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arXiv:2604.19524 · The European Physical Journal Plus

Multi-slit time-reversed Young interference: source-space grating laws, quadratic-phase effects, and Talbot-like revivals

Jianming Wen

physics.opticsphysics.app-phphysics.class-phquant-phSubmitted Apr 21, 2026• Announced Apr 22, 2026• 1 citation
arXivHTMLPDF

Abstract

We develop a compact theory of time-reversed Young (TRY) interference beyond the symmetric two-slit geometry by considering equally spaced three-slit, finite $N$-slit, and infinite periodic slit arrays. In the TRY configuration, a point emitter illuminates the aperture, a position-fixed detector records the signal, and the response is reconstructed in source space by correlating the detector record with the source-coordinate label. We show that the three-slit case already reveals the essential new physics beyond two slits: a quadratic Fresnel phase survives, modifies the reconstructed interference law, and lifts the nominal dark fringes in the generic case. For a general equally spaced $N$-slit array, we identify the exact reconstructed response and show that the familiar textbook grating factor is recovered only when the quadratic phase is negligible, compensated, or reduced to a common phase across the array. In that ideal limit, the reconstructed peaks are source-space analogues of classical grating orders rather than outgoing diffraction beams. For an infinite periodic TRY array, we further show that the same discrete quadratic phase generates full and fractional Talbot-like revivals in source space, governed by a reciprocal-distance condition rather than the conventional Talbot propagation law. These results show that the symmetric two-slit TRY geometry is exceptional, while multi-slit TRY systems naturally combine source-space discrimination with sensitivity to aperture-wide phase structure and periodic-array revival physics.

Journal reference
Eur. Phys. J. Plus 141, 903 (2026)
DOI
10.1140/epjp/s13360-026-08126-1
Comments
This is a theoretical extension of TRY configuration to multi-slit scenarios

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Young interference is usually read as the gradual statistical accumulation of random detection events. Here we show that a time-reversed Young (TRY) geometry has a different statistical character: the fringe is not a marginal distribution of detector positions, but a conditional response indexed by a programmed source coordinate. With a fixed detector and a scanned source basis, the observable is an operational hybrid correlator between detector signal and source label. The resulting interference is deterministic at the response-function level, while noise enters only through estimation precision. We formulate this distinction using Fisher information, estimator variance, and noise scaling, clarifying why TRY naturally supports calibration, lock-in readout, null-fringe sensing, and source-plane superresolution.

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Time-reversed Young (TRY) interferometry reconstructs interference from a fixed detector by reading out a programmable source-label distribution. This work formulates the architecture as a source-coded Bayesian response sensor. For a perturbation parameter θ, the detected source-label histogram is a posterior distribution determined by a programmed source prior, an optical likelihood for a fixed-detector click, and an evidence factor equal to the click probability. The key point is not the Bayesian identity itself, but its physical implementation: in TRY the prior is imposed before propagation and can therefore reshape the response ensemble actually sampled by the detector. The normalized posterior is shown to respond through a centered likelihood score, and the detected-event Fisher information is the posterior variance of this score. This identifies posterior-weighted score contrast, rather than local response magnitude alone, as the relevant sensing resource. The framework separates posterior-shape information from evidence information, giving a resource-aware way to judge near-null response enhancement. It also yields practical design rules: a two-label source code converts a weak perturbation into a fixed-detector label imbalance, while the multiparameter score covariance provides a route to nuisance rejection and gives a minimal-label rank condition for sensing multiple perturbations. A passive double-slit implementation with weak one-slit phase and loss perturbations is proposed, requiring only fixed-detector source scans before and after calibrated perturbations. Practical tolerances associated with source-programming error, drift, background, imperfect coherence, and polarization mismatch are analyzed, and extensions to multi-aperture and integrated photonic systems are formulated. The results position TRY as a source-programmable Bayesian sensing architecture complementary to conventional detector-plane Young interferometry.

