1 Introduction

The confinement of the noble metals to the nanometric scale allows for obtaining materials with new optical and nonlinear optical properties which are connected to the so-called surface plasmon resonance (SPR). The excitation of metal nanoparticles (NP) by the external electromagnetic field leads to dipole plasma oscillations that result in enhancement of the local electric field inside and in close proximity of the NP. Consequently, the intense resonance band appears in the absorption spectra. The position of this band depends, in particular, on the electron effective mass in a given metal, shape and size of NP, and the dielectric constant of the medium in which NP are incorporated.

As a matter of fact, usually optical nonlinearity in Au island structures is studied under resonant with SPR condition (560 nm). However, there are a lot of other laser sources of radiation. So it is interesting to know what would be the nonlinear response and its nature of the structures in question in the case of nonresonant excitation. It is the main purpose of these studies.

During the last decade, the applications of metal nanostructures with particular properties have been discussed in photocatalysis [1], photonics [2], optical data recording [3], and biology [4].

The gigantic third-order optical susceptibility χ (3) of Au NP at resonance excitation of the surface plasmon has been reported during the last years in [5–9]. In particular, in our paper [9] the Au nanostructured films deposited on a glass substrate have been studied. It was shown that for the light wavelength 532 nm, which is close to the SPR peak at 560 nm and the laser pulse duration τ = 10 ns, the third-order optical susceptibility Reχ (3) = −8.2 × 10−5 esu can be obtained. Such a high value of χ (3) has been attributed to the enhancement of the local electric field and the heating of electrons in conduction band. A fast and strong third-order nonlinearity of Au nanostructures is promising for such applications in optoelectronics and photonics as optical switching, optical correlators, dynamic holography devices and others.

From the fundamental and practical points of view, it is important to have information about the optical nonlinearity of metal nanostructures not only at surface plasmon resonance, but for the wavelengths shifted from the resonance as well. The role of the plasmon oscillations is decreased in such a case and the other factors may become important. In particular, for the wavelength shorter than the SPR band the interband transitions have to be taken into account.

In this paper, we present the results of the experimental studies of nonlinear response of Au NP to the femtosecond laser light with the wavelengths 800, 460 and 400 nm (i.e. at the red and blue sides of the SPR) and reveal the origin of the third-order nonlinearity.

It is known [10, 11] that under strong femtosecond pulse excitation the amplitude and shape of the SPR band might change even if the excitation frequency is shifted from the SPR. We use the pump-probe technique to reveal possible influence of such changes to the value and sign of measured nonlinear susceptibilities at these wavelengths of the pump waves.

2 Experiment

The technique of the Au nanostructures preparation is as follows. At first, the solid Au layers are obtained by thermal vacuum deposition on a dielectric substrate. Then the samples are annealed at high temperature. The deposition on a polished glass surface is carried out at 10−5 Torr vacuum with the rate of 0.2–6 nm/min. The Au films obtained in such a way are of 15–25 nm thick and have a polycrystalline structure. The annealing is carried out at ~600–700 °C in laboratory air. As a result the films are dispergated and get an island structure. The size, shape and density of NP considerably depend on the initial film thickness, temperature and annealing time. Even with controlled input parameters some scatter of data is observed from the sample to sample and in different parts of the same sample. Figure 1 presents an electron microphotograph of the Au NP obtained after annealing the initial amorphous Au film at 620 °C.

Fig. 1
figure 1

Scanning electron microscope image of gold nanoparticles obtained after annealing of the amorphous gold films at 620 °C

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The shape of a particular NP is close to flattened nanosphere partly deepened in a substrate. The structures with the 60 nm mean diameter NP are used in our experiment.

