Bulk photogalvanic effects beyond second order

Examining the bulk photogalvanic effect (BPE) at nonperturbative laser fields, it is shown that illuminating a thin noncentrosymmetric crystal, quasicrystal, or nanotube the point group of which is $D_{n>\mathrm{}2\mathrm{}},$ $C_{(3,5,\dots )h},$ or $D_{(3,5,\dots )h}$ with a monochromatic linearly polarized field, at practically any orientation, induces a nonvanishing directed current component $j_z$ along its polar axis. This is in contrast to the vanishing $j_z$ predicted by the commonly employed photogalvanic tensor. Similarly, we discuss the appearance of an angular-dependent $j_z,$ already for $C_{\mathrm{}(n>\mathrm{}2\mathrm{})v}$ and $C_{n>\mathrm{}2\mathrm{}},$ and circular dichroism in the BPE that are not resolved in second order. We suggest the possible observation of these currents in, e.g., thin $\alpha$-quartz and ${\mathrm{LiNbO}}_3:\mathrm{Fe}$ crystals and single-walled chiral carbon nanotubes.