2. Result
The paraxial approximation to a laser field is no longer valid if the beam waist of the laser is in the order of its wavelength.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 tightlyfocused, copropagating 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 offlaser axis by about the beam waist than when onlaser 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 copropagating 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 0thorder field in is considered. (b) In the case of nonparaxial approximation where highorder 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. 3. References
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