Manipulation of a photon's spatial wave function in optical fibers
Cody Leary
Photons, or light particles, have four independent internal degrees of freedom. Two of thes-- the light's color (wavelength) and its polarization-- are better known. The remaining two so-called "transverse spatial" degrees of freedom, which are less often studied, determine the spatial distribution properties, or wave function, of a photon emanating from a laser cavity.
In this project we will study and learn to manipulate the transverse spatial wave functions of photons propagating in optical fibers. An optical fiber consists of a cylindrical glass medium about 10 microns in diameter surrounded by a second glass material with a lower refractive index, which "traps" photons inside the fiber via the phenomena of total internal reflection, thereby forcing them to propagate down the fiber. In the fiber, a photon's wave function can exist in any of a number of discrete states-in direct analogy with the various possible electron orbitals in a hydrogen atom-- which may be manipulated while still in the fiber. A crucial tool for "sorting out" and measuring these fiber output states is known as the two-dimensional photon parity interferometer, a basic prototype of which was built and calibrated this year by a Wooster senior, and which we will construct an improved version of in order to expand its measurement capabilities.
There are many possible avenues of research which may be explored using this tool to probe the content of photon wave functions in optical fibers, as we modify the our fiber apparatus in order to achieve control over these degrees of freedom, including but not limited to: the "sorting" of the optical fiber output photons with respect to the amount of "orbital angular momentum" (the "twisting" of a photon's wave function around its direction of propagation) it possesses; and the analysis of output photons with respect to their two-dimensional parity properties.
The project will involve building and working with optical fibers and components, laser cavities, interferometers, and symbolic matrix techniques in Mathematica for theoretical modeling of the various phenomena involved.
