Controlling the spectral shape of nonlinear Thomson scattering with proper laser chirping

Effects of nonlinearity in Thomson scattering of a high intensity laser pulse from electrons are analyzed. Analytic expressions for laser pulse shaping in frequency (chirping) are obtained which control spectrum broadening for high laser pulse intensities. These analytic solutions allow prediction of the spectral form and required laser parameters to avoid broadening. Results of analytical and numerical calculations agree well. The control over the scattered radiation bandwidth allows narrow bandwidth sources to be produced using high scattering intensities, which in turn greatly improves scattering yield for future x- and gamma-ray sources.

Figure 1

Left: An example of the normalized on-axis spectra of reflected radiation calculated for low $a_0=0.05$ (blue line) and high $a_0=0.4$ (red color) scattering lasers, demonstrating the appearance of bandlike structure in the spectrum. Right: Qualitative illustration of the broadening and band formation mechanism in the nonlinear response of an electron to a strong electromagnetic wave. A laser pulse impinges the electron from the left side (from $z\to -\infty$). As functions of time, the blue line and shaded area represent the laser pulse envelope, the green line shows the frequency of the reflected wave in accordance with Eq. (2), and the red dashed line shows the longitudinal coordinate of the electron.

Figure 2

Left: On-axis radiation spectra plotted as a function of laser pulse amplitude $a_0$ (vertical axis). The spectra are in arbitrary units, from numerical integration of Eq. (14). Laser pulse duration is ${\tau }_L=600$. The dashed black line represents the redshift of the peak of the spectrum according to Eq. (1). Right: On-axis radiation spectrum for $a_0=1$ from the analytical expression of Eq. (16) (black circles) for such frequencies as make the order of the Bessel function given by Eq. (17) an integer, overplotted with the full spectrum from numerical integration (blue line).

Figure 3

Left: Normalized on-axis intensity spectra for different values of $a_0$ for the case of a laser pulse with duration ${\tau }_L=600$. Laser pulse is properly chirped according to Eq. (18). Results obtained with the help of numerical integration are shown with solid lines. Markers of corresponding color present the analytical solution using Eqs. (16), (23) and (24). Right: Numerically obtained on-axis radiation spectra for a properly chirped laser pulse for different values of $a_0$ (vertical axis) in the logarithmic scale.

Figure 4

Peak value of the on-axis photon spectrum as a function of $a_0$ for the cases of unchirped (green solid line) and properly chirped (blue solid and black dashed lines) pulses. The black dashed line represents the fit to the numerical data given by Eq. (26).

Figure 5

Left: Normalized vector potential as a function of time in periods for the case of the unchirped laser pulse (blue color) and chirped laser pulse with $a_0=0.5$ for laser pulse with duration ${\tau }_L=60$. Right: Laser pulse spectra (normalized to the peak value of the unchirped pulse spectrum) for the case of unchirped laser pulse (blue color) and chirped laser pulses with $a_0=0.2$ (red color) and $a_0=0.5$ (green color) for laser pulse with duration ${\tau }_L=600$.