To study the dynamics of the nonlinear optical response of the metal nanostructures the well known pump-probe technique is used. A Coherent, Inc. femtosecond laser system that includes a femtosecond generator Mira-900F operating at 800 nm and a Legend HE amplifier serves as a light source. The output pulse energy of such a system is about 2.5 mJ at the 1 kHz repetition rate. Laser pulse duration is about 100 fs, estimated with autocorrelation technique. The probe “white light” continuum is generated by a focused laser beam in a sapphire plate. The “white light” pulse duration is about 180 fs. A part of the amplifier output at 800 nm is used as a pump beam. To get the 400 nm radiation, we use the frequency doubled 800 nm Mira-900F output. The spectrum of the probe beam is registered with a SPEC-10 CCD detector after the pulse passes through a sample.

To measure the value and the sign of the optical nonlinear susceptibility of the Au island films, the same laser system and conventional Z-scan technique [12] are used.

3 Results and discussion

An absorption spectrum of the Au nano-island film in the vicinity of SPR for NP mean diameter of about 60 nm and height about 12 nm is presented in Fig. 2. The corresponding SPR maximum is located at 560 nm. Relatively broad SPR with the extended long-wave tail can be attributed to size dispersion of the NP. Noticeable rise of the absorption with the decreasing wavelength is observed at the short wave side of the SPR which is the evidence of the lower band to band transition, known as L3–L2 transition at about 3 eV (400 nm) [13].

Fig. 2
figure 2

The absorption spectrum of the nanostructured Au film shown in Fig. 1 in the vicinity of SPR band at λ = 560 nm

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The SPR band is presented in Fig. 3, measured before (solid curve) and during the action of a powerful femtosecond laser pulse (dashed curve) at 800 nm with the power P p = 80 mW (the intensity is about 109 W/cm2). The effect of the femtosecond laser pulse, as it is seen from the figure, consists of decrease of the SPR absorption maximum. The relative change of transmittance ∆T/T is about 10−2. Most probably the resonance broadening occurs at the same time. We could not measure it because the spectral width of the measuring system is about 80 nm, i.e. much smaller than that of the SPR band. It should be noted that the measured value of ∆T/T for the Au NP ensemble under study is about two orders of magnitude bigger than that for Ag NP of 20–30 nm size reported in [14].

Fig. 3
figure 3

A part of the SPR spectrum before (solid curve) and under (dashed curve) the action of the power femtosecond laser pulses (λ = 800 nm, P p = 80 mW)

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A nonlinearity response time is an important question for practical applications of any nonlinear medium. The measurement results of the kinetics are presented in Fig. 4. A considerable induced transmittance, as one can see, is observed within the time scale comparable to the pulse duration (~0.2 ps). The relaxation of the induced changes of the optical density occurs in two stages, with two different characteristic times τ 1 = 2 ps (fast) and τ 2 = 200 ps (slow). The relaxation times τ 1 and τ 2 are extracted from the fit of the equation

Fig. 4
figure 4

Kinetics of the absorption changes at SPR peak at room temperature and λ = 800 nm pumping. The solid line is the biexponential fit of the experimental data (dark circles) which yields τ 1 = 2 ps and τ 2 = 200 ps. The inset shows the initial part of the temporal dependence with higher resolution

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$$ D(x) = A_{1} e^{{ - t /\tau_{1} }} + A_{2}e^{{ - t /\tau_{2} }} $$
(1)

to the experimental data.

Comparing with the published data [10, 14–17] we conclude that the observed dynamics with two characteristic times is a signature of the electron gas heating and subsequent relaxation. The heating results from the electron–electron scattering whereas the fast and slow relaxations take place via thermalization of the hot carriers and heat exchange of NP with the air and substrate, respectively.

