The paraxial approximation to a laser field is no longer valid if the beam waist of the laser is in the order of its wavelength. In such a case, a laser beam propagating even in a free space is not purely transverse but contains the significant longitudinal field. The investigation reveals that Thomson scattering characteristics by a relativistic electron (80MeV) of a tightly-focused, co-propagating laser field is sensitive to the electron¡¯s initial transverse position and phase with respect to the laser field: the electron radiates more strongly when it is initially located off-laser axis by about the beam waist than when on-laser axis. The enhancement of about 2000 in the radiation power is noticed for the focused (beam waist of 5 ¥ìm) laser intensity of 1 x 1018 W/cm2 compared to a paraxial Gaussian beam case.
Fig. 1. Schematic diagram of the interaction geometry between an electron and a co-propagating laser pulse. The black and white dot illustrate the electrons which propagate to z = 0 and when the laser pulse is absent, respectively.
Fig. 2. Peaks of the angular radiation powers with respect to initial positions (x0, y0) for the z=0nm and 200 nm electron, showing the initial positions (x0, y0) of the z=0nm and 200 nm electron favorable to strong radiation. (a) In the case of the paraxial approximation, that is, only the 0th-order field in is considered. (b) In the case of non-paraxial approximation where high-order fields up to are considered. (c) the same as in (b) but only a transverse acceleration is considered. Note that the intensity is about the same as in (b). (d) the same as in (c) but for the z=200 nm electron.
 International conference on ultrahigh intensity lasers development, science and emerging applications, Cassis, France, Sept 25-29, 2006.
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