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Singularity Functions for Shear

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In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...

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Related Experiment Video

Updated: Jan 10, 2026

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces

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Published on: June 7, 2019

Phase Characterization of Singular Metasurfaces.

Yanel Tahmi^1,2, Matthieu Ansquer², Pierre-Marie Coulon¹

¹Université Côte d'Azur, CNRS-CRHEA, Rue Bernard Gregory, Valbonne 06560, France.

|November 24, 2025

Summary

This summary is machine-generated.

Quadriwave lateral shearing interferometry accurately measures orbital angular momentum (OAM) beams from metasurfaces. Pancharatnam-Berry phase metasurfaces show better performance than effective refractive index ones.

Keywords:

QLSI metrology optical vortex phase singular metasurface

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Last Updated: Jan 10, 2026

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Published on: April 1, 2020

Area of Science:

Optics and Photonics
Metasurface Technology
Quantum Information Science

Background:

Controlled generation and characterization of light beams with orbital angular momentum (OAM) are crucial for advanced applications.
Metasurfaces are powerful tools for structuring light, but measuring their complex phase profiles, especially with phase singularities, is challenging.

Purpose of the Study:

To apply quadriwave lateral shearing interferometry (QLSI) for accurate phase mapping of OAM beams generated by metasurfaces.
To compare the performance of metasurfaces based on effective refractive index (ERI) modulation and Pancharatnam-Berry (PB) phase for OAM beam generation.

Main Methods:

Utilized quadriwave lateral shearing interferometry (QLSI) as a quantitative phase imaging technique.
Retrieved spatially resolved phase maps of OAM beams generated by metasurfaces.
Evaluated metasurfaces designed with ERI modulation and PB phase mechanisms.

Main Results:

QLSI successfully reconstructed both perfect and imperfect singular phase profiles of OAM beams.
PB-phase metasurfaces demonstrated superior phase accuracy and enhanced fabrication tolerance compared to ERI-based metasurfaces.
QLSI proved to be a reliable tool for characterizing complex optical fields and validating metasurface performance.

Conclusions:

QLSI is a robust metrological technique for characterizing structured light, particularly OAM beams.
PB-phase metasurfaces offer advantages in performance and fabrication for structured light generation.
This work validates QLSI as a key diagnostic tool for next-generation photonic devices utilizing structured light.