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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:

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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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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A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
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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.

Linear Approximation in Frequency Domain

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Updated: Jul 9, 2026

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

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Published on: November 30, 2012

Linear and nonlinear waveguides induced by optical vortex solitons.

A H Carlsson, J N Malmberg, D Anderson

|December 8, 2007

Summary

This study numerically and analytically investigates optical vortex solitons in Kerr media, revealing insights into induced linear and nonlinear waveguides for fundamental and first-order modes.

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Last Updated: Jul 9, 2026

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Area of Science:

Optics and Photonics
Nonlinear Physics

Background:

Optical vortex solitons are key phenomena in nonlinear optics.
Kerr media exhibit intensity-dependent refractive index changes.

Purpose of the Study:

To analyze linear and nonlinear waveguides induced by optical vortex solitons.
To investigate fundamental and first-order guided modes.
To examine both focusing and defocusing nonlinearities.

Main Methods:

Numerical simulations of light propagation.
Analytical mathematical modeling.
Analysis of waveguide properties.

Main Results:

Characterization of waveguide formation by optical vortex solitons.
Identification of distinct behaviors for focusing and defocusing Kerr media.
Detailed analysis of fundamental and first-order guided modes.

Conclusions:

Optical vortex solitons effectively induce waveguides in Kerr media.
The study provides a comprehensive understanding of guided modes in these nonlinear structures.