Novel Effects in Optical Coherence: Fundamentals and Applications

We describe our recent contributions to the field of optical coherence. We discuss a series of experiments that exploit a variety of novel mechanisms of optical interference to unveil new behaviors of light. More specifically, we discuss how we explored the conditions under which light is forced to exhibit new properties. These effects are not only fundamentally important but they open the door for a wide variety of applications. In Chapter 1 we review the fundamental concepts that are utilized along the thesis. In Chapter 2 we discuss how extreme conditions in a quantum measurement process allowed us to exploit a form of spin-orbit interaction in an optical beam that produces weak values (WVs) in the azimuthal variables. These interferometric WVs lead to a shift in the angular position and orbital angular momentum (OAM) of an optical beam. The OAM spectrum is shifted as a consequence of the breakup in the polarization symmetry, realized by a differential geometric phase. We show how these effects can be used to amplify angular rotations. In the same chapter, we discuss another technique that uses interferometric WVs for direct measurement of the quantum wavefunction. We improve the state-of-the-art of this technique by incorporating compressive sensing (CS) through the implementation of random projection operators. Our technique allowed us to demonstrate the measurement of a 19 200 dimensional state. In Chapter 3, we introduce the Wigner distribution in the azimuthal space. The Wigner distribution in the angular domain provides valuable insight into understanding the wave behavior of the light field in the conjugate bases of OAM and azimuthal angle. In addition, we discuss how our technique allows one to determine the azimuthal first-order degree of coherence of a partially coherent beam. In Chapter 4 we describe how the random fluctuations of light give rise to the formation of correlations in the OAM components and angular positions of pseudothermal light. The presence of these correlations is manifested through a new family of exotic interference structures in the OAM distribution of random light. We describe these effects in the context of the azimuthal Hanbury Brown and Twiss effect. In Chapter 5, we exploit quantum correlations to perform quantum imaging. We present a CS protocol that tracks a moving object by removing static components from a scene. The implementation is carried out on a quantum imaging scheme to minimize both the number of photons and the number of measurements required to form a quantum image of the tracked object. This procedure tracks an object at low light level, permitting us to more effectively use the information content in each photon. Another effect that has been recently predicted is the finite probability of a photon to follow looped paths in a three-slit interferometer. This produces an apparent deviation from the most conventional form of the superposition principle. However, the probability of observing these exotic paths is very small and…