2)    Macroscopic response 
a)    Model description:
We solve the wave equation in 2D cylindrical or 3D Cartesian geometry, depending on the problem under consideration, using either a finite difference or a pseudo-spectral method. Different approximations can be made, from the paraxial and slowly varying envelope approximations to the solution of the full wave equation. The source term is given by the solution of the Schrödinger equation in the strong field approximation (SFA).

b)    Applications:
-    HHG with twisted beams:
Twisted beams, e.g. Laguerre-Gauss (LG) beams, carry orbital angular momentum (OAM). They allow producing high-order harmonic beams with angular momentum l_q = q×l₁, of great interest for many fundamental studies, such as the exchange of OAM in light-matter interactions. Different generation configurations could be used: single beam, collinear two-color beams, or one-color crossing beams.
The pictures below depict the far-field diffraction patterns of H27, produced by two LG beams, crossing with a small angle at focus. The main beam, carrying an l_m = +1 OAM, diffracts on the transient grating produced by the perturbative beam, carrying an lp = ±2 OAM. The series of rings with increasing or decreasing radii correspond to diffraction orders with increasing or decreasing OAM. When l_p = -2 (top picture), the OAM decreases from the right to the left. The situation is reversed when l_p = +2 (bottom picture).
 

Far-field diffraction pattern of H27 produced by two crossing beams carrying l_m = +1 and l_p = -2 OAM.

Far-field diffraction pattern of H27 produced by two crossing beams carrying lm = +1 and lp = +2 OAM

Reference : R. Géneaux, A. Camper, T. Auguste, O. Gobert, J. Caillat, R. Taeïb, and T. Ruchon, Nat. Commun. 7:12583 doi: 10.1038/ncomms12583 (2016).