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Standing Waves in a Cavity

Standing Waves in a Cavity

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:

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...

Modes of Standing Waves: II

Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.

Plane Electromagnetic Waves II

Plane Electromagnetic Waves II

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.

Modes of Standing Waves - I

Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This phenomenon...

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Related Experiment Video

Updated: Jun 16, 2026

Characterization of Anisotropic Leaky Mode Modulators for Holovideo

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Published on: March 19, 2016

Waveguide laser mode patterns in the near and far field.

|February 4, 2010

Summary

This study reconciles differing notations in dielectric waveguide research by rederiving mode equations. This facilitates analysis of waveguide laser modes and selection of optimal mirror apertures for fundamental mode oscillation.

Area of Science:

Optics and Photonics
Electromagnetism
Waveguide Theory

Background:

Discrepancies exist in mathematical notations between dielectric waveguide researchers and those focused on waveguide lasers.
Standardizing notation is crucial for clear communication and accurate modeling in optical engineering.

Purpose of the Study:

To reconcile differing notations used in the fields of dielectric waveguides and waveguide lasers.
To rederive equations for field components of modes in large radius hollow dielectric waveguides using a more common notation.
To analyze the free-space field distributions resulting from specific mode combinations at waveguide terminations.

Main Methods:

Re-derivation of electromagnetic field component equations for dielectric waveguide modes.

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Mathematical analysis of linear combinations of modes to achieve linearly polarized fields.

Calculation of Fresnel and Fraunhofer diffraction patterns for launched waveguide modes.

Main Results:

Unified notation for dielectric waveguide mode equations is presented.
Linear combinations of modes producing linearly polarized fields are identified.
Formulas for Fresnel and Fraunhofer field distributions are derived for mode identification and mirror aperture selection.

Conclusions:

The derived equations and field distributions aid in identifying oscillation modes within dielectric waveguides.
This work provides a basis for selecting appropriate mirror apertures to ensure fundamental waveguide mode oscillation.
Standardized notation enhances the understanding and application of dielectric waveguide theory in laser systems.