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We numerically study the propagation of a Laguerre-Gaussian beam through polar molecular media via the exact solution of full-wave Maxwell-Bloch equations where the rotating-wave and slowly-varying-envelope approximations are not included. It is found that beyond the coexistence of odd-order and even-order vortex harmonics due to inversion asymmetry of the system, the light propagation effect results in the intensity enhancement of a high-order vortex harmonics. Moreover, the orbital momentum successfully transfers from the fundamental laser driver to the vortex harmonics which topological charger number is directly proportional to its order.

We theoretically investigate high-order harmonic generation (HHG) from aligned N(2) molecules with a driving field composed of two-color circularly polarized laser pulses. It is shown that the combination of N(2) molecules and the waveform-controlled laser field allows us to select either long or short quantum path, depending on molecular alignment angles, while in atom Ar, two paths show comparable contribution to HHG. The selection of single quantum path in aligned N(2) molecules leads to an ultrabroad and smooth XUV supercontinuum, giving rise to isolated attosecond pulses generation. Moreover, we can control the intensity ratio of two attosecond pulses by adjusting the molecular alignment angles, providing an opportunity for attosecond pump-probe technique.

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