1. Introduction

Composite systems of noble metal nanoparticles embedded in dielectric material matrices with high refractive index often exhibit large third-order optical nonlinearities and fast response time because of the enhancement of the local field near and inside the metal particles around the surface plasmon resonance (SPR). And it has been attracting great attentions because of their essential applications in all-optical switches, optical correlators, phase conjugators and optical computing [1,2]. Several kinds of dielectric materials [3,4], polymer films [5] and semiconductors [6] have been chosen as the host matrices to enhance the nonlinearity of the composite systems. Very recently, we reported a maximum value of the third-order nonlinear optical susceptibility [χ ⁽³⁾] of Ag:Bi₂O₃ [7] thin composite films with Ag concentrations varying from 13.2% to 59.3%. The maximum value of χ ⁽³⁾ is 4.1×10^-10 esu, it occurs at an Ag concentration of about 35.7%. Up to now, the annealing effect of linear and nonlinear optical properties of Ag nanoparticles embedded in bismuth oxide has not been reported. It is therefore important to study which one plays the key role in nonlinear enhancement and ultrafast response of the Ag:Bi₂O₃ composite materials after annealing.

In this letter, we present a systematic study of the annealing effect of the optical absorption properties, nonlinearities and ultrafast response of Ag nanoparticles embedded in Bi₂O₃ matrices. We used a scanning spectroscopic ellipsometer to obtain the thickness and the refractive index of Ag:Bi₂O₃ thin films at room temperature. The ultrafast response and optical Kerr effect (OKE) were studied through the off-resonance femtosecond (fs) time-resolved OKE technique [8].

2. Experimental

Samples were deposited by cosputtering of Ag (with the purity 99.99%), controlled by a dc power supply, and Bi2O3 (with the purity 99.9%), controlled by an rf power supply, respectively. The fabrication procedures have been detailed elsewhere in details [7]. After deposition, the Ag:Bi₂O₃ thin films were annealed in a high vacuum chamber (with the pressure 2.0×10^-6 mbar) for an hour at a temperature ranging from 300°C to 800°C. All the Ag:Bi₂O₃ thin films have the Ag concentration of about 35% in atomic ratio as measured by Rutherford back scattering method either before or after thermal annealing. The third-order nonlinear susceptibility, χ ⁽³⁾, of Ag:Bi₂O₃ composite films were examined via a time-resolved optical Kerr effect and pump-probe experiment. The femtosecond laser pulse was generated from a Ti/sapphire laser system (Coherent Mira 900 B) operating at 76 MHz. The full width at half maximum (FWHM) of the pulse was about 120 fs, the central wavelength of the laser beam was 800 nm and was nearly resonant with the Q band of the samples. The pump and probe beams were split from the laser output, the pump beam was chopped at 1620 Hz and it went through an optical delay line controlled by a computer. A polarizer P1 was put into the probe beam path to set its polarization to be 458 with respect to that of pump beam. Two beams were focused on the same spot of the sample with a spot size of about 50 µ m by a lens with f=5 cm. The transmitted probe beam passed through an analyzer P2 with crossed polarization to P1. The signal was detected by a photodiode connected with a lock-in amplifier and the data were stored into a computer. For pump-probe measurement, the polarization of both pump and probe beams was set to be parallel.

3. Results and discussion

The absorption spectra of Ag:Bi₂O₃ composite films were measured by UV-VIS-NIR scanning spectrophotometer (UV-3101 PC, SHIMADZU) in the 300-800 nm wavelength range. The results are shown in Fig. 1. The data were automatically corrected by the spectrophotometer to deduct the absorbance from the substrate. The curves A-F show the absorption peaks as the results of different

 

Fig. 1. The optical absorption spectra of Ag:Bi₂O₃ composite films with different annealing temperature. Curve A, as-deposited film; curves B, C, D, E, and F, films annealed for 1hour at 300, 400, 500, 600, and 700°C, respectively.

