Generating a three dimensional dark focus from a single conically refracted light beam

We report here the generation of a three dimensional dark focus from a single focused monochromatic Gaussian beam that undergoes conical refraction when it propagates along one of the optic axes of a biaxial crystal. We study the resulting ring intensity pattern behind the crystal as a function of the ratio between the ring radius and the beam waist and derive the particular parameter values for which a three dimensional dark focus with null intensity at the ring center is formed. We have performed experiments with a $\mathrm{K}\mathrm{G}\mathrm{d}(\mathrm{W}{\mathrm{O}}_4{)}_2$ biaxial crystal reporting the generation of a bottle beam in full agreement with our theoretical investigations.