Linear and nonlinear optical tools to measure the dephasing time of localized surface plasmon-polaritons.

Localized surface plasmon-polaritons in small metal particles play an important role in a number of laser-induced surface processes. The intensity and the width of the corresponding resonances are determined by the dephasing time of the plasmon. To get information on the dephasing times, the linear spectroscopy methods are of limited use because of their inability to discriminate between the homogeneous and inhomogeneous line broadening. Consequently, the linear extinction spectra provide only the lower limit of the surface plasmon dephasing time. Nonlinear techniques, such as autocorrelation measurements of second and third harmonic generation employing bandwidth-limited femtosecond pulses and performed with an interferometric accuracy, were intended to give a direct access to the dephasing time of the plasmon excitation. In this contribution, we present the results of the theoretical modeling of the second and third harmonic autocorrelation functions and show that these particular nonlinear techniques suffer from the inhomogeneous broadening to almost the same extent as the linear extinction measurements. Moreover, the general relations between the linear absorption spectrum and second and third harmonic autocorrelation functions produced by an arbitrary inhomogeneous distribution of resonance frequencies are found, provided the resonance itself may be modeled as a slightly anharmonic classical oscillator. Finally, we propose one particular combination of linear and nonlinear results that may help to discriminate between homogeneous and inhomogeneous contributions to the line shape, and analyze the assumptions that lead to the unambiguous determination of the surface plasmon dephasing time.