A Scaling Law of Photoelectron Angular Distributions in One-Cycle Laser Pulses

The photoelectron angular distributions (PADs) from above-threshold ionization of atoms irradiated by one-cycle laser pulses satisfy a scaling law. The scaling law denotes that the main features of the PADs are determined by four dimensionless parameters: (1) the ponderomotive number u_p =U_p /ħω, the ponderomotive energy U_p in units of laser photon energy; (2) the binding number ε_b =E_b /ħω, the atomic binding energy E_b in units of laser photon energy; (3) the number of absorbed photons q; (4) the carrier-envelope phase Ф₀, the phase of the carrier wave with respect to the envelope. We verify the scaling law by theoretical analysis and numerical calculation, compared to that in long-pulse case. A possible experimental test to verify the scaling law is suggested.