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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:

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Updated: May 21, 2026

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

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Published on: November 30, 2012

Waveguide characteristics of coupled in-plane waves.

Jie Pan¹, Jing Lu, Xiaojun Qiu

¹School of Mechanical and Chemical Engineering, The University of Western Australia, Crawley, Western Australia 6009, Australia. pan@mech.uwa.edu.au

The Journal of the Acoustical Society of America

|June 21, 2012

Summary

Coupling effects in thin plate waveguides significantly alter wave propagation. This study reveals how mode couplings, especially at spatial coincidence, determine waveguide characteristics and enable analytical solutions.

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Area of Science:

Solid Mechanics
Wave Propagation
Acoustics

Background:

In-plane wave propagation in thin plates is typically modeled using orthogonal functions.
Poisson and shear effects introduce coupling between displacement components, influencing wave characteristics.
Existing models often neglect these couplings, potentially limiting accuracy.

Purpose of the Study:

To investigate the impact of coupled in-plane wave dynamics in thin plate waveguides.
To analyze how Poisson and shear effects influence waveguide mode properties.
To develop an understanding of conditions leading to simplified analytical solutions.

Main Methods:

Describing in-plane waves as superpositions of orthogonal functions satisfying edge conditions.
Analyzing the coupled displacement components due to Poisson and shear effects.
Identifying conditions of spatial coincidence for significant mode coupling.

Main Results:

Coupling between uncoupled mode pairs significantly affects waveguide mode characteristics.
Spatial coincidence of uncoupled modes is crucial for pronounced coupling effects.
At specific frequencies, certain modes are dominated by single uncoupled mode pairs, allowing analytical solutions.

Conclusions:

The coupling of uncoupled modes is a primary determinant of thin plate waveguide behavior.
Understanding spatial coincidence is key to predicting and analyzing waveguide modes.
Analytical solutions are feasible for specific waveguide modes, offering valuable insights into their properties.