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Related Concept Videos

Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...
Shear and Bending Moment Diagram: Problem Solving01:24

Shear and Bending Moment Diagram: Problem Solving

When analyzing a beam supporting concentrated loads and a distributed load, drawing the shear and bending moment diagrams is essential. These diagrams help understand the internal forces and moments acting on the beam, which is crucial for designing safe and efficient structures. Follow these steps to create the shear and bending moment diagrams:
Draw a Free-Body Diagram: Start by drawing a free-body diagram of the entire beam, including the concentrated loads, distributed load, and reaction...
Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal centroidal axes. The...
Flexural Stress01:16

Flexural Stress

When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
Hooke's Law states that within the material's elastic limits, stress is directly proportional to strain. In a member experiencing a bending moment, the strain at any point is relative to its distance...
Unsymmetric Bending01:18

Unsymmetric Bending

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The orientation of the...
Bending of Curved Members - Neutral Surface01:16

Bending of Curved Members - Neutral Surface

In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...

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Related Experiment Video

Updated: Jul 2, 2026

Flapping Soft Fin Deformation Modeling using Planar Laser-Induced Fluorescence Imaging
06:20

Flapping Soft Fin Deformation Modeling using Planar Laser-Induced Fluorescence Imaging

Published on: April 28, 2022

Full-vector mode solver for bending waveguides based on the finite-difference frequency-domain method in cylindrical

Jinbiao Xiao1, Hongxing Ni, Xiaohan Sun

  • 1Electronic Engineering Department, Southeast University, Nanjing, China. jbxiao@seu.edu.cn

Optics Letters
|August 19, 2008
PubMed
Summary

A new full-vector mode solver accurately analyzes bending waveguides using the finite-difference frequency-domain method. This approach effectively models the leaky characteristics of these optical components.

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Fabrication of Zero Mode Waveguides for High Concentration Single Molecule Microscopy

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Area of Science:

  • Computational electromagnetics
  • Photonics and optical engineering
  • Waveguide theory

Background:

  • Bending waveguides are crucial components in integrated optical circuits.
  • Accurate modeling of bending waveguides, especially their leaky nature, is essential for device design and performance prediction.
  • Existing methods may face challenges in efficiently and accurately simulating the complex electromagnetic fields in bent structures.

Purpose of the Study:

  • To develop and present a robust full-vector mode solver for analyzing bending waveguides.
  • To incorporate perfectly matched layer (PML) absorbing boundary conditions to accurately capture radiation losses.
  • To validate the solver's effectiveness using a practical example of a bending rib waveguide.

Main Methods:

  • Utilized the finite-difference frequency-domain (FDFD) method.
  • Employed a local cylindrical coordinate system for direct derivation from Maxwell's equations.
  • Integrated Yee's mesh for discretization and PML absorbing boundary conditions to simulate leaky modes.

Main Results:

  • The developed FDFD mode solver successfully analyzes bending waveguides.
  • The incorporation of PML boundary conditions effectively demonstrates the leaky nature of the waveguides.
  • Numerical simulations on a bending rib waveguide confirm the solver's accuracy and effectiveness.

Conclusions:

  • The proposed full-vector mode solver provides an accurate and efficient tool for analyzing bending waveguides.
  • The method is capable of accurately simulating the radiation losses characteristic of bent optical structures.
  • This approach offers a valuable contribution to the design and optimization of photonic integrated circuits.