Carrier-envelope phase controlled isolated attosecond pulses in the nm wavelength range, based on coherent nonlinear Thomson-backscattering

Abstract

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.

Isolated attosecond pulses of μJ energy via coherent Thomson-backscattering, driven by a chirped laser pulse

“…In equation (3) we have made use of the B = n L × E/c, connecting the magnetic induction and the electric field strength of a plane wave. As it is well known, the equations of motion (2)-(3) have a general analytic solution [29][30][31] and in [12] we determined an explicit particular solution of equations (2)-(3) for a laser pulse corresponding to equation (1) with k = 0. Using this solution, we are able to evaluate the spectrum of radiation emitted by an electron, which is given in the far-field by the following formula [32]:…”

“…Since the frequency-dependence of the coherence factor equation (5) influences the spectrum of the collective radiation in an essential way [12], we plot the magnitude of C N (ω) in Figure 1 for electron nanobunches of different lengths. For each length, we plot |C N (ω)| both for a realistic electron nanobunch with stochastic electron positions characterized by a uniform distribution in the transverse direction and a Gaussian distribution in the longitudinal direction (solid lines), and for a rather artificial electron nanobunch with an equidistant spacing of electron positions (dashed lines).…”

“…Next we show the polar angle dependence of the spectral amplitude of the collective radiation in Figure 3, computed on the basis of equation (6) for the bunch parameters mentioned above. The collective nature of the radiation causes a narrower radiation cone compared to Figure 2, because of the sensitive dependence of the coherence factor on the polar angle, which was investigated in [12].…”

“…Thomson-backscattering of an intense laser pulse on a relativistic electron bunch is a well-known source of (hard) X-and gamma-ray radiation [4][5][6][7][8][9][10]. In our earlier works [11,12], we already showed that Thomson-backscattering of a linearly polarized near-infrared few-cycle laser pulse on a suitable electron bunch may provide isolated attosecond pulses also in the XUV -soft X-ray spectral range, including the 2.33-4.37 nm water window. According to our calculations, these attosecond pulses are almost linearly polarized and extremely well collimated, and their carrier-envelope phase difference (CEP) is locked to that of the laser pulse.…”

Signatures of the Carrier Envelope Phase in Nonlinear Thomson Scattering

“…In this regime the process has been studied with regard to the laser strength parameter a 0 , the shape of the laser pulse both longitudinally and transversely [8][9][10][11][12], the bandwidth of the emitted radiation [13,14] and methods to reduce it [15]. In [16], it was shown that the phase of the field of the emitted radiation is linked to that of the laser pulse. Moreover, ref.…”