Related Experiment Video
Updated: Jan 27, 2026

A Microfluidic Device for Quantifying Bacterial Chemotaxis in Stable Concentration Gradients
Published on: April 19, 2010
Propagation of a Bessel-Gaussian beam in a gradient-index medium
Abstract:
Based on the ABCD matrix method and Collins diffraction integral formula, analytical expression for Bessel-Gaussian beam propagation in a gradient-index medium is derived. The propagation trajectory, intensity, and phase distributions of the zeroth-order, second-order, and superposition cases are numerically investigated. The effect of beam waist radius w0 on the properties of beam propagation in a gradient-index medium is discussed in detail. The result shows that the beam is focused at z/L=N/2 (N=0,1,2,…) and propagates periodically in the medium. Evolution of the vortical structure of the superposed Bessel-Gaussian beam is investigated, showing that the superposed beam forms new singularities, and the rotation of the beam occurs mainly near the singularities.
Related Concept Videos
What is an Electrochemical Gradient?
The chemical gradient relies on differences in the abundance of a substance on the outside versus the inside of a cell and flows from areas of high to low ion concentration. In contrast, the electrical gradient revolves around an...
Beams
Based on geometry, beams can be straight, tapered, or curved. Straight beams are the most common type and have a constant cross-section throughout their length. Tapered beams, on the other hand, have a varying cross-section along...
Propagation of Waves
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Propagation of Action Potentials
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
Deflection of a Beam
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
Prismatic Beams: Problem Solving
The design begins with analyzing the beam as a free body to identify moments and force balances, thereby determining support reactions. Next, the...

