Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position with respect to time...
Real-World Applications of Space Curves01:29

Real-World Applications of Space Curves

Modern aerospace navigation depends on the accurate prediction of motion in three-dimensional space. In defense applications, radar systems continuously track both interceptors and moving aerial targets to find whether their flight paths will result in a collision. These motions are modeled mathematically as space curves, which represent paths that change continuously with time. Each object’s position is described by a vector function that specifies its location in terms of time-dependent...
Curvilinear Motion: Normal and Tangential Components01:27

Curvilinear Motion: Normal and Tangential Components

When a car traverses a curved road, its motion can be elucidated by breaking it down into tangential and normal components. The car-centric coordinates attached to the vehicle move with it.
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...
Tangent Planes to a Parametric Surface01:22

Tangent Planes to a Parametric Surface

A tangent plane provides a linear approximation to a curved surface at a specific point, capturing the local behavior of the surface. It can be understood as the plane that just touches the surface at that point and is defined by the tangent directions of curves lying on the surface. These tangent directions arise naturally when the surface is described parametrically, allowing systematic construction of the plane.For a surface expressed in parametric form, the position of any point is...
Equations of Motion: Rectangular Coordinates and Cylindrical Coordinates01:21

Equations of Motion: Rectangular Coordinates and Cylindrical Coordinates

Understanding the motion of particles is a fundamental aspect of classical mechanics, and the choice of the coordinate system plays a pivotal role in unraveling the complexities of their dynamics.
When a particle moves relative to an inertial frame, the equations of motion can be expressed using rectangular components. If the motion is confined to the x-y plane, the equations having the x and y coordinates only can be used to simplify the mathematical representation.
However, when particles...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Spectral element method for optical planar waveguide modal analysis.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same author

A multi-agentic framework for real-time, autonomous freeform metasurface design.

Science advances·2025
Same author

Statistically correlated disordered freeform random metasurfaces: generation and electromagnetic numerical simulation.

Optics express·2025
Same author

Diffraction by gratings: from the C-method to the stochastic C-method.

Journal of the Optical Society of America. A, Optics, image science, and vision·2025
Same author

Polynomial modal method for crossed slanted gratings.

Journal of the Optical Society of America. A, Optics, image science, and vision·2025
Same author

Modal analysis of diffraction by snake gratings using a tensor product of pseudo-periodic functions and Legendre polynomials.

Journal of the Optical Society of America. A, Optics, image science, and vision·2023

Related Experiment Video

Updated: Jul 16, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
10:39

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Published on: October 11, 2016

Complex coordinate implementation in the curvilinear coordinate method: application to plane-wave diffraction by

Kofi Edee1, Gérard Granet, Jean-Píerre Plumey

  • 1Laboratoire des Sciences et Matériaux pour l'Electronique et d'Automatique, CNRS/UMR 6602, Université Blaise Pascal, Les Cézeaux, 63177 Aubière Cedex, France.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|March 16, 2007
PubMed
Summary

This study introduces an efficient electromagnetic modeling technique for plane-wave diffraction on nonperiodic surfaces using the curvilinear coordinate method (CCM). The enhanced CCM effectively handles complex geometries and electromagnetic fields for accurate surface modeling.

More Related Videos

Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population
09:02

Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population

Published on: January 31, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Related Experiment Videos

Last Updated: Jul 16, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
10:39

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Published on: October 11, 2016

Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population
09:02

Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population

Published on: January 31, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Area of Science:

  • Electromagnetics
  • Computational physics
  • Surface science

Background:

  • Plane-wave diffraction analysis is crucial for understanding wave interactions with surfaces.
  • Traditional methods often struggle with nonperiodic surface geometries.
  • The curvilinear coordinate method (CCM) offers a framework for surface modeling.

Purpose of the Study:

  • To develop an efficient electromagnetic model for plane-wave diffraction by nonperiodic surfaces.
  • To adapt the curvilinear coordinate method (CCM) for enhanced modeling capabilities.
  • To integrate the perfectly matched layer (PML) concept into the CCM framework.

Main Methods:

  • Utilizing the curvilinear coordinate method (CCM) for electromagnetic modeling.
  • Employing a Fourier basis expansion within the CCM framework.
  • Reformulating the CCM in a complex coordinate system to incorporate the perfectly matched layer (PML).

Main Results:

  • The adapted CCM effectively models plane-wave diffraction on nonperiodic surfaces.
  • The integration of PML simplifies and enhances the modeling process.
  • Validation was performed for a perfectly conducting surface, demonstrating model efficiency.

Conclusions:

  • The complex coordinate CCM provides an efficient and effective approach for electromagnetic modeling of diffraction.
  • This method offers a robust solution for analyzing wave interactions with complex, nonperiodic surfaces.
  • The integration of PML is a key advancement for improving accuracy and computational efficiency.