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We develop a compact theory of time-reversed Young (TRY) interference beyond the symmetric two-slit geometry by considering equally spaced three-slit, finite NNN-slit, and infinite periodic slit arrays. In the TRY configuration, a point emitter illuminates the aperture, a position-fixed detector records the signal, and the response is reconstructed in source space by correlating the detector record with the source-coordinate label. We show that the three-slit case already reveals the essential new physics beyond two slits: a quadratic Fresnel phase survives, modifies the reconstructed interference law, and lifts the nominal dark fringes in the generic case. For a general equally spaced NNN-slit array, we identify the exact reconstructed response and show that the familiar textbook grating factor is recovered only when the quadratic phase is negligible, compensated, or reduced to a common phase across the array. In that ideal limit, the reconstructed peaks are source-space analogues of classical grating orders rather than outgoing diffraction beams. For an infinite periodic TRY array, we further show that the same discrete quadratic phase generates full and fractional Talbot-like revivals in source space, governed by a reciprocal-distance condition rather than the conventional Talbot propagation law. These results show that the symmetric two-slit TRY geometry is exceptional, while multi-slit TRY systems naturally combine source-space discrimination with sensitivity to aperture-wide phase structure and periodic-array revival physics.
Young interference is usually read as the gradual statistical accumulation of random detection events. Here we show that a time-reversed Young (TRY) geometry has a different statistical character: the fringe is not a marginal distribution of detector positions, but a conditional response indexed by a programmed source coordinate. With a fixed detector and a scanned source basis, the observable is an operational hybrid correlator between detector signal and source label. The resulting interference is deterministic at the response-function level, while noise enters only through estimation precision. We formulate this distinction using Fisher information, estimator variance, and noise scaling, clarifying why TRY naturally supports calibration, lock-in readout, null-fringe sensing, and source-plane superresolution.
This work presents a structural reexamination of Young’s double-slit experiment by identifying a missing stage in its standard formulation and restoring it within a finite, geometry-based framework. The conventional treatment assumes continuous propagation, neutral boundaries, and observation on a single fixed screen, reducing the experiment to a geometric division of a continuous entity. Using exact geometry, interference is described by the condition , which defines a family of hyperbolas in space. From the triangle inequality, the number of interference fringes for monochromatic light is shown to be finite and exactly determined. The commonly observed linear fringe pattern arises from the far-field approximation and represents only a partial cross-section of this global structure. A central result of this work is the identification of the in-slit stage as a necessary part of the experiment. The slit is treated as a finite region in which particles interact with boundary-defined electromagnetic environments, leading to directional redistribution prior to propagation. This interpretation is supported by an asymmetric single-slit experiment using different materials, which produces a reversible asymmetric pattern inconsistent with a purely geometric model. The framework is extended to limiting and classical cases, including tiny apertures and diffraction phenomena such as the Poisson spot, where symmetry and lack of comparison may conceal boundary-dependent effects. The suppression of interference in which-way detection experiments is interpreted as a modification of the electromagnetic environment within the slit. These results show that interference in Young’s experiment is a finite, spatial, and timing phenomenon that cannot be fully described by post-slit geometry alone. Restoring the in-slit interaction provides a complete factual description and introduces material-dependent effects absent from standard treatments.
In Young's Double Slit Experiment (YDE) and improved versions, waves causing interference travel different distances.As speed of light is constant, waves require different time spans to reach the point of interference.Thereby, if the waves are generated simultaneously at the slits/source, they cannot meet on the screen anywhere outside the mid-line.Formation of fringes is commonly interpreted as interference caused by the meeting (super-positioning) of two waves generated simultaneously.The reality is that fringes are formed by interference of waves generated at different times.However, unless impacted by other phenomena, two waves generated at different times converging to form fringes, as this paper shows, will mandatorily come in same phase to the interference point, producing constructive interference.Interference observed, however, is not only constructive.The effect on the phase of waves while bending (diffraction) is also to be considered.Consequently, it addresses three phenomena causing phase shifts: (1)different starting times,(2)bending at slits, and (3)distances traveled (In contrast, the first two are overlooked by the conventional approach).(Dirac and Feynman Path Integral methods on quantum particles have different approaches).The paper reveals the widespread misconception in the analysis of YDE and would impact the wave/particle and other YDE interpretations.
