Poincaré

by tagermer

Poincaré Cube
Poincaré Cube

This set is the first in a series taken at the Cimetière de Montparnasse in Paris. Henri Poincaré (1854-1912) was a famous mathematician, who contributed many things to a wide number of fields of mathematics. One of them is very important to the field of optical polarimetry. Polarization is a property that light has, because, as an electromagnetic field, the electric and magnetic fields must each be perpendicular to each other and to the direction of propagation. The electric field can be in a single plane containing the propagation direction, in which case it is called linearly polarized, or it can be rotating one way or another, in which case it is called circularly polarized.

In my day job, I am a physicist, and I use the polarization behavior of how materials scatter light to identify and differentiate different sources of scatter. Polarization states are often represented by a point on a unit sphere, referred to as the Poincaré  sphere. Points along the equator correspond to linear polarization states, with the longitude corresponding to half the angle of the electric field, while those at the north and south poles correspond to right- and left-circular polarizations, respectively. Points inside the sphere correspond to various degrees of depolarization, with the very center of the sphere being completely unpolarized, random light. So, the Poincaré sphere represents the topology of the statistics of the electromagnetic fields.

In any case, when I arrived at the cemetery, I made a bee line for Poincaré’s family grave, which is easy to find, since it is very close to the Avenue Thierry entrance and right up against the outside wall.  All of the stereographic projections are thus titled “Poincaré Sphere (Stereo n),” while the cube is titled “Poincaré Cube.”

See the entire Poincaré collection here or enjoy them below. Enjoy!

Poincaré Sphere (Stereo 6)
Poincaré Sphere (Stereo 6)

Poincaré Sphere (Stereo 1)
Poincaré Sphere (Stereo 1)

Poincaré Sphere (Stereo 2)
Poincaré Sphere (Stereo 2)

Poincaré Sphere (Stereo 4)
Poincaré Sphere (Stereo 4)

Poincaré Sphere (Stereo 3)
Poincaré Sphere (Stereo 3)

Poincaré Sphere (Stereo 5)
Poincaré Sphere (Stereo 5)

Advertisements