A proposal for a novel source of isolated attosecond XUV-soft x-ray pulses with a well controlled carrier-envelope phase difference (CEP) is presented in the framework of nonlinear Thomsonbackscattering. Based on the analytic solution of the Newton-Lorentz equations, the motion of a relativistic electron is calculated explicitly, for head-on collision with an intense fs laser pulse. By using the received formulas, the collective spectrum and the corresponding temporal shape of the radiation emitted by a mono-energetic electron bunch can be easily computed. For certain suitable and realistic parameters, single-cycle isolated pulses of ca. 20 as length are predicted in the XUV-soft x-ray spectral range, including the 2.33-4.37 nm water window. According to our analysis, the generated almost linearly polarized beam is extremely well collimated around the initial velocity of the electron bunch, with considerable intensity and with its CEP locked to that of the fs laser pulse.

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New theoretical and numerical results are presented regarding isolated attosecond XUV -soft X-ray pulses, that can be generated by Thomson-backscattering of a high-intensity single-cycle nearinfrared laser pulse on a suitable nanobunch of MeV electons. A simple approximate formula is derived for the cut-off frequency of the collective radiation spectrum, which is then employed to find the length of the nanobunch which emits an isolated pulse of 16 as length. Detailed analysis of the spectral, temporal and spatial features of this attosecond pulse is given. It is also shown that the 100 nJ pulse energy, corresponding to 2.1 × 10 18 W/cm 2 peak intensity of the laser pulse, can be increased to reach the µJ pulse energy both by increasing the intensity or by setting a suitable down-chirp of the laser pulse.