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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: Apr 19, 2026

Determination of the Excitation and Coupling Rates Between Light Emitters and Surface Plasmon Polaritons

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Published on: July 21, 2018

Probing complex reflection coefficients in one-dimensional surface plasmon polariton waveguides and cavities using

David T Schoen¹, Ashwin C Atre, Aitzol García-Etxarri

¹Stanford University , 476 Lomita Mall, Stanford, California 94305, United States.

|December 30, 2014

Summary

Researchers developed a new method using STEM EELS to measure reflection coefficients in plasmonic cavities. This allows for the precise engineering of custom cavities with predictable resonant properties.

Keywords:

Fabry−Pérot electron energy loss spectroscopy nanoscale cavity optical antenna plasmonics transmission electron microscopy

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Last Updated: Apr 19, 2026

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Area of Science:

Plasmonics
Nanophotonics
Materials Science

Background:

Resonant properties of plasmonic cavities depend on cavity size, SPP dispersion, and boundary reflection coefficients.
In small cavities, reflection phase is comparable to propagation phase, complicating analysis.
Previously, reflection phase was inferred indirectly from resonant frequencies.

Purpose of the Study:

To present a direct method for measuring complex reflection coefficients at cavity boundaries.
To demonstrate the use of these measurements for engineering custom plasmonic cavities.
To enable analytical prediction of cavity resonant wavelengths and mode densities.

Main Methods:

Utilized scanning transmission electron microscope electron energy loss spectroscopy (STEM EELS).
Measured complex reflection coefficients of a truncation in a 1D surface plasmon waveguide.
Applied measurements to engineer custom cavities with tailored reflecting boundaries.

Main Results:

Successfully measured complex reflection coefficients of cavity boundaries.
Demonstrated the ability to engineer custom cavities with predictable optical properties.
Showed that resonant wavelengths and mode densities can be analytically predicted.

Conclusions:

Direct measurement of reflection coefficients provides crucial insight into plasmonic cavity behavior.
This method enables the design of advanced plasmonic devices with engineered optical responses.
Facilitates precise control over resonant properties and mode localization in nanophotonic structures.