Large nonlinear absorption in single aggregate of silver nanoparticles observed with z-scan imaging technique

The general challenge in investigating the origin of the ultrasensitive response from a single nanoparticle or nanostructure has been focused on a smart optical setup in the last few decades.^1–5 The nonlinear optical properties of such a single nanostructure need a single optical setup used in the experiment sustained by an integrated high resolution imaging part^1–3 so that it can overcome the diffraction limit.^4,5 Furthermore, the nonlinear optical characters in metallic nanomaterials have been intensively studied by many different multidisciplinary scientists^6–16 due to their tremendous nanotechnology implementations. In addition, an attractive single nanostructure or a nanochip is very interesting to study for the future engineering nanorobot industry so that it may support, for example, an expanded space exploitation with various multitasking nanotechnology devices, such as a healing system through the injection of nanomedicine in the human body, high sensitivity metallic core–shell nanosensors,^17–40 and many other ultralow energy nanodevices with their ultrafast nonlinear optical (NLO) properties.^41,42

In this paper, a newly modified z-scan technique⁶ with an integrated imaging system is proposed to investigate a single aggregation of Ag nanoparticles (NPs). As a matter of fact, one discovered a large nonlinear absorption coefficient, α₂ = 8.90 × 10⁹ cm/GW, and Im(χ⁽³⁾) = 2.57 × 10⁻³ esu, which are among the largest NLO metallic nanomaterials. The detailed measurements, studies, and application impact, as well as its origin, are provided in Secs. II and III, including their physical discussion and explanations.

The sample of Ag NPs was ordered from Nanostructured and Amorphous Materials, Inc. (NanoAmor, USA). These Ag NPs have an average diameter of ∼20 nm and are in aggregation form with the smallest size of aggregation of ∼300 nm measured using both the scanning electron microscope (SEM) of Hitachi (model S-3000N) and a newly modified z-scan imaging technique as depicted in Fig. 1. The Ag aggregate sample for the z-scan imaging experiment was prepared by diluting the Ag aggregates in methanol, spin-coating them on a glass substrate, and then putting them on a hot plate at 100 °C for ∼2 h in order to evaporate the solvent of methanol. The heating time was restricted to such time in anticipating the enlargement of Ag NP aggregation based on our prior finding knowledge and understanding about temperature dependence on aggregation size in Ref. 43.

After the position of single aggregates of Ag NPs located at the focal point of the z-scan imaging setup was selected by the 3D translation stage and observed with the used CCD camera (model DP72 from Olympus), I inserted the light source of deuterium and halogen (Avalight-DHS from Avantes) passed through a fiber behind objective lens 1 (OL1) in Fig. 1 and then put the spectrometer head (Avaspec-3648 from Avantes) connected to a computer just behind the sample in order to record the absorption and transmittance spectra of the single aggregate target.

The details of the experimental setup of the z-scan imaging technique are shown in Fig. 1. An OL focuses a laser beam onto the sample, which can be moved along the z direction or axis, and another OL2 with a higher numerical aperture (NA) is placed in front of the sample in order to collect the image of the single nanostructure. The image of the sample is then captured using a high resolution charge couple device (CCD) camera, and the transmittance in each z position due to the interaction of the sample and laser light is simultaneously recorded using a spectrometer. Such a z-scan imaging technique is actually a novel modified z-scan technique with imaging from the one in Ref. 6. In our setup, I use a continuous-wave (CW) laser with a wavelength of ∼407 nm and 0.85 NA OL2 with its magnification and working distance being 20× and ∼650 µm, respectively, so that the resolution or diffraction limit (λ/2NA) is ∼240 nm, which is small enough to study a single aggregation of nanoparticles.

To utilize this setup, I chose a single aggregate of Ag NPs as our sample searching among other aggregations embedded in a glass substrate. The reason was because Ag NPs exhibited a large third-order susceptibility (χ⁽³⁾) of 2.4 × 10⁻⁹ esu at 400 nm induced by the optical Kerr effect,⁷ and when Ag NPs were aggregated into fractal clusters, they had even much larger χ⁽³⁾, which was about 10⁻⁵ esu measured at 539 nm with a picosecond laser of Nd:YAlO₃.⁸ 

Figure 2 shows the absorption and transmittance spectra of a single aggregate with a diameter of ∼1.56 µm of Ag NPs assessed at visible wavelengths. I found that the transmittance and linear absorption coefficients, α₀, measured at 407 nm of this single aggregate is 87% and 148.3 cm⁻¹, respectively. The scale parameters in this figure were provided based on true measured values so that they did not need to be normalized.

