1. Introduction

Optical response of transparent solids embedded with metal nanoparticles [1] is dramatically enriched by surface plasmons that enhance electromagnetic field in the proximity of the metal-dielectric interface. The sensitivity of the spectral position and strength of the surface plasmon resonance (SPR) to the parameters of the both metal particles and host matrix makes it possible to tailor the optical properties of glass-metal nanocomposites (GMN) by varying size, shape and packing density of the particles and by changing the particle-matrix interface [2–4]. Such a tunability of optical properties along with compatibility with all-solid-state opto-electronic circuits and strong optical nonlinearity has attracted attention to these composite materials, which are often seen as key element in future photonic devices [5,6].

Metallic inclusions in bulk glasses can be made in the course of glass melting or by secondary thermal treatment of the melted glass [7]. Ion exchange [8] and ionic implantation [9,10] with subsequent treatment in reducing atmosphere can also be used for the formation of metal nanoparticles in the subsurface layer of glasses. Linear and nonlinear optical properties of GMN show pronounced spectral features in the vicinity of SPR [2,11–13]. In this spectral range, GMNs demonstrate ultrafast light-induced absorption change. It is mainly due to the dynamics of collective electronic excitations, which have been studied by Z-scan [9,14] and pump-probe [2,3,11–13,15] techniques. Relatively slow component of GMN nonlinear response also observed in experiments is often attributed to interfacial and thermal phenomena [11].

However, wavelength dependence of GMN optical nonlinearity had rarely been characterized. Pump-probe experiments [2,3,10,11,16,17] were mainly focused on the dependence of the optical nonlinearity on probe wavelength only, while the pump wavelength was usually close to the surface plasmon frequency. At the same time, the magnitude of the third-order optical nonlinearity depends on both pump and probe wavelengths. Since the pump beam controls nonlinear absorption, its wavelength should essentially influence the nonlinear optical response of GMN.

In this paper, we report two-dimensional spectral mapping of the optical nonlinearity of copper-based GMN. By tuning of both pump and probe wavelengths near the SPR we perform femtosecond pump-probe measurements of light-induced transmission in two glass-copper nanocomposites. The first one contains Cu nanoparticles uniformly distributed within the glass matrix, while in the second nanocomposite, Cu nanoparticles are concentrated within a 400 nm thick subsurface layer of the glass plate.

2. Experiment

In the experiment, we studied a boron-silicate glass containing copper nanoparticles that display SPR centered at 567 nm. In copper, SPR lays in the vicinity of the interband transition from filled d band to unoccupied states in p conduction band. This spectral degeneracy has attracted a lot of interest to copper-based GMN (see, e.g. Refs. 10–12).

Two different GMNs were used in the experiment. The first one was created by melting boron-silicate glass in slightly reducing atmosphere using the batch containing 0.5 wt% of copper. Since neutral copper is hardly solvable in the glass matrix, annealing of the glass results in phase decomposition and formation of homogeneously distributed copper nanoparticles. The average size and density of nanoparticles were about 10 nm and 10¹³ cm⁻³, respectively. The obtained red-colored GMN (so-called copper ruby glass) will be referred to as Cu-bulk.

The second GMN was produced using copper to sodium and potassium ion exchange in a boron-silicate glass. Polished 1 mm thick glass sample initially containing 16.2 wt% of alkaline oxides was ion-exchanged in the eutectic melt of copper and sodium sulfates for 30 minutes at 540C. After thermal treatment at 450C for one hour in hydrogen atmosphere the reactive diffusion of hydrogen [18]r esulted in the formation of copper nanoparticles of ~20 nm in diameter in ~400 nm thick subsurface layer with the average particle density of 5⋅10¹⁴ cm⁻³. The obtained GMN will be referred to as Cu-surf.

In the pump-probe transmission measurements (see Fig. 1 ), the tunable in the spectral range 400-670 nm pump excites the sample, while its transmission is probed by femtosecond continuum. Pump pulses of 50 fs duration with energy of up to 0.1 mJ are produced by second harmonic of an optical parametric amplifier pumped by amplified pulses of Ti:Sapphire laser at 50 Hz repetition rate. The pump-probe delay can be varied using 2.0-ns optical delay line. The differential transmission ΔT/T(τ) = (T_on – T_off)/T_off is measured as a function of the probe temporal delay τ relatively to the pump, T_on and T_off are transmission of the sample probed with and without the pump, respectively. The experiments are performed at room temperature. Temporal and spectral profiles of the differential transmission in the spectral range of 450-670 nm measured at several pump intensities are visualized using a two-channel imaging spectrometer described elsewhere [19].

 

Fig. 1 Pump-probe measurements setup. Inset shows the induced transmission change ΔT/T of the Cu-bulk GMN (pump intensity 3 GW/cm², λ = 567 nm) as a function of the pump-probe delay.

