Abstract
The coherence of an optical beam having multiple degrees of freedom (DoFs) is described by a coherency matrix G spanning these DoFs. This optical coherency matrix has not been measured in its entirety to date—even in the simplest case of two binary DoFs where G is a 4 × 4 matrix. We establish a methodical yet versatile approach—optical coherency matrix tomography—for reconstructing G that exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science. Here G is reconstructed from a minimal set of linearly independent measurements, each a cascade of projective measurements for each DoF. We report the first experimental measurements of the 4 × 4 coherency matrix G associated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young’s double slit to spatial parity and orbital angular momentum modes.
Highlights
The coherence of an optical beam having multiple degrees of freedom (DoFs) is described by a coherency matrix G spanning these DoFs
We establish a methodical yet versatile approach—optical coherency matrix tomography—for reconstructing G that exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science
We report the first experimental measurements of the 4 × 4 coherency matrix G associated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young’s double slit to spatial parity and orbital angular momentum modes
Summary
Vector beams correlate polarization with spatial position[13], scattering from complex photonic structures and devices may couple the relevant field DoFs14,15, and reliance on multimode optical fibers for spatial multiplexing is reviving interest in joint polarization-spatial-mode characterization[16]. In exploring these settings, it has recently proven fruitful to adopt the Hilbert-space formulation used in quantum mechanics to the needs of classical coherence theory10,11—an approach that has early prescient antecedents[17,18]. Even in the simplest case of two binary DoFs6 (e.g., polarization, a bimodal waveguide[36,37], two coupled single-mode waveguides[38,39], spatial-parity modes[40,41,42,43,44], etc.), the associated 4 × 4 coherency matrix G, which is a complete representation of second-order coherence[10,11], has not been measured in its entirety to date
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