Optically Incoherent Photonic Mutual Information
While traditional evaluations of optical information transfer rely on disjointed abstractions to bridge electromagnetic propagation, coherence, and communication theory, we introduce an end-to-end framework that directly connects rigorous subwavelength wave physics to Shannon mutual information. By lifting the Maxwell current-to-field Green's function to propagate second-order field correlations (the mutual intensity), we establish a unified linear channel model that encapsulates coherent communication, phase retrieval, and incoherent imaging. Applying this framework, we demonstrate that the mutual-information-optimized photonic front end is dictated jointly by available spatial degrees of freedom, source statistics, and detection laws. For coherent sources measured by square-law detectors, we identify a structural transition: when detectors outnumber sources, topology-optimized front ends shift from point-focusing to interferometric mixing. This mixing leverages interference cross terms to make relative source phases information-bearing, yielding mutual information that surpasses the point-focusing amplitude-only baseline. Conversely, for spatially incoherent sources, the channel reduces to the Hadamard square of the Green's function. In this regime, under an isotropic source covariance, we prove that point-focusing uniquely maximizes the mutual information at fixed Frobenius norm. Under source correlations, the optimized front ends instead favor optical mixing. Finally, we derive closed-form upper bounds on achievable incoherent mutual information, governed entirely by the coherent singular values of the underlying electromagnetic operator. Potential applications include near-field microscopy, direct-detection optical datalinks, reference-free phase retrieval, fluorescence and thermal imaging, and structure-agnostic benchmarks for end-to-end-designed computational imagers.