Wakefield manipulation via phase-matching of co-propagating laser modes in an underdense plasma channel

We propose the use of higher-order phase-matched laser modes to control the properties of the transverse wake generated by a laser pulse propagating in a parabolic plasma channel in the context of laser-plasma accelerators. For generating a transversely asymmetric wake in the quasi-linear regime we consider the superposition of Hermite modes H₂₀ + H₀₂ and Laguerre modes L₁₀ + L₀₂. It is shown that we can arbitrarily tune the horizontal and vertical transverse wakefields independently of the longitudinal accelerating field. This allows for the realization of flat beams in laser-plasma accelerators with matched propagation. We also consider the possibility of varying the frequency of two modes with different geometric mode numbers such that they propagate at the same group velocity. Specifically, we consider the case of L₀₀+ L₁₀, whereby we can fix the longitudinal accelerating wakefield but vary the strength of the transverse fields. The ability to use multiple modes of different mode numbers and colors that propagate at the same group velocity will allow for greater control of accelerated beam properties.