Optical coherence is a fundamental property of light, playing a key role in understanding interference, propagation, and light-matter interactions for both classical and quantum light. Measuring the coherence properties of an optical field is crucial for a wide range of applications. However, despite many proposed measurement schemes, significant challenges still remain. In this work, we present a protocol to measure the full-dimensional coherence properties of a partially coherent beam. The method is based on tomographing the complex coherent modes of the partially coherent field within its coherence time. Once the complex coherent modes are reconstructed, all coherence properties including field correlation and its higher-order correlations (e.g., intensity correlation) can be recovered for beams that are either spatially uniformly or non-uniformly correlated. We perform a proof-of-principle experiment to measure the complex field correlation and intensity correlation of a structured partially coherent beam synthesized by random modes. Additionally, we discuss the application of full-dimensional complex coherence function tomography in coherence-based multi-cipher information security. The robustness of our system in complex environments is also evaluated.
Optical coherence is a fundamental property of light, playing a key role in understanding interference, propagation, and light-matter interactions for both classical and quantum light. Measuring the coherence properties of an optical field is crucial for a wide range of applications. However, despite many proposed measurement schemes, significant challenges still remain. In this work, we present a protocol to measure the full-dimensional coherence properties of a partially coherent beam. The method is based on tomographing the complex coherent modes of the partially coherent field within its coherence time. Once the complex coherent modes are reconstructed, all coherence properties including field correlation and its higher-order correlations (e.g., intensity correlation) can be recovered for beams that are either spatially uniformly or non-uniformly correlated. We perform a proof-of-principle experiment to measure the complex field correlation and intensity correlation of a structured partially coherent beam synthesized by random modes. Additionally, we discuss the application of full-dimensional complex coherence function tomography in coherence-based multi-cipher information security. The robustness of our system in complex environments is also evaluated.
Abstract Optical encryption strategies utilizing fully coherent light have been widely explored but often face challenges such as speckle noise and beam instabilities. In this work, we introduce a novel protocol for multi-channel optical information encoding and encryption using vectorial spatial coherence engineering of a partially coherent light beam. By characterizing the beam’s spatial coherence structure with a 2×2 2 × 2 coherence matrix, we demonstrate independent control over the three components of the coherence Stokes vector. This allows for three-channel optical information encoding and encryption, with applications in color image representation. Unlike existing methods based on fully coherent light modulations, our approach utilizes a two-point dependent coherence Stokes vector, proving resilient to random noise in experimental scenarios. Our findings provide a robust foundation for higher-dimensional optical encoding and encryption, addressing limitations associated with partially coherent light in complex environments.
Optical coherence is a well-established branch of physical optics in which the statistical properties of fluctuating optical fields are described in terms of correlation functions over continuous spatial and temporal degrees of freedom (DoFs). Nevertheless, in any practical setting, only discrete DoFs are ever accessible. In these scenarios, the modes are fixed, stable, and deterministic, and partial coherence arises from random relative complex amplitudes, a configuration we refer to as 'structured coherence'. Advances in structured coherence have recently unveiled new conceptual ground in optical communications and information processing in which partial coherence may be preferable to full coherence, which we call a 'coherence advantage'. We formulate structured coherence in terms of coherence matrices to investigate these recent theoretical and experimental breakthroughs. We first review optical fields characterized by a binary DoF via 2x2 Hermitian coherence matrices and introduce key concepts that take on new significance for larger-dimensional modal sets. Next, we examine the structured coherence of two binary DoFs, which can be described by 4x4 coherence matrices. We introduce the concept of coherence rank, entropy swapping, and optical cross-purity. In the perspective outlined here, coherence is viewed as a 'resource', which can be exchanged between DoFs, concentrated into a DoF or into particular modes, or spread over the DoFs. We then examine larger-dimensional modal sets, which allow for more versatile applications in optical information processing. The formulation presented here lends itself particularly to the manipulation of partial optical coherence in integrated photonic platforms, thereby opening myriad avenues for novel fundamental investigations of structured coherence and exploiting the coherence advantage in optical communications and information processing.
A scheme is discussed for measuring Nth-order coherences of two orthogonally polarized light fields in a single spatial mode at very limited experimental cost. To implement the scheme, the only measurements needed are the Nth-order intensity moments after the light beam has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific settings of the wave plates. It is shown that this method can be applied for arbitrarily large N. A set of explicit values is given for the settings of the wave plates, constituting an optimal measurement of the Nth-order coherences for any N. For Fock states the method introduced here corresponds to a full state tomography. Applications of the scheme to systems other than polarization optics are discussed.
In the age of information explosion, the conventional optical communication protocols are rapidly reaching the limits of their capacity, as almost all available degrees of freedom (e.g., wavelength, polarization) for division multiplexing have been explored to date. Recent advances in coherent mode division multiplexing have greatly facilitated high-speed optical communications and secure, high-capacity information storage and transfer. However, coherent mode division multiplexing is quite vulnerable to even minute environmental disturbances which can cause significant information loss. Here, we propose and experimentally demonstrate a paradigm shift to incoherent mode division multiplexing for high-security optical information encryption by harnessing the degree of coherence of structured random light beams. In contrast to the conventional techniques, our approach does not require mode orthogonality to circumnavigate unwanted mode crosstalk. In addition, our protocol has, in principle, no upper bound on its capacity. Thanks to the extreme robustness of structured random light to external perturbations, we are able to achieve highly accurate information encryption and decryption in the adverse environment. The proposed protocol opens new horizons in an array of fields, such as optical communications and cryptography, and it can be relevant for information processing with acoustical, matter as well as other types of waves.
We explore the concepts of coherence and entanglement as they apply to both the classical and quantum natures of light. In the classical domain, we take inspiration from the tools and concepts developed in foundational quantum mechanics and quantum information science to gain a better understanding of classical coherence theory of light with multiple degrees of freedom (DoFs). First, we use polarization and spatial parity DoFs to demonstrate the notion of classical entanglement, and show that Bell's measure can serve as a useful tool in distinguishing between classical optical coherence theory. Second, we establish a methodical yet versatile approach called 'optical coherency matrix tomography' for reconstructing the coherency matrix of an electromagnetic beam with multiple DoFs. This technique 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. Third, we report the first experimental measurements of the 4 x 4 coherency matrix 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. In the quantum domain, we use the modal structure of classical fields to develop qubits and structure Hilbert spaces for use in quantum information processing. Advancing to three-qubit logic gates is an important step towards the success of optical schemes for quantum computing. We experimentally implement a variety of two- and three- qubit, linear and deterministic, single-photon, controlled, quantum logic gates using polarization and spatial parity qubits. Lastly, we demonstrate the implementation of two-qubit single-photon logic using polarization and orbital angular momentum qubits.
A new class of phase-retrieval methods for 2-D fields is introduced. Phase-space tomography can be used for the experimental determination of the amplitude and phase structure of a quasi-monochromatic wave field in a plane normal to its propagation direction. The wave field ψ(r) may represent either a scalar electromagnetic (EM) field or the quantum-mechanical (QM) wave function of a matter wave. The complex wave field may be coherent or partially coherent, in which case the method reconstructs the two-point spatial correlation function, Γ(r, r′) = ⟨ψ(r)ψ*(r′)⟩. (In the QM case, the analogous quantity is the density matrix.) The experiment uses only intensity measurements and refractive optics (lenses), and the data-analysis algorithm is noniterative and requires no deconvolution.