We demonstrate that hybrid laser wakefield and direct acceleration (LWDA) can be significantly improved by using two laser pulses with different polarizations or frequencies. The improvement entails higher energy and charge of the accelerated electrons, as well as weaker sensitivity to the time delay between the leading (pump) pulse responsible for generating the wakefield, and the trailing laser pulse responsible for direct laser acceleration (DLA). When the two laser pulses have the same frequency, it is shown that it is advantageous to have their polarization states orthogonal to each other. A specific scenario of a frequency-doubled ($lambda_{rm DLA}=lambda_{rm pump}/2$) DLA laser pulse is also considered, and found to be an improvement over the single-frequency ($lambda_{rm DLA} = lambda_{rm pump}$) scenario.
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