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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:

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Updated: Jun 16, 2026

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

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Published on: August 5, 2013

Modes of a diffraction grating optical resonator.

A Hardy, D Treves

|February 6, 2010

Summary

This summary is machine-generated.

This study details an open resonator with a spherical mirror and reflection grating. Designing the grating allows control over energy coupling without significantly altering the resonator's eigenmodes.

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Area of Science:

Optics and Photonics
Electromagnetism
Resonator Physics

Background:

Open resonators are crucial components in various optical systems.
Controlling energy coupling in resonators is essential for device efficiency.
Previous methods for energy coupling often affected resonator modes.

Purpose of the Study:

To describe a novel open resonator design incorporating a reflection grating.
To numerically calculate the eigenmodes and eigenvalues of this resonator.
To demonstrate the ability to control energy output via grating design.

Main Methods:

Numerical calculation of eigenmodes and eigenvalues.
Utilizing the Fox and Li iterative method for simulation.
Designing a reflection grating for controlled energy coupling.

Main Results:

The study successfully calculated the eigenmodes and eigenvalues of the open resonator.
It was shown that grating design influences the amount of energy coupled out.
The eigenmodes remained largely unaffected by the grating's energy coupling adjustments.

Conclusions:

The described open resonator offers a method for tunable energy coupling.
Grating design provides a powerful tool for controlling resonator output.
This approach allows for efficient energy extraction without compromising resonator performance.