In the z-scan imaging experiments technically carried out by using the setup based on Fig. 1, the employed OL1 has a focal length of 8.8 mm, producing a focused beam with a beam waist of ω₀ = ∼8 µm. The thickness of the single aggregate of Ag NPs (with an average diameter of ∼20 nm) deposited on a glass substrate is ∼1.56 µm, which is shorter than the Rayleigh range (z₀) of the focused beam (z₀ = πω₀²/λ = 770 µm), a requisite that simplifies the analysis of the z-scan results. Figures 3(a) and 3(b) demonstrate the two-dimensional (2D) and three-dimensional (3D) images of the sample interacted with the laser light at each z position. From 2D images recorded at each z position, the diffraction pattern or rings induced by the interaction between the sample and the laser beam become larger and larger as the sample was moved far away from the focal point. To investigate and analyze the intensity profile of each image observed at each z position, I obtained the 3D images of the data in Fig. 3(a) as shown in Fig. 3(b) and the profile of the interaction between the laser beam and the sample. The captured image profile due to light-matter interaction was recorded in each z position. When the sample was located at the focus point or at z = 0, the intensity profile in the center of z scan image was reduced. Furthermore, it was gradually increased as the sample was moved further away from the focal point. Such z-scan imaging has a novelty knowledge contribution from the previous well known z-scan imaging shown in Ref. 6.

Figure 4 displays the open aperture z-scans of the single aggregate of Ag NPs measured at different irradiances. I observed the irradiance dependence of nonlinear optical processes in this single aggregate. First, at low irradiance, the induced absorption or two photon absorption (TPA) effect occurred. As the irradiance was increased, the reverse saturable absorption (RSA) process was induced. Finally, when the irradiance was further increased to two orders higher than that used to observe the TPA effect, the saturable absorption (SA) process was induced. To explain the mechanism of these nonlinear optical properties observed in Figs. 4(a)–4(c), a three-level model as described in Fig. 5 with its theory was developed according to Ref. 9 to explain the NLO phenomena. This model involved a ground state S₀ and two excited singlet states of S₁ and S₂, respectively. The rate equations for the populations N₁, N₂, and N₃ of states S₀, S₁, and S₂ can be written as follows:

where σ₁₂ and σ₂₃ are the absorption cross sections for the transition from S₀ to S₁ and from S₁ to S₂ and τ₂₁ and τ₃₂ are relaxation times from S₁ to S₀ and from S₂ to S₁, respectively. The irradiance dependence absorption coefficient, α, can be obtained from the steady-state solution, and dN_i/dt = 0 from the three-level model of Eqs. (1) and (2),

where I_s is the saturation irradiance for the S₀ → S₁ transition. If I/I_s ≪ 1, Eq. (3) can be simplified as follows:

and the solution for the transmittance as a function of z position, T(z), can be written as¹⁰ 

where L_eff = (1−exp(−α₀L))/α₀ is the effective sample thickness and α₂ = α₀((σ₂₃/σ₁₂)−1)/I_s is the nonlinear absorption coefficient. It is obvious from Fig. 4 that for a low irradiance of 9.50 × 10⁻⁹ GW/cm², σ₂₃/σ₁₂ > 1 and induced absorption or TPA is found, while at a high irradiance of 4.8 × 10⁻⁷ GW/cm², σ₂₃/σ₁₂ < 1 and SA is observed. In the case of RSA, the study was examined at 12.1 × 10⁻⁹ GW/cm² and is shown in Fig. 4(b). It shall be pointed out that there is, so far, no exact solution for T(z) to fit the experimental data. The single aggregate of Ag NPs possesses the highest nonlinear absorption coefficient, with α₂ = 8.90 × 10⁹ cm/GW or Im(χ⁽³⁾) = 2.57 × 10⁻³ esu, which are about 10 and 100 times larger than those for a AgInSbTe thin film¹¹ and Ag fractal clusters,⁸ respectively. I attribute this giant α₂ to both the enhancement of local fields and their fluctuations as well where the eigenmodes in this single aggregate are localized. The comparison of some materials with such a large nonlinear absorption coefficient is listed in Table I. Further research in engineering such an incredible finding may be expanded to obtain the chemical physics mystery there, particularly in studying their polarization NLO dependence.^44–46 However, the significant contribution of this z-scan imaging technique has guided an important way to the interdisciplinary scientific community to be on track of the single NLO nanochip world.

In conclusion, I have introduced a modified z-scan imaging technique, which is very important to study nonlinear optics focusing on a single nanostructure. The applied technique enabled us to measure the nonlinear absorption coefficient in a single aggregate of Ag NPs. I observed that this Ag single aggregate exhibits a large nonlinear absorption coefficient, which is one among the largest NLO nanomaterials. The large nonlinear absorption coefficient, α₂ = 8.90 × 10⁹ cm/GW, and Im(χ⁽³⁾) = 2.57 × 10⁻³ esu make the single aggregate of Ag NPs very interesting for potential applications in various photonic circuits with an integrated optical multitasking sensors, thermal conductivity nanochip, and nanodevices.

This work was supported by NEDO/METI under the “superhybrid materials R&D project,” Japan. The author is grateful to Professor Bin Cai, Professor Okihiro Sugihara, Professor Toshikuni Kaino, and Professor Tadafumi Adschiri who were a part in the big team under the above-mentioned project. Moreover, the publication fee of this publication was covered by innovative research grant 2021 at Pattimura University. Finally, the author is grateful to the non-profit organization of A-ASA for their unconditional support.

The author has no conflicts to disclose.

H.I.E. planned and carried out most of the experimental work and data analyses, as well as the insights, and guided discovery explanations of this work.

The data that support the findings of this study are available from the corresponding author upon reasonable request.