Second harmonic generation using laser beams transformed by internal conical refraction

The internal conical refraction (CR) of light in biaxial crystals has attracted a renewed interest in recent years. This effect leads to a very specific transformation of light beams passed along one of the optical axes of a biaxial crystal. When laser beam is focused through the crystal, a bright ring arises in the focal plane. Under certain conditions, this annular focus has a fine structure of two rings separated by a dark ring (the so-called Poggendorff rings). This CR pattern has a complex evolution upon propagation, where two axial intensity spikes are formed at some distances from the focal plane together with rich intermediate substructures. One of potentially interesting application fields, which has remained much less explored, is the use of the CR effect in nonlinear optics. In the present report, the generation of second harmonic (SH) with laser beams transformed by the CR effect is considered.