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3. Results and discussion

Both Cu-bulk and Cu-surf GMNs show pronounced absorption resonance in the vicinity of the SPR at 567 nm. The measured optical density of the Cu-bulk GMN is presented in Fig. 2a (solid line), while dash red line shows the optical density calculated from Maxwell-Garnett model [1].

 

Fig. 2 (a) Optical density of the Cu-bulk GMN. The dash line represents contribution of the SPR at nanoparticles density of 10¹³ cm⁻³. (b-d) Light-induced transmission change in the Cu-bulk GMN pumped at 567, 610 and 550 nm, respectively, with the pump intensity of 3 GW/cm². ΔT/T spectra at pump-probe delays 0, 2, 4 and 8 picoseconds are vertically shifted for clarity. Arrows correspond to central wavelength of the pump pulses.

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One can observe from Fig. 2a that optical transition from the filled d band to unoccupied p band of Cu atoms strongly influences the optical density of the Cu-bulk GMN in the wavelength range below SPR. This indicates that in Cu-based composites, both interband and intraband processes contribute to the linear absorption [11].

Figures 2b,c,d, show time-resolved differential transmission spectra for pump wavelengths λ_pump = 567, 610 and 555 nm, respectively. These wavelengths were chosen to compare differential transmission induced by the pump at the SPR (567 nm), outside the SPR contour in long wavelength region (610 nm), and in the region of d-p interband transitions in copper (550 nm). The spectra of ΔT/T at pump-probe delays of 0, 2, 4, and 8 picoseconds are vertically shifted for clarity. One can observe from Fig. 2 that (i) the spectral position of the pump-induced transmission maximum matches well that of the SPR at 567 nm, and (ii) for all pump wavelengths, the ΔT/T profile well corresponds to the Lorentzian shape of the SPR in Cu (the dash line in Fig. 2a). This indicates that in the Cu-bulk, the light-induced absorption at 520 nm < λ < 670 nm is due to intraband transitions (free electrons), while the linear absorption at λ<570 nm is strongly influenced by the interband transition. One can also observe from Fig. 2 that pumping of the Cu-bulk GMN at 610 nm and 567 nm (i.e. inside and outside the SPR contour) produces comparable transmission changes.

The measurements were performed at several pump intensities. We observed linear dependence of differential transmission on the pump intensity in the whole spectral range. This evidences that light-induced absorption is governed by the third-order nonlinearity of the GMN.

Figure 2 shows that electron ensemble transfers its energy to the copper lattice in about 10 picoseconds. In order to reveal kinetics of the light-induced absorption in the sub-picosecond time scale, we performed measurements of the light-induced transmission for pump-probe delays of 0-2 picoseconds (see Fig. 3 ). One can observe from Fig. 3a that light-induced transmission change reaches its maximum during about 2 ps, this time corresponds to the thermolization of electrons. The comparison of Fig. 2a and Fig. 3b shows that when excited electrons are thermolized the wavelength dependence of the pump-induced transmission change corresponds to that of the surface plasmon. For the first time this was demonstrated in [11], however, the light-induced transmission change in the Cu-bulk GMN (see Figs. 2 and 3) lasts longer in comparison with that characterized in [11].

 

Fig. 3 Temporal evolution of the transmission spectrum of the Cu-bulk nanocomposite during first 2 ps after excitation by 50 fs long pulse at λ = 567 nm and intensity of 3 GW/cm². (a) Temporal profile of the pump-induced transmission change at 567 nm. (b) Wavelength dependence of ΔT/T at different pump-probe delays (in picosecunds). The curves are vertically shifted for clarity; dot line corresponds to the pump wavelength.

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Since we observed linear dependence of the induced transmission on the pump intensity, the results of the pump-probe experiment can be described in terms of the third-order susceptibility χ⁽³⁾, which is a function of the pump (λ_pump = 2πc/ω_pump) and probe (λ_probe = 2πc/ω_probe) wavelengths. When probe, E _probe = E (ω_probe)exp{- iω_probe t} + c. c., and pump, E _pump = E (ω_pump)exp{- iω_pump t} + c. c., waves propagate in an isotropic medium, the third-order susceptibility can be introduced in the following constitutive equation for the Fourier component of the nonlinear polarization at the frequency of the probe wave [20], ${\colorbox[rgb]{}{$P$}}^{(3)}({\omega }_{probe})=6\pi {\chi }^{(3)}{\left|\colorbox[rgb]{}{$E$}({\omega }_{pump})\right|}^2\colorbox[rgb]{}{$E$}({\omega }_{probe}).$Thus the dielectric permittivity is $\epsilon =n^2+24\pi {\chi }^{(3)}{\left|E({\omega }_{pump})\right|}^2$, where n is refractive index of the host matrix. For the change of absorption coefficient, $\Delta \alpha$, this gives:

Figure 4a depicts tone and contour plots of Im{χ⁽³⁾} in the λ_pump (horizontal) and λ_probe (vertical) coordinates. Cross-sections presented in Figs. 4b,d show the dependence of nonlinear susceptibility on the pump wavelength at λ_probe = 567 nm and that on the probe wavelength at λ_pump = 567 nm, respectively.

