Anomalous Multiphoton Photoelectric Effect in Ultrashort Time Scales

In a multiphoton photoelectric process, an electron needs to absorb a given number of photons to escape the surface of a metal. It is shown for the first time that this number is not a constant depending only on the characteristics of the metal and light, but varies with the interaction duration in ultrashort time scales. The phenomenon occurs when electromagnetic energy is transferred, via ultrafast excitation of electron collective modes, to conduction electrons in a duration less than the electron energy damping time. It manifests itself through a dramatic increase of electron production.

Figure 1

Schematic representation of the resonant laser excitation of the interface or surface plasmon coupled system. For ultrashort laser pulse durations, energy is transferred through the ponderomotive forces $F_p$ corresponding to the interface and plasmon fields to the conduction electron population of the overlayer.

Figure 2

Photoelectron emission versus incidence angle $\theta$ for $p$-polarized (●) and $s$-polarized (▲) laser pulses (at 50 fs and for $I=1\mathrm{GW}/{\mathrm{cm}}^2$).

Figure 3

Photoelectron current versus laser intensity (pulse duration 50 fs) for several typical samples: ultrathick (200 nm) gold (●), massive aluminum (▲), and gold overlayers of thickness: 18 nm (◆), 28 nm (▼), and 43 nm (red circles). For the optimum overlayer thickness (43 nm), the number of absorbed photons in the photoemission process turns out to 3 instead of 4 (as required by the generalized photoelectric equation). The same slope changes ($4\to 3$) occur for samples of thickness 18 and 28 nm at higher laser intensity (i.e., at higher plasmon amplitude).

Figure 4

Photoelectron current versus laser pulse intensity for an optimum sample (gold overlayer thickness near 40 nm), for pulse durations: 50 fs (■), 400 fs (●), and 1.2 ps (▼). In the femtosecond regime (50–400 fs), the photoelectric emission shows the absorption of an anomalous number of photons (3 instead of 4). In the picosecond range, the slope turns back ($3\to 4$) to the normal number of photons required by the generalized photoelectric equation.

Figure 5

Photoelectron energy spectra of the ultrathick sample (i.e., without interface plasmon excitation) as a function of the laser pulse duration (for $I=1\mathrm{GW}/{\mathrm{cm}}^2$): 400 fs (▲), 800 fs (◆), 1.2 ps (●), 1.6 ps (▼). In the femtosecond regime, the spectra shift toward higher energies [15, 24], due to a growing of the surface plasmon amplitude. In the picosecond range, the spectra shift toward lower energies due to a decreasing of the plasmon amplitude in the long-pulse regime.

Figure 6

Photoelectron current as a function of the gold overlayer thickness (at 50 fs and for $I=0.3\mathrm{GW}/{\mathrm{cm}}^2$). For a gold overlayer thickness of nearly 43 nm the photoelectron emission exhibits a dramatic enhancement compared to the ultrathick gold or massive aluminum samples.