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Ag:Bi₂O₃ composite films with different annealing temperatures. According to the calculation, the non-annealed peak position should be around 580 nm. When the samples are annealed below 600°C, the strong absorption peaks due to the SPR effect are found in the range of 580–600 nm. The resonant peaks increase and have a red-shift about 20 nm with increasing the annealing temperature. The observed red-shift of the plasmon band is a characteristic feature of the composite films which have large concentration of silver nanoparticles [4]. But, when annealed at 600°C or above, the peak position has a big jump on the absorption spectra. This large peak shift about 90 nm indicates that the structure of over 600°C annealed Ag:Bi₂O₃ composite films changed evidently. With increasing the annealing temperature, the linear absorptance also increases. According to the size and dielectric dependence [8] based on the change of the Ag nanoparticles size and the change in the effective permittivity of the surrounding matrix as predicted by effective medium approximation theory [9,10], the red-shift can be explained well. When the annealing temperature comes to 700°C, the absorption intensity drops and is less than that of 600°C. It looks like that when the annealing temperature is 800°C, the structure of the sample is destroyed and we attribute it to the thermal instability of the Bi₂O₃ materials.

The crystallinity and the mean diameter of the Ag:Bi₂O₃ nanocomposite thin films were characterized by x-ray diffraction (XRD) with CuK_α radiation. The mean diameter d of Ag particles is estimated using Scherrer’s equation,

where λ is the wavelength of x-ray source and _β (rad) the full width at half-maximum of the x-ray diffraction peak at the diffraction angle θ.

 

Fig. 2. XRD pattern for Ag:Bi₂O₃ composite films. A, the as-deposited film; the other films are annealed at B, 300°C for 1 h; C, 400°C for 1 h; D, 500°C for 1 h; E, 600°C for 1 h ;and F, 700°C for 1 h. The Ag nanoparticles peak after 600°C annealed is zoomed in the inset.

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Figure 2 shows the XRD patterns of the as-deposited Ag:Bi₂O₃ composite film A and heat treated films B-F. In the as-deposited film A, there is a weak peak. While in films E and F, two obvious peaks are observed, which are assigned to Bi₂O₃ and Ag diffraction peaks, respectively. These peaks boost up with the increase of the heat-treatment temperature. To illustrate the mean diameter of the Ag nanoparticles clearly, the Ag peak of the samples annealed at 600°C is zoomed in the inset of Fig. 2. From the results of the inset, the mean diameter of the Ag nanoparticles is estimated to be about 50 nm. These results mean that the Ag particles were successfully embedded in Bi₂O₃ thin films and their sizes depended on the heat treatment conditions. It’s also right for the linear absorption peak shifts over 600°C.

All the femtosecond time-resolved OKE experiments of Ag:Bi₂O₃ thin films were performed at room temperature [11]. The values of the effective χ ⁽³⁾ were measured relative to that of a reference, CS₂, taken to be 1×10^-13 esu in the fs regime [12]. In the calculation, we invoke Eq. (2a) for the effective χ ⁽³⁾ of the samples [13]:

Where I is the OKE signal intensity at zero delay time, α is the linear absorption coefficient, n is the refractive index, and L is the interaction length. Subscripts s and r denote sample and reference, respectively. The calculated values of χ ⁽³⁾ versus annealing temperature of the Ag:Bi₂O₃ composite films are plotted in Fig. 3.

 

Fig. 3. Dependence of third-order nonlinear optical susceptibility [χ ⁽³⁾] on annealing temperature. Solid circle and line indicates the experimental value and the Lorentz model fitting result, respectively.

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Easily, one can find that with increasing the annealing temperature, the values of χ ⁽³⁾ change and reach a maximum value of 2.1×10^-9 esu at 600°C. By comparison with the as-deposited film [χ ⁽³⁾=4.1×10^-10 esu], nonlinear enhancement is clearly demonstrated in the Ag:Bi₂O₃ composite films and it depends on the annealing temperatures. When the annealing temperature is higher than 600°C, nonlinear enhancement effect decreases gradually. To understand the intrinsic physical properties more, the profile of values of χ ⁽³⁾ is fitted to a solid line by using Lorentz model. The experimental results are quantitatively in good agreement with the Lorentz simulation as follow:

where ${\chi }_{\mathit{\text{fit}}}^{\left(3\right)}$ is the fitted third-order nonlinear susceptibility of the films, T is the annealing temperature. The values are 1.9, 8247.9, 277.5, and 584.8 for the fitted coefficients A, B, C, and T₀, respectively.