To verify these assumptions, we measure the dynamics of the SPR changes at liquid nitrogen temperature T ≈ 77 K (λ p = 800 nm). It is expected that under these conditions the heat exchange between the electrons and surrounding medium will change. Figure 5 shows the results of the measurement. From the figure one can see that, in general, the induced changes of the plasmon resonance maximum are similar to that at room temperature. During and just after the excitation the fast decrease of the absorption maximum is observed (τ < 0.2 ps). The relaxation of the changes occurs still with two relaxation times τ 1 = 1 ps and τ 2 = 15 ps. It is clear, however, that while τ 1 is nearly unaffected by the sample cooling, τ 2 becomes at least one order of magnitude smaller. Such a decrease of τ 2 suggests a conclusion that this is the time of the heat transfer from the NP to the substrate, in agreement with our expectations.

Fig. 5
figure 5

Kinetics of the absorption changes at SPR peak at liquid nitrogen temperature T = 77 K and λ = 800 nm pumping. The solid line is the biexponential fit of the experimental data (dark circles) which yields τ 1 = 1 ps and τ 2 = 15 ps

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Similar measurements of the induced absorption changes in the plasmon resonance maximum in the nanostructured Au film are carried out also with the femtosecond laser tuned to the short wave side off the plasmon resonance at room temperature (λ = 400 nm, P p = 40 mW). The results are shown in Fig. 6.

Fig. 6
figure 6

Kinetics of the absorption changes at SPR peak at room temperature and λ = 460 nm pumping. The solid line is the biexponential fit of the experimental data (dark circles) which yields τ 1 = 5 and τ 2 = 200 ps

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The observed dynamics of the transmittance resemble that described above. A sharp increase of transmittance during the time of <0.2 ps after laser pulse excitation is followed by biexponential decay with two characteristic times τ 1 = 5 ps and τ 2 = 200 ps. The increase of τ 1, i.e. the electron gas thermalization time in NP lattice, is clearly seen from the figure. This result can be viewed as evidence that the free electron gas is heated much stronger when exciting it at 400 nm as compared to excitation at 800 nm. This can be understood if we take into account that at 400 nm excitation both the intraband and the interband (one-photon) transitions take place, quantum energy of this radiation (2.7 eV) being 1.7 times higher than that for 800 nm (1.55 eV) excitation.

By means of the Z-scan technique the complex third-order susceptibility χ (3) has been measured at 800 and 460 nm. The results are shown in Figs. 7 (800 nm) and 8 (460 nm). The curves (a, b) represent the transmittance with the closed and open apertures, respectively. The real part of the third-order nonlinear optical susceptibility χ (3) as it follows from Figs. 7a and 8a is positive (Reχ (3) > 0). The imaginary part of susceptibility χ (3) is positive for 800 nm and shows vivid induced nonlinear refraction (Fig. 7b) while for 460 nm the nonlinear absorption is not observed (Fig. 8b).

Fig. 7
figure 7

The Z-scan results for λ = 800 nm and room temperature: a closed aperture; b open aperture. The solid lines show the theoretical fit

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Fig. 8
figure 8

The Z-scan results for λ = 460 nm and room temperature: a closed aperture; b open aperture. The solid lines show the theoretical fit

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The standard fitting procedure [12] allows for evaluating Reχ (3) = +1.7 × 10−7 esu, and Reχ (3) = +1 × 10−7 esu at 800 and 460 nm, respectively. The values are obviously a great deal lower than that obtained in resonant with SPR conditions (Reχ(3) ~ 10−4 esu). They are, nevertheless, high enough so that the island (nanostructured) Au films could be also viewed as a promising optical nonlinear medium for practical applications, in spectral domains aside the SPR.

As it was mentioned above the nonlinear absorption occurs at λ = 800 nm and is absent at λ = 460 nm. The nonlinear absorption at 800 nm can be attributed to two-photon transitions and free-carrier heating in conduction band because of intraband transitions. The energy of two quanta 2ħω 800nm = 3.1 eV overpasses ΔE = 2.8 eV [10] for the transitions from the occupied d-band to partially occupied p, s states of the Au NP. The two-photon absorption was not observed at 460 nm because of the fact that one-photon absorption takes place at this wavelength.

The measured susceptibilities Reχ (3) for two wavelengths are both positive and close in values. The contribution to Reχ (3) at 800 nm is connected to the intraband transitions and, in part, interband two-photon transitions, as well as to the broadening of the plasmon resonance and decreasing of its amplitude in accordance with the Kramers–Kronig relation. In our opinion, the main contribution to χ (3) comes from the selective excitation of the free electrons in conduction band by laser light and further thermalization of free electron gas because of electron–electron scattering.

As for the role of the plasmon resonance, we have to make some remarks. A theory that considers the nonlinear dipole plasmon oscillations caused by the laser light field in metal NP of spheroid shape has been developed in [18]. For the case, when the light wave electric field vector is parallel to the main axes of a spheroid, the theory gives the following equation for the third-order contribution d (3) to the induced dielectric moment

$$ d^{\left( 3 \right) } = \frac{{V\delta (e_{\text{p}} )}}{{16\pi R_{\parallel }^{2} }}\frac{{(em)^{2} \omega_{\text{PL}}^{3} }}{{(\omega_{\text{R}}^{2} - \omega^{2} )}}E_{0}^{3} \left[ {\frac{3\cos \omega t}{{\omega_{\text{R}}^{2} - \omega^{2} }} + \frac{\cos 3\omega t}{{\omega_{\text{R}}^{2} - (3\omega )^{2} }}} \right], $$
(2)

where R || is the NP size along the main axis, E 0 is the light wave electric field ω R and ω PL are the frequencies of the surface and the volume plasmon oscillations, respectively, V is the NP volume, m and e are the mass and charge of the electron, δ (e P ) is the measure of deviation of the spheroid form the ideal sphere. The contribution to the nonlinear refraction in Eq. (2) is due to the first term only.

According to Eq. (2), d (3) should be negative because of the negative sign of δ(e P) [18]. This is in agreement with our previous measurements of χ (3) within the SPR band [9]. At the same time, Eq. (2) predicts the strong dependence of d (3) on frequency detuning from the SPR max. At λ = 800 nm and λ = 460 nm, the contribution from the plasmon resonance diminishes the absolute values of χ (3) but it is too small to revert its sign, which remains positive.

It should be noted that such a behavior of the nonlinear response and change of its sign from negative at SPR resonance to positive at long-wave excitation (800 nm in our case) is in agreement with the theoretical results published in [19].

The radiation at λ = 460 nm is 100 nm detuned to the short wave side of the SPR maximum, i.e., it approaches the area of the interband absorption. The third-order optical nonlinearity in this case is determined by the band to band and intraband transitions. The contribution to the third-order optical susceptibility χ (3) of the plasmon oscillations induced by this radiation is not high but it is larger than that at λ = 800 nm (because of smaller detuning from the SPR) but still it is not enough to change the positive sign of the resulting χ (3).

4 Conclusions

The studies of the nonlinear optical response of flattened spheroid Au NP with mean diameter about 60 nm on glass substrates are carried out aside the surface plasmon absorption peak (λ spr = 560 nm). The wavelengths of the femtosecond laser pulses are chosen at the short wave side (460 nm) and long-wave side (800 nm) from the SPR. The third-order nonlinear optical susceptibilities are shown to be Reχ (3)800nm  = +1.7 × 10−7 esu and Reχ (3)460nm  = +1 × 10−7 esu. The kinetics of the nonlinear optical response has been studied for both wavelengths as well. The analysis of the nature of the observed nonresonant nonlinear response shows that the main mechanism of the nonlinearity at wavelengths 800 and 460 nm is related to the heating of the electrons in the conduction band and their further thermalization as a result of the electron–electron scattering. At 460 nm the contribution to the nonlinear susceptibility because of interband d → s, p transitions is also possible.

The nonlinear optical response in the structures under study is strong and fast. Thus, the nanostructured Au films as the optical nonlinear media are promising for various practical applications, both in resonant and nonresonant with respect to SPR conditions of the excitation.