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

TL;DR

This paper develops a comprehensive theory of multi-slit time-reversed Young interference, revealing new physics such as quadratic phase effects, grating laws, and Talbot-like revivals in source space.

Contribution

It extends the understanding of TRY interference beyond two slits, identifying the role of quadratic phases and source-space revivals in complex slit arrays.

Findings

Quadratic Fresnel phase modifies interference laws and lifts dark fringes.

Reconstructed response in N-slit arrays depends on phase compensation.

Infinite arrays exhibit Talbot-like revivals governed by reciprocal-distance conditions.

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.