New Phase-Matching Selection Rule To Generate Angularly Isolated Harmonics

High harmonic generation (HHG) is an ideal probing source. In general, all harmonics are coupled with the corresponding input laser when generated, and for applications, they are separated using additional spectrometers. Herein, we report the angular isolation of relativistic harmonics at a predicted emission angle upon generation and, most importantly, a new phase-matching chain selection rule is derived to generate harmonics. Based on the laser plasma mechanism involving two non-collinear relativistic driving lasers, the nth harmonic carrying the information of both input lasers originates from its adjacent (n - 1)th harmonic coupled with one of the input lasers. Meanwhile, the intensity and emission angle of the generated isolated harmonic are both greatly increased compared with those in the gas scheme. These results are satisfactorily verified by theoretical analysis and three-dimensional particle-in-cell simulations, which have physical significance and are essential for practical applications.