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Beams with Symmetric Loadings

Beams with Symmetric Loadings

The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...

Beams with Unsymmetric Loadings

Beams with Unsymmetric Loadings

Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...

Vector Components in the Cartesian Coordinate System

Vector Components in the Cartesian Coordinate System

Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...

Spherical and Cylindrical Capacitor

Spherical and Cylindrical Capacitor

A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field,...

Deflection of a Beam

Deflection of a Beam

Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...

Generation of Straight or Branched Actin Filaments

Generation of Straight or Branched Actin Filaments

The straight or branched structure formation of actin filaments is controlled by nucleating proteins such as the formins and Arp2/3 complex. Formin-mediated assembly results in straight filaments, whereas Arp2/3 protein complex-mediated assembly results in branched actin filaments.
Arp2/3 Complex
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Related Experiment Video

Updated: Jul 16, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

On-chip generation of adjustable cylindrical vector beams.

C Cisowski, C Klitis, P Maidment

|September 15, 2023

Summary

We developed a novel photonic device to generate reconfigurable cylindrical vector (CV) beams. This innovation overcomes limitations in current photonic integrated circuits for structured light generation.

Area of Science:

Optics and Photonics
Integrated Photonics
Structured Light

Background:

Cylindrical vector (CV) beams possess unique vectorial properties valuable for advanced applications.
Photonic integrated circuits (PICs) are increasingly used for structured light generation but lack reconfigurability.
Existing PICs have limited ability to generate diverse CV beams.

Purpose of the Study:

To propose and demonstrate a novel design for reconfigurable CV beam generation.
To overcome the reconfigurability limitations of current PICs for structured light.
To enable the generation of a wider variety of CV beams from a single device.

Main Methods:

Utilized annular gratings with polarization-dependent responses.
Embedded gratings within a microring resonator.

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Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

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Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Published on: April 1, 2020

Related Experiment Videos

Last Updated: Jul 16, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Published on: February 4, 2018

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Published on: April 1, 2020

Conducted proof-of-principle experiments with spatially resolved Stokes measurements.

Main Results:

Successfully generated reconfigurable CV beams.
Demonstrated the device's viability through experimental validation.
Validated the polarization-dependent response of the annular gratings.

Conclusions:

The proposed microring resonator with embedded annular gratings offers a new pathway for reconfigurable CV beam generation.
This design significantly enhances the versatility of structured light generation in PICs.
The technology holds promise for applications requiring adaptable vectorial light fields.