Electron dynamics and surface plasmon resonance nonlinearities in metal nanoparticles

doi:10.1016/S0301-0104(99)00304-3

Chemical Physics

Volume 251, Issues 1–3, 1 January 2000, Pages 215-226

https://doi.org/10.1016/S0301-0104(99)00304-3 Get rights and content

Abstract

The ultrafast surface plasmon resonance nonlinearities and their connection with the conduction band electron dynamics are discussed in metal nanoparticles in the light of the results of high sensitivity femtosecond pump-probe experiments in silver nanoparticles embedded in a glass matrix. The optical response is interpreted in terms of frequency shift and broadening of the surface plasmon resonance and is related to the changes of the metal nanoparticle dielectric function induced by ultrafast perturbation of the electron distribution. Alteration of the interband absorption is found to be responsible for the observed red shift and very short time delay broadening of the surface plasmon resonance, in agreement with numerical simulations and with measurements in silver films. On a longer time scale, a new nonlinear mechanism due to increase of the electron scattering off the surfaces is demonstrated. This mechanism, specific to confined system, plays an important role in the ultrafast nonlinear optical response of small nanoparticles.

Introduction

The physical properties of homogeneous bulk materials are usually expressed in terms of characteristic lengths, such as delocalization and screening lengths or mean free paths, which reflect intrinsic constraints on the charge motion. In artificial media obtained by interfacing materials of different constitutions, interruption and confinement of the charge motion by a boundary is expected to drastically modify these properties whenever the confinement extension is brought below such a characteristic length. The most conspicuous consequence of the confinement in the optical properties of reduced dimensionality systems is the appearance of morphological resonances related either to quantum or dielectric confinements 1, 2, 3, 4, 5, 6. Their spectral characteristics (frequency, shape, width) reflect the impact of the boundaries on the electron properties and their alteration as compared to the ones in the bulk material.

The possibility to alter the properties of composite materials, and even control them to meet technological requirements or perform certain functions, makes them a very important class of materials for technological applications 6, 7. Apart from its fundamental interest, investigation of the modified electron properties and of the interaction mechanisms at the origin of the new linear and nonlinear properties of these materials is thus also of technological interest.

In this context the study of metal nanoparticles is particularly interesting since electron-surface interactions are known to play a central role in their linear optical properties 1, 3, 4. The case of noble metal nanocrystals of spherical shape embedded in a transparent dielectric matrix is certainly the simplest one, the morphological resonance here being the characteristic surface plasmon resonance (SPR), a consequence of the dielectric confinement. This new resonance is associated to a collective response of the electrons and, in a classical model, corresponds to resonant electron density oscillation within a nanoparticle 1, 3, 4.

With the advance of the femtosecond lasers, electron interaction processes can now be directly addressed in the time domain, permitting selective analysis of their alteration by confinement. In metallic systems, the conduction electrons can be selectively driven out of equilibrium, without heating of the lattice, using femtosecond techniques 8, 9, 10. Investigation of the resulting ultrafast changes of the SPR spectral features can thus bring selective information on the electron interaction processes in confined systems and on their role in the optical nonlinear response of the composite material. Furthermore, as not too small metal nanoparticles can be conveniently described using a small solid approach, the electron dynamics in nanoparticles can be compared to the one in the bulk material. The latter has been extensively studied 8, 9, 10, 11, 12, 13 providing thus the possibility to clearly trace the impact of the dielectric and quantum confinements on the ultrafast optical response.

Studies of the ultrafast SPR dynamics have been recently reported in copper and gold nanoparticles embedded in a glass matrix 14, 15, 16, 17, showing that electron distribution perturbation induces a strong broadening of the surface plasmon resonance. Because of the partial frequency overlap between the surface plasmon resonance and the interband transitions, bulk-like interband induced mechanisms are expected to play a central role in the observed response hampering observation of new intraband surface induced processes and masking new nonlinear features. Furthermore, experiments were performed in the strong perturbation regime where very large transient electron temperature are induced making difficult modeling of the transient optical response.

