Unitary Transformations of Optical Beam Arrays

Abstract

The ability to control the spatial mode of light is extended across photonics from fundamental tests of quantum mechanics to telecommunications. Recently, a device known as 'Multi-plane light converter' (MPLC) has been introduced as a platform for the implementation of general spatial transformations of light. The main result of this thesis is the demonstration of an MPLC as a dynamically reconfigurable device. We do this using a system of parallel optical beams (the free space counterpart of a set of wave guides in integrated optics). We call a 'two-beam array' to the system composed of two of such parallel beams. We test the full space of unitary transformations for a two-beam array obtaining an average transformation fidelity of 0.85 ± 0.03. This high fidelity suggests MPLCs are a useful tool for quantum and classical information processing. We also report two different results where the underlying degree of freedom is the spatial mode of light. The laser beam quality, also known as M2 parameter, is the figure of merit that compares the beam size in the near and far fields to the ones of a diffraction limited beam. We develop a method to determine M2 using the complex electric field at a single plane. This method avoids the standard procedure to get M2 which uses multiple intensity measurements, fitting and an inherent pre-characterization. Our method is particularly useful in optical design and simulations where the complex electric field is known. In the context of quantum measurement and state characterization, we theoretically propose and experimentally demonstrate a method to perform a 'joint weak-measurement' optimizing the measurement resources. Typical joint weak-measurements use one read-out system per measured observable, while our method allows to measure correlations between pairs of observables using a single internal degree of freedom of a particle as read-out. We experimentally implement our scheme to directly measure the density matrix of photon polarization states using the photon's transverse spatial mode as read-out system.