Time-reversed Young (TRY) interferometry holds a detector channel fixed while a source coordinate is scanned or programmed. We describe this measurement through a single accepted source-detector probability law obtained from scalar Fresnel propagation, the programmed source prior, and detector acceptance. The conventional fixed-source Young distribution, the source and detector marginals, and the fixed-detector TRY distribution are then different reductions of that common record. Standard information measures can therefore be assigned without ambiguity to the probability law actually measured. For a symmetric double-slit response with matched source and detector windows, the fixed-source and fixed-detector conditional distributions have the same entropy; the physically useful information from detector conditioning is instead expressed by grid-stable entropy deficits and Kullback-Leibler information gains. The canonical example gives a modest prior-to-posterior information gain and establishes a transparent baseline for more selective source programming, detector modes, or operating points. Finite slit width, finite-source element width, finite detector pixels, and finite-count entropy estimation are included to connect the ideal model with experiments. A phase scan then shows that conditional entropy and Fisher information characterize different properties of the same likelihood, while a two-mode coherence model separates record entropy from optical coherence entropy and distinguishes coherent superposition from incoherent mixture. The framework gives a unified statistical interpretation of fixed-detector, source-programmed Young interferometry while keeping optical reciprocity, Bayesian conditioning, local parameter sensitivity, and quantum state disturbance conceptually distinct.
A well-known phenomenon in both optics and quantum mechanics is the so-called Talbot effect. This near field interference effect arises when infinitely periodic diffracting structures or gratings are illuminated by highly coherent light or particle beams. Typical diffraction patterns known as quantum carpets are then observed. Here the authors provide an insightful picture of this nonlocal phenomenon as well as its classical limit in terms of Bohmian mechanics, also showing the causal reasons and conditions that explain its appearance. As an illustration, theoretical results obtained from diffraction of thermal He atoms by both N-slit arrays and weak corrugated surfaces are analyzed and discussed. Moreover, the authors also explain in terms of what they call the Talbot-Beeby effect how realistic interaction potentials induce shifts and distortions in the corresponding quantum carpets.
Time-reversed Young (TRY) interferometry reconstructs interference from a fixed detector by reading out a programmable source-label distribution. This work formulates the architecture as a source-coded Bayesian response sensor. For a perturbation parameter θ, the detected source-label histogram is a posterior distribution determined by a programmed source prior, an optical likelihood for a fixed-detector click, and an evidence factor equal to the click probability. The key point is not the Bayesian identity itself, but its physical implementation: in TRY the prior is imposed before propagation and can therefore reshape the response ensemble actually sampled by the detector. The normalized posterior is shown to respond through a centered likelihood score, and the detected-event Fisher information is the posterior variance of this score. This identifies posterior-weighted score contrast, rather than local response magnitude alone, as the relevant sensing resource. The framework separates posterior-shape information from evidence information, giving a resource-aware way to judge near-null response enhancement. It also yields practical design rules: a two-label source code converts a weak perturbation into a fixed-detector label imbalance, while the multiparameter score covariance provides a route to nuisance rejection and gives a minimal-label rank condition for sensing multiple perturbations. A passive double-slit implementation with weak one-slit phase and loss perturbations is proposed, requiring only fixed-detector source scans before and after calibrated perturbations. Practical tolerances associated with source-programming error, drift, background, imperfect coherence, and polarization mismatch are analyzed, and extensions to multi-aperture and integrated photonic systems are formulated. The results position TRY as a source-programmable Bayesian sensing architecture complementary to conventional detector-plane Young interferometry.