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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:

The de Broglie Wavelength

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...

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.
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Modes of Standing Waves - I

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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...

$Interference and Diffraction$ 02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.

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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Related Experiment Video

Updated: Mar 5, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

Single-mode dispersive waves and soliton microcomb dynamics.

Xu Yi¹, Qi-Fan Yang¹, Xueyue Zhang^1,2

¹T.J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA.

Nature Communications

|March 24, 2017

Summary

This summary is machine-generated.

Researchers explored dissipative Kerr solitons, finding that a single-mode dispersive wave can stabilize soliton operation. This discovery enhances applications in frequency metrology and precision clocks.

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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

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Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

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Published on: August 5, 2013

Area of Science:

Nonlinear optics
Quantum optics
Resonator physics

Background:

Dissipative Kerr solitons are self-sustaining optical wavepackets crucial for nonlinear resonator physics.
They compensate for dispersion and optical loss using Kerr nonlinearity.
Applications include frequency metrology, precision clocks, and spectroscopy.

Purpose of the Study:

Investigate the limiting case of dissipative Kerr solitons radiating power into a single cavity mode.
Analyze the impact of this single-mode dispersive wave on soliton properties.
Identify operating points for enhanced stability in soliton comb generation.

Main Methods:

Theoretical study of dissipative Kerr soliton dynamics.
Analysis of the optical analogue of