English: Fluorescence and birefringence of 445 nm laser in calcite crystal.

The blue laser beam is only visible when the blue light is scattered, for example, by dust particles. Due to the 1.3s exposure time, no individual dust particles can be seen. Dust particles are present in the air, but not in the crystal. In the crystal, some part of the blue light is absorbed and re-emitted as orange light, which is called fluorescence. Most of the blue light just continues to the other end of the crystal.

On the lower left you can see the laser beam going in. Part of the light is reflected on the front surface of the crystal; this is the beam you see on the upper left. In the crystal, the two polarisations are refracted by different angles, forming two beams in the crystal. At the end surface, the two beams (both of which are polarised along the axes of the crystal) are refracted back to their original direction, forming the two parallel beams on the right. Inside the crystal, the two beams cause fluorescence and non-polarised orange light is emitted from each point along both beams in every direction. As this light leaves the crystal, it's separated into two orthogonal polarisations, which are refracted by different angles, so that the observer sees four orange beams. The additional spots and beams you can see result from internal reflections.