Interplay of vortex and non-vortex beam components in a variable two-crystal cascade conical refraction

In a two-crystal cascade conical refraction, a collimated light beam propagates along the optical axes of two biaxial crystals arranged in a series. In a variable cascade modification, the beam formed by the first crystal is imaged by a lens through the second crystal. Such an arrangement enables additional control over the cascade parameters and the output light beam properties. It is shown that the imaging stage of a variable cascade can drastically change the internal structure of the outgoing beam consisting of superimposed vortex and non-vortex components. In a degenerate case of two identical crystals, the conical refraction caused by the first crystal can be completely reversed by the second crystal, so that the output vortex component vanishes, and the input non-vortex light beam is restored. In sharp contrast, in a variable cascade, the vortex beam component does not vanish and, depending on the focal length of the imaging lens, can hold a significant fraction of the total beam power even in the apparently degenerate case. To describe the variable cascade, the existing theory of cascade conical refraction is complemented with a wave-optical description of the imaging stage, taking into account the effects of magnification and the focal length of the lens. The results of numerical simulations are in a good agreement with experimental observations. A concept of generalized cascade conical refraction is introduced.