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Plane Electromagnetic Waves I

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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.
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Sinusoidal Sources

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Consider a plane wavefront traveling in position x-direction with a constant speed. This wavefront can be utilized to obtain the relationship between electric and magnetic fields with the help of Faraday's law.

Standing Waves in a Cavity

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A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:

Gauss's Law: Planar Symmetry

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...

Propagation of Waves

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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.
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Related Experiment Video

Updated: Jun 12, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Partially coherent fundamental Gaussian wave generated by a fluctuating planar current source.

¹S.R.Seshadri@att.net

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|May 29, 2010

Summary

This summary is machine-generated.

This study analyzes how spatial coherence affects electromagnetic wave propagation from a planar source. Higher coherence generally leads to more focused beams and increased radiated power.

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Area of Science:

Electromagnetism
Wave Propagation
Optics

Background:

Understanding electromagnetic wave propagation is crucial in various fields.
The influence of source coherence on wave characteristics is a key area of research.

Purpose of the Study:

To analyze the propagation characteristics of spatially localized electromagnetic waves.
To investigate the effects of source spatial coherence on radiation intensity and power.

Main Methods:

Utilizing a Gaussian Schell-model source for analysis.
Treating a linearly polarized fundamental electromagnetic Gaussian wave.
Examining the electric field perpendicular to the propagation direction.

Main Results:

The degree of coherence significantly impacts the radiation intensity distribution.
Higher source coherence influences the total radiated power.
Spatial coherence determines the beam's focusing properties.

Conclusions:

Source spatial coherence is a critical parameter in controlling electromagnetic wave propagation.
The Gaussian Schell-model provides a useful framework for these analyses.
Findings have implications for designing and controlling electromagnetic radiation.