Self-healing of the Montgomery pattern

TL;DR

This paper investigates the self-healing properties of the Montgomery pattern, revealing a quantized recovery distance and demonstrating robustness against obstructions through experimental validation.

Contribution

It introduces the concept of quantized self-healing in Montgomery patterns, contrasting with previous diffraction-free beam studies, and confirms this through experimental holographic setups.

Findings

Recovery distance is quantized in integer multiples of the self-imaging period.

Montgomery pattern demonstrates robustness against obstructions up to 20 times its spot size.

Theoretical predictions are validated experimentally using programmable holography.

Abstract

Self-healing -- the ability of a structured beam to reconstruct its transverse profile after partial obstruction -- has been demonstrated for diffraction-free beams, where the recovery distance varies continuously with obstruction size. Here, we investigate self-healing in the Montgomery pattern, a self-imaging of tightly localized optical fields. Using Babinet's principle, we show theoretically that the recovery distance is quantized in integer multiples of the self-imaging period -- a qualitative distinction from all previously studied self-healing beams. We confirm these predictions experimentally using a programmable holographic setup with circular disk obstructions of size up to $20\times$ of the spot size of the Montgomery pattern at the self-imaging plane, establishing the robustness of the Montgomery pattern against scatterers and obstructions in the beam path.