Low emittance electron beam generation from a laser wakefield accelerator using two laser pulses with different wavelengths

Ionization injection triggered by short wavelength laser pulses inside a nonlinear wakefield driven by a longer wavelength laser is examined via multi-dimensional particle-in-cell simulations. We find that very bright electron beams can be generated through this two-color scheme in either collinear propagating or transverse colliding geometry. For a fixed laser intensity $I$, lasers with longer/shorter wavelength $\lambda$ have larger/smaller ponderomotive potential ($\propto I \lambda^2$). The two color scheme utilizes this property to separate the injection process from the wakefield excitation process. Very strong wakes can be generated at relatively low laser intensities by using a longer wavelength laser driver (e.g. a $10 \micro\meter$ CO$_2$ laser) due to its very large ponderomotive potential. On the other hand, short wavelength laser can produce electrons with very small residual momenta ($p_\perp\sim a_0\sim \sqrt{I}\lambda$) inside the wake, leading to electron beams with very small normalized emittances (tens of $\nano\meter$). Using particle-in-cell simulations we show that a $\sim10 \femto\second$ electron beam with $\sim4 \pico\coulomb$ of charge and a normalized emittance of $\sim 50 \nano\meter$ can be generated by combining a 10 $\micro\meter $ driving laser with a 400 $\nano\meter$ injection laser, which is an improvement of more than one order of magnitude compared to the typical results obtained when a single wavelength laser used for both the wake formation and ionization injection.