement damping and broadening by observing the nonlinear optical signatures of Ag nanoparticles at different excitation intensities over several wavelengths [25]. More recently, X. Hou et al. [26] observed the RSA to SA transition for Au nanorods and similarly attributed it to plasmon damping and broadening using both continuous and ultrashort pulsed lasers.

The χ⁽³⁾ values of nanoscale metals depend on both nonlinear absorption and refraction. Since ΔT/T measurements address absorption, it is not possible to describe strong and complex optical nonlinearities because it does not consider nonlinear refraction. By combining the dielectric function obtained via ellipsometry with the ΔT/T spectra, the real and imaginary components of χ⁽³⁾ could be expressed as

The real and imaginary components of χ⁽³⁾ of the Au nanorods composite are shown in Fig. 4. Both components show distinct dispersions with regions of positive and negative values that reflect the interband transitions and plasmon modes [4,8]. These regions indicate that Au nanorods exhibit nonlinear absorption and refraction. Thus, depending on the wavelength region in the vicinity of the plasmon modes, it shows SA or RSA and positive or negative nonlinearity. In the vicinity of the longitudinal and transverse plasmon modes, the maximum magnitudes of the imaginary components of χ⁽³⁾ are −1.4 x 10⁻¹⁸ and −0.2 x 10⁻¹⁸ m²/V², respectively. Using a figure of merit (FOM) as Im[χ⁽³⁾]/α, the FOM of the longitudinal and transverse modes are −2.1 x 10⁻¹⁸ and −0.6 x 10⁻¹⁸ m²/V², respectively. Thus the magnitude ratio between the longitudinal and transverse modes is 3.5. This enhanced FOM of the longitudinal mode can be attributed to the suppressed interband contribution of Au at longer wavelengths [9]. As a result of the strong wavelength dependence of the χ⁽³⁾, direct comparison to previous reported values at single wavelength is not always feasible. Au nanorod shape is especially difficult because reported values of the χ⁽³⁾ utilize NPs with longitudinal plasmon resonance spanning from visible to near infrared regions. Note that the excitation laser pulse width, wavelength and repetition also influence the quantity values. Longer pulse width (>150 fs) and high repetition rate (> 10 kHz) add thermal effects to the nonlinear response [28]. Consequently, the reported values of the χ⁽³⁾ of Au nanorods span a range of about three orders of magnitude [13,15].

 

Fig. 4 The third-order susceptibility of the Au nanorods embedded in PVA film.

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Finally, the dispersion of χ⁽³⁾ is a key quantity in nonlinear applications from biological therapy and diagnostic to optoelectronic devices where modulation of the refractive index by an optical field is required. Interestingly, the maximum and minimum intensities of the χ⁽³⁾ components of the PVA/Au nanorod composite occurs at wavelengths that are not at the peak resonance wavelength of the steady-state spectra, especially in the vicinity of the longitudinal plasmon mode (Figs. 3(a) and 4). Maximum SA (i.e. minimum intensity of Im[χ⁽³⁾]) is located at 730 nm which is blue-shifted by 40 nm compared to the longitudinal mode. Similarly, maximum positive and negative nonlinearities expressed by the Re[χ⁽³⁾] are located off peak resonance. The data clearly shows that the nonlinear optical properties of plasmonic nanostructures vary greatly from their steady-state optical properties [29]. Thus this approach offers a substantially better view of the physical behavior of the system compared to simple pump-probe spectroscopy or Z-scan methods. Hence, the results highlight the importance of the dispersion of the quantity χ⁽³⁾. Knowing the dispersion of the χ⁽³⁾ value should enable substantially better simulations of plasmonic metamaterials.

4. Conclusion

In summary, we examined the third-order nonlinearity χ⁽³⁾ of the Au nanorods composite by spectroscopic ellipsometry and pump-probe spectroscopy in the visible range (370 – 800 nm). The Au nanorods were fabricated by the seed-mediated growth method. These NPs were dispersed in PVA and spin-coated on a silica glass substrate. The results clarify the complex dispersion of the χ⁽³⁾ with several regions of positive and negative nonlinearities and SA and RSA. Compared to bulk Au, the Au nanorods exhibit enhanced χ⁽³⁾ due to the longitudinal plasmon resonance and suppressed interband damping at longer wavelength. In particular, our experimental results indicate a significant 40-nm blueshift of the maximum intensity of SA compared to the steady-state longitudinal plasmon mode. Moreover, positive and negative nonlinearity regions were observed throughout the visible spectrum exhibiting maximum and minimum intensities of 1.2 x 10⁻¹⁸ and −0.9 x 10⁻¹⁸ m²/V² at 690 and 783 nm, respectively.