Photoionization of an ambient gas by a weakly relativistic, femtosecond laser pulse leaves behind the pulse a flat-top plasma column. The uniform-density core of the column is surrounded by a micron-thin shell, within which the density of plasma species falls down to zero. As the laser pulse ponderomotive force drives the wave of charge separation (the laser wake), electron fluid velocity oscillates along this boundary layer. Coupling velocity oscillations to the transverse density gradient forms an azimuthally polarized rotational current confined within the boundary layer. At each radial offset, this current oscillates with a local (THz-scale) Langmuir frequency, transforming the cylindrical electrostatic plasma wave into a radially evanescent Fourier component of an electromagnetic signal. Summing up these Fourier components yields the time-domain THz signal which is (a) non-local (i.e. not phase-locked to the Langmuir oscillation at any given location), (b) contains the entire frequency band from zero to the Langmuir frequency of the density plateau, and (c) is detectable at a distance orders of magnitude larger than the plasma column radius. A few millimeters away from the column, rapid evanescence of the higher-frequency components transforms the signal into a radially polarized, single-cycle picosecond pulse with a kV m−1-scale electric field. Detecting this pulse with existing (e.g. electro-optical) techniques may bring information on the efficiency of laser coupling to the plasma, the amplitude of wake fields, and the structure of the column boundary.