#

Parity-based Measurement and Control of the Spatial Wave Function of Photons

## Mohammad Saif Ahmad

###
2012

The experiment involved parity based measurement and control of the spatial wave functions of photons. To achieve this the theory was developed for a 1-dimensional parity based interferometer. This interferometer was capable of taking a laser beam input that consisted of a speci c solution set of Hermite-Gaussian modes and span of this solution set as well. The resulting theory was then modeled for several types of input beams and simulated for several special cases. The mathematical relationships governing the interferometer were exploited and simpli ed to establish a general matrix with complex entries that would model the output of any beam input to the interferometer. It was then proven that this governing matrix was unitary.

The modeled interferometer was then built and the results of multiple input beams were analyzed through the theory and simulations that were built based o of the general interferometer matrix. By analyzing certain properties of beams that were input to the interferometer one could in e ect determine certain properties of the photons that could not otherwise be measure without losing the usefulness of the photon. By tweaking parameters within the interferometer one could also change the output of the interferometer without changing the input beam. This is changing the spatial wave function of the photon. In this respect the experiment achieved its purpose although much can still be done to optimize the interferometer set up and e ectively learn more about the input beams.