Reflection of a few-cycle laser pulse on a metal nano-layer: generation of phase dependent wake-fields

The reflection and transmission of a few-cycle femtosecond Ti:Sa laser pulse impinging on a metal nano-layer have been analysed. The thickness of the layer was assumed to be of the order of 2-10 nm, and the metallic free electrons were represented by a surface current density at the plane boundary of a dielectric substrate. The target studied this way can be imagined for instance as a semi-transparent mirror produced by evaporating a thin aluminum layer on the surface of a glas plate. The exact analytical solution has been given for the system of the coupled Maxwell-Lorentz equations describing the dynamics of the surface current and the scattered radiation field. It has been shown that in general a non-oscillatory frozen-in wake-field appears following the main pulse with an exponential decay and with a definite sign of the electric field. The characteristic time of these wake-fields is inversely proportional with the square of the plasma frequency and with the thickness of the metal nano-layer, and can larger then the original pulse duration. The magnitude of these wakefields is proportional with the incoming field strength, and the definite sign of them is governed by the cosine of the carrier-envelope phase difference of the incoming ultrashort laser pulse. As a consequence, when we let such a wake-field excite the electrons of a secondary target (say an electron beam, a metal plate or a gas jet), we obtain 100 percent modulation depth in the electron signal in a given direction. This scheeme can perhaps serve as a basis for the construction of a robust linear carrier-envelope phase difference meter.