In general, the nonlinear enhancement of the third-order susceptibility at high Ag composition can be ascribed to two effects: local field enhancement and Mie resonance of the particles [14]. It is thought here that the origin of the optical nonlinearity is from their intraband electron transition [7]. Hence the intrinsic χ ⁽³⁾ is originated from the intraband transition of Ag:Bi₂O₃, and is enhanced by the local field effect, which comes from the structure of metal nanoparticles embedded in high-index matrices. For annealing temperatures ranging from 300°C to 600°C, the values of χ ⁽³⁾ increase with the annealing temperatures. In other words, the nonlinearity enhancement increases with the size of metal nanoparticles. However, when the annealing temperature is 700°C, not only has Ag nanoparticles crystallized much better but Bi₂O₃ has a sharp reflection as well than that of 600°C from Fig. 2. It means the size of Ag and Bi₂O₃ nanoparticles become larger. If the metal clusters become large enough to get connected, the local field will be averaged out and the local field enhancement effect will be reduced. So the value of χ ⁽³⁾ will begin to decrease.

Figure 4 shows the fs time-resolved OKE signals of as-deposited, 400°C annealed and 600°C annealed samples, respectively. A clear time evolution profile, which consists of an ultrafast rise (about 200 fs) and the following sub-picosecond decay process, is shown in all three types of samples. Since the excitation wavelength of the excited laser is far from both the transition band of Ag and the SPR band of Ag:Bi₂O₃ composite films, the ultrafast OKE response rise might come from the photo-induced anisotropy, which contributed mainly by free electrons near the Fermi level [8,15]. The OKE signals of these samples show bi-exponential decay behaviors-a sub-picosecond fast decay process and a long-lived decay process. Since the time constant of the slow decay process is much larger than the time region of this experiment, the bi-exponential decay process can be simulated as an exponential decay process plus a positive offset. The time constants after de-convolution are 0.6, 0.8 and 1.5 ps for as-deposited, 400°C, and 600°C heat treated composite films, respectively. Obviously, the relaxation becomes slow with increasing annealing temperature (i.e., particle size). It might demonstrate the hot electron-phonon coupling at the nanoparticle surface with influence of size-dependence surface effect [16–18].

 

Fig. 4. Femtosecond OKE response of Ag:Bi₂O₃ thin films with different annealing temperatures. Open symbol: experimental data; Solid line: fit of experimental data using exponential decay convolved with 100 fs Gaussian pulse.

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4. Conclusion

In summary, the optical absorption properties, nonlinearities and ultrafast response of Ag:Bi₂O₃ composite films with different annealing temperatures are revealed through several measurement techniques. The wavelength of optical linear absorption peak corresponding to the SPR for the nanocomposite films shift to the long wavelength (red-shift) with increasing the annealing temperature. And a large shift occurs as the composite film is annealed over 600°C. The XRD results demonstrate this phenomenon in terms of the changes in the samples crystallinity. We have performed fs OKE experiments and calculations for Ag:Bi₂O₃ composite films, which are annealed at different temperatures. The third-order nonlinear optical susceptibility χ ⁽³⁾ of the films is enhanced after annealing. With increasing the annealing temperature, the maximum value of χ ⁽³⁾ observed is 2.1×10^-9 esu, which occurs after heat treatment at 600°C. The time of the fast decay process in the ultrafast response is about 0.6, 0.8 and 1.5 ps for different heat treated composite films. It suggests that the time increase of relaxation is depended on the annealing temperature. These experimental results point out the importance of the nanoparticle size and the crystallinity when studying the optical properties of composite films.