Density-dependent carrier-envelope phase shift in attosecond pulse generation from relativistically oscillating mirrors

The carrier-envelope phase (CEP) f(0) is one of the key parameters in the generation of isolated attosecond pulses. In particular, "cosine" pulses (f(0) = 0) are best suited for generation of single attosecond pulses in atomic media. Such "cosine" pulses have the peak of the most intense cycle aligned with the peak of the pulse envelope, and therefore have the highest contrast between the peak intensity and the neighboring cycles. In this paper, the dynamics of single attosecond pulse generation from a relativistically oscillating plasma mirror is investigated. We use an elementary analytical model as well as particle-in-cell simulations to study few-cycle attosecond pulses. We find that the phase of the field driving the surface oscillations depends on the plasma density and preplasma scale length. This leads us to a counterintuitive conclusion: for the case of normal incidence and a sharp plasma-vacuum boundary, the CEP required for the generation of a single attosecond pulse phase is closer to f(0) = p/2 (a "sine" pulse), with the exact value depending on the plasma parameters.