Single cycle laser pulse propagating inside a plasma causes controllable asymmetric plasma electron expulsion from laser according to laser carrier envelope phase (CEP) and forms an oscillating plasma bubble. Bubbles transverse wakefield is modified, exhibiting periodic modulation. Injection scheme for a laser wakefield accelerator combining a single cycle low frequency laser pulse and a many cycle high frequency laser pulse is proposed. The co-propagating laser pulses form a transversely oscillating wakefield which efficiently traps and accelerates electrons from background plasma. By tuning the initial CEP of the single cycle laser pulse, injection dynamics can be modified independently of the many cycle pulse, enabling control of electron bunches spatial profile.
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