 

Fig. 4 (a) Contour plot of the Im{χ⁽³⁾} in the λ_pump (horizontal) and λ_probe (vertical) coordinates. The value of the third-order susceptibility is in 10⁻¹³ esu units. (b) Im{χ⁽³⁾} as a function of λ_pump at λ_probe = 567 nm (solid line). (c) Im{χ⁽³⁾} as a function of λ_pump at 567 nm (1), 555 nm (2), 578 nm (3), 610 nm (4) and 522 nm (5). (d) Im{χ⁽³⁾} as a function of λ_probe at λ_pump = 567 nm (solid line). The SPR spectral shape is shown by dash line.

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One can see from Fig. 4b that the Im{χ⁽³⁾} as a function of λ_pump does not reproduce the spectral profile of SPR shown by the dash line. Specifically, the Im{χ⁽³⁾} contour is wider then that of the SPR. In contrast, the Im{χ⁽³⁾} as a function of λ_probe well reproduces the SPR profile (see Fig. 4d). These observations indicate that in the spectral range of 520-620 nm, decrease in the population at the Fermi level is weakly dependent on the pump wavelength. Therefore, in our experiment, the pump pulse induces nearly same decrease of absorption at blue and red wings of the surface plasmon spectrum, while the interband transition play a minor role in the light-induced absorption change in Cu-based nanocomposites (compare with [10]).

Since the SPR is due to the absorption by thermalized electrons, the dependence of Im{χ⁽³⁾} on λ_probe is governed by the decrease of the electron population caused by the pump pulse. Hence Im{χ⁽³⁾} as a function of λ_probe reproduces the shape of the Lorentzian absorption contour taken with opposite sign. From the dependence of Im{χ⁽³⁾} on λ_probe measured at several pump wavelengths (see Fig. 4c) one can conclude that the same mechanism is responsible for the light-induced absorption change under pumping outside the SPR absorption contour.

We also performed similar measurements with Cu-surf GMN, in which nanoparticles were localized in ~400 nm thick subsurface layer with metal concentration of about 20 vol%. We found that this four orders increase in the metal concentration manifests itself in a dramatic enhancement of the optical nonlinearity. Specifically, the measured resonance value of the third-order susceptibility in Cu-surf GMN was about three and a half orders higher than that in Cu-bulk, Im{χ⁽³⁾} ~- 3 × 10⁻¹⁰ esu.

The third-order optical nonlinearity of GMN can be presented as [21]:

In contrast to the Cu-bulk GMN, the wavelength dependence of the optical density of the Cu-surf does not coincide with the Lorentzian absorption contour (see dash line in Fig. 5a ) at the red region of the studied spectral range. This can be caused by a high volume concentration of the nanoparticles in the subsurface layer that distorts the SPR spectral profile. However, the time-resolved spectra of the pump-induced transmission in Cu-surf (see Fig. 5b) demonstrate the same features as those in Cu-bulk composite (Fig. 2b). The inhomogeneity of the nanoparticles distribution manifests itself in the broadening of the ΔT/T spectral shape in comparison with the Lorentzian SPR contour.

 

Fig. 5 (a) Wavelength dependence of the optical density of the Cu-surf GMN (solid line). The dash line shows the surface plasmon contribution to the optical density calculated from the Maxwell-Garnett model. Arrow indicates pump wavelength (567 nm) in the pump-probe experiment. (b) Wavelength dependence of the light-induced transmission in the Cu-surf GMN measured with pump intensity of 1 GW/cm² at 567 nm. ΔT/T spectra at different delays between pump and probe pulses (shown in picoseconds) are vertically shifted for clarity.

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4. Conclusion

By tuning the femtosecond pump and probe wavelengths we mapped the nonlinear absorption of the copper-glass nanocomposites within 520 - 620 nm range. The pump induced 20% transmission rise at 3 GW/cm². This corresponds to the imaginary part of the third-order nonlinearity of about −6 × 10⁻¹⁴ esu and −3 × 10⁻¹⁰ esu for the glass with metal concentration of about 0.02 vol% and 20 vol%, respectively. We show that the Im{χ⁽³⁾} as a function of λ_pump does not reproduce the spectral profile of SPR being wider then the latter. In contrast, the Im{χ⁽³⁾} as a function of λ_probe well reproduces the SPR profile in copper. The symmetry of the nonlinear absorption band with respect to the SPR central frequency indicates that d- electrons of copper contribute differently in the linear and nonlinear absorption processes.