Phase-matched harmonic generation in strongly magnetized plasma

Harmonic generation in underdense spatially homogeneous plasma is generally expected to be inefficient: in an unmagnetized uniform plasma the fundamental and its harmonics cannot be phase matched, resulting in third-harmonic generation efficiencies of no more than ${10}^{\ensuremath{-}5}$. Here, we describe how a strong uniform magnetic field allows phase-matched harmonic generation in constant-density plasma. We derive phase-matching relations for type-I and type-II second-, third-, and fourth-harmonic generation, and confirm these relations with particle-in-cell simulations. These simulations show that for weakly relativistic femtosecond pulses the efficiencies of second-, third-, and fourth-harmonic generation can reach at least 70%, 14%, and 2%, respectively. Additionally, if driven by a two-color beam, third-harmonic generation is found to be over 70% efficient and fourth-harmonic generation is found to be over 30% efficient.