[Paper Review] Does the structure of light influence the speckle size?

Xiaobo Hu, Meng-Xuan Dong+3 more|arXiv (Cornell University)|Jun 15, 2019

Optical measurement and interference techniques4 citations

TL;DR

This study investigates whether the structured intensity profile of higher-order Laguerre-Gaussian (LG) modes affects speckle size in random media. Using both theoretical modeling and experimental validation, the authors demonstrate that speckle size depends solely on the illuminated area's effective diameter, not on the beam's ring-like intensity structure or orbital angular momentum. The key finding is that speckle size scales identically with LG modes and homogeneous Gaussian apertures, enabling a unified analytical expression based on modal indices p and ℓ.

ABSTRACT

It is well known that when a laser is reflected from a rough surface or transmitted through a diffusive medium, a speckle pattern will be formed at a given observation plane. Speckle is commonly produced by laser beams with a homogeneous intensity, for which, well-known relations have been derived, relating the speckle size to the area of illumination. Here we investigate the speckle generated by higher-order Laguerre-Gaussian (LG) modes, characterized by a non-uniform intensity distribution of concentric rings.We show that the ring-structure of the LG modes does not play any role in the speckle size, which happens to be the same as that obtained for a homogeneous intensity distribution. This allow us to provide with a simple expression that relates the speckle size to the spot size of the LG modes. Our findings will be of great relevance in many speckle-based applications.

Motivation & Objective

• To determine whether the non-uniform intensity structure of Laguerre-Gaussian (LG) modes influences speckle size in diffusive media.
• To resolve conflicting prior reports suggesting that topological charge or orbital angular momentum affects speckle size.
• To establish a general analytical expression linking speckle size to the modal indices (p, ℓ) of LG modes.
• To experimentally verify that speckle size matches that of a homogeneous-intensity aperture with the same effective spot size.
• To enable broader use of structured light in speckle-based applications by decoupling speckle size from beam complexity.

Proposed method

• Theoretical derivation of speckle size using the 2D spatial autocorrelation function of the scattered intensity field.
• Modeling the effective illuminated area of LG modes as a Gaussian beam with spot size w(z) = w₀√(2p + |ℓ| + 1), derived from the radial intensity profile.
• Experimental comparison using a spatial light modulator (SLM) to generate both LG modes and equivalent homogeneous-intensity circular apertures with identical effective diameters.
• Speckle patterns were recorded via CCD camera at a fixed distance from a ground glass diffuser, and mean speckle size was quantified via full width at half-maximum (FWHM) of the 3D intensity autocorrelation.
• Theoretical predictions were compared with experimental data across varying p and ℓ values, including cases with ℓ=0 and p=0.
• Statistical averaging of FWHM across x and y directions in the autocorrelation profile to obtain mean speckle size Δs.

Experimental results

Research questions

• RQ1 Does the ring-structured intensity profile of LG modes alter the mean speckle size in a diffusive medium?
• RQ2 Is the speckle size influenced by the topological charge ℓ or orbital angular momentum of the beam?
• RQ3 Can a single analytical expression describe speckle size for both LG modes and homogeneous-aperture illumination?
• RQ4 Does the complexity of the beam’s intensity profile (e.g., multiple rings) affect speckle statistics beyond the effective illuminated area?
• RQ5 Is the speckle size independent of beam structure when the effective spot size is held constant?

Key findings

• The speckle size produced by LG modes is identical to that of a homogeneous-intensity circular aperture with the same effective spot size, confirming that beam structure does not influence speckle size.
• The speckle size scales inversely with the effective diameter of the illuminated area, with the effective radius given by r = w₀√(2p + |ℓ| + 1), where w₀ is the fundamental mode waist.
• Experimental measurements of speckle FWHM for LG modes and homogeneous apertures show near-identical values across all tested p and ℓ combinations, with no statistically significant difference.
• The theoretical model based on the effective illuminated area accurately predicts speckle size for both beam types, with high agreement in all cases (p=0, ℓ=0, and general ℓ≠0, p≠0).
• The reduction in speckle size with increasing p or ℓ is solely due to the enlargement of the illuminated area, not due to the beam’s phase structure or OAM content.
• The study confirms that orbital angular momentum (OAM) and topological charge do not affect speckle size, resolving prior conflicting claims.