Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Plane Electromagnetic Waves I

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...

Electromagnetic Wave Equation

Electromagnetic Wave Equation

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...

Standing Electromagnetic Waves

Standing Electromagnetic Waves

Electromagnetic waves can be reflected; the surface of a conductor or a dielectric can act as a reflector. As electric and magnetic fields obey the superposition principle, so do electromagnetic waves. The superposition of an incident wave and a reflected electromagnetic wave produces a standing wave analogous to the standing waves created on a stretched string.
Suppose a sheet of a perfect conductor is placed in the yz-plane, and a linearly polarized electromagnetic wave traveling in the...

Equations of Wave Motion

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.

Second Uniqueness Theorem

Second Uniqueness Theorem

Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...

Propagation of Waves

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
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...

You might also read

Related Articles

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

Sort by

Same author

Null curves in diffraction patterns.

Applied optics·2010

Same author

Increased optical resolution from a sampled wavefront.

Applied optics·2010

Same author

Optical applications of von Neumann's alternating-projection theorem.

Optics letters·2009

Same author

Restoration of images possessing a finite Fourier series.

Optics letters·2009

Same author

Restoration of images possessing a finite Fourier seriesa: errata.

Optics letters·2009

Same author

Phase retrieval and the polarization identity.

Optics letters·2009

Search research articles

Related Experiment Video

Updated: Jun 20, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Unitary operators in the homogeneous wave field.

W D Montgomery¹

¹Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan S4S OA2, Canada.

|August 25, 2009

Summary

Diffraction, phase conjugation, and rigid motions are unitary operators in wave fields. Their commutation relations reveal known and novel symmetries in homogeneous, band-limited wave fields.

Area of Science:

Physics
Optics
Wave phenomena

Background:

Band-limited fields are crucial in signal processing and wave optics.
Homogeneous wave fields exhibit uniform properties across space.
Unitary operators preserve the norm in Hilbert spaces, essential for quantum mechanics and wave mechanics.

Purpose of the Study:

To identify and characterize unitary operators acting on band-limited fields.
To explore the commutation relations between diffraction, phase conjugation, and rigid motion operators.
To elucidate the symmetries inherent in homogeneous diffracted wave fields.

Main Methods:

Mathematical formulation of diffraction, phase conjugation, and rigid motions as operators.
Application of group theory and operator algebra to analyze these operators.

More Related Videos

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Related Experiment Videos

Last Updated: Jun 20, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Derivation of commutation relations for the identified operators.

Main Results:

Diffraction, phase conjugation, and rigid motions are demonstrated as unitary operators.
Commutation relations for these operators are explicitly derived.
New symmetries of homogeneous, band-limited wave fields are uncovered.

Conclusions:

The identified unitary operators provide a framework for understanding wave field symmetries.
The derived commutation relations offer insights into the underlying structure of these fields.
This work contributes to the theoretical understanding of wave propagation and optical systems.