The situation is much simpler in the case of silver nanoparticles embedded in a dielectric matrix where the surface plasmon resonance is well separated from other optical transitions (Fig. 1) and can be described using a simplified approach. Using a high resolution two-color pump-probe technique, we have investigated the SPR dynamics induced by perturbation of the conduction band electron distribution in these systems. Measurements were performed in the low perturbation regime as a function of the probe wavelength and of the nanoparticle size yielding evidence for both an induced red shift and broadening of the SPR. We will focus here on these systems and discuss the physical origins of their ultrafast optical nonlinear response and their connection with the relaxation dynamics of the conduction band electrons.

Section snippets

Surface plasmon resonance

The optical properties of metallic systems are related to both the conduction and bound electron responses. The conduction band electrons in bulk noble metals follow a quasi-free electron behavior and their contribution to the dielectric constant, ε, is remarkably well described by the Drude formula [18]

$ε^{f} (ω)=1− ω_{p}^{2} ω[ω+i/τ_{o} (ω)],$ where ω_p is the plasma frequency (ω_p²=n_ee²/ε₀m, n_e being the conduction band electron density and m the electron effective mass); τ_o is the electron optical relaxation

Femtosecond experimental setup

Experiments were performed using a two-color femtosecond pump-probe technique where the two pulses were created from the pulse train delivered by a home-made tunable 25 fs Ti:sapphire laser. The electron distribution is first selectively perturbed by a near infrared pump pulse of frequency ω_pp at the fundamental frequency of the oscillator. The excitation wavelength being far from any absorption resonance of the composite material, only free electron (intraband) absorption takes place. A

Surface plasmon resonance dynamics

The transient differential transmissions ΔT/T measured in the different samples show comparable behaviors. The results are displayed in Fig. 2 for the R=13 nm silver nanoparticle sample and different probe photon energies, ℏω_pr. The pump fluence is 100 μJ/cm², corresponding to ΔT_e^me∼160 K. Similar results were obtained over the investigated pump fluence range with, in particular, no variation of the signal decay and a linear dependence of the amplitude of ΔT/T on the incident pump power [28].

Nonlinear response: interband contribution

Assuming a Drude model for the intraband part of the nanoparticle dielectric constant, the SPR frequency depends only on the conduction band electron density, n_e, and on the real part of the interband contribution, $ε_{1}^{b} (Ω_{R})$ to the dielectric constant (Eq. (9)). In our measurements, no interband transition is involved in the excitation process and n_e is thus constant. Neglecting band structure modifications for our nanoparticles sizes [25], the SPR frequency shift can thus be ascribed to the

Nonlinear response: intraband contribution

In silver, the interband induced damping of the SPR is a very transient process and cannot account for the long delay broadening (t≥ 50 fs). This has thus to be ascribed to alteration of the intraband electron scattering processes, i.e., decrease of the electron optical relaxation time (Eq. (12)). Information on the electron distribution dependence of the electron interactions in a confined metallic system can thus be obtained [28].

On a time scale shorter than the electron-lattice coupling

Conclusion

The impact of ultrafast excitation and relaxation of the conduction band electrons on the surface plasmon resonance properties has been analyzed in silver nanoparticles embedded in a glass matrix. Experiments were performed by selectively perturbing the electron gas and probing the sample absorption changes in the vicinity of the SPR using a high resolution two-color femtosecond pump-probe technique in the low perturbation regime. The ultrafast optical nonlinear response associated to electron

Acknowledgements

The authors acknowledge S. Omi from HOYA corporation for providing the silver nanoparticle samples and M. Kammener for participating in the electron dynamics modeling.

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Electron dynamics and surface plasmon resonance nonlinearities in metal nanoparticles

Abstract

Introduction

Section snippets

Surface plasmon resonance

Femtosecond experimental setup

Surface plasmon resonance dynamics

Nonlinear response: interband contribution

Nonlinear response: intraband contribution

Conclusion

Acknowledgements

Chem. Phys.

Phys. Rep.

Physica B

Physica B

J. Phys. Soc. Jap.

Adv. in Phys.

Phys. Rev. Lett.

Phys. Rev. B

Phys. Rev. B

Phys. Rev. Lett.

Phys. Rev. B

Appl. Phys. Lett.

Phys. Rev. Lett.

Phys. Rev. Lett.

Phys. Rev. B

Phys. Rev. B