  Ultrashort laser pulses are widely used for transient field-free molecular
orientation -- a phenomenon important in chemical reaction dynamics, ultrafast
molecular imaging, high harmonics generation, and attosecond science. However,
significant molecular orientation usually requires rotationally cold molecules,
like in rarified molecular beams, because chaotic thermal motion is detrimental
to the orientation process. Here we propose to use the mechanism of the echo
phenomenon previously observed in hadron accelerators, free-electron lasers,
and laser-excited molecules to overcome the destructive thermal effects and
achieve efficient field-free molecular orientation at high temperatures. In our
scheme, a linearly polarized short laser pulse transforms a broad thermal
distribution in the molecular rotational phase space into many separated narrow
filaments due to the nonlinear phase mixing during the post-pulse free
evolution. Molecular subgroups belonging to individual filaments have
much-reduced dispersion of angular velocities. They are rotationally cold, and
a subsequent moderate terahertz (THz) pulse can easily orient them. The overall
enhanced orientation of the molecular gas is achieved with some delay, in the
course of the echo process combining the contributions of different filaments.
Our results demonstrate that the echo-enhanced orientation is an order of
magnitude higher than that of the THz pulse alone. The mechanism is robust --
it applies to different types of molecules, and the degree of orientation is
relatively insensitive to the temperature. The laser and THz pulses used in the
scheme are readily available, allowing quick experimental demonstration and
testing in various applications. Breaking the phase space to individual
filaments to overcome hindering thermal conditions may find a wide range of
applications beyond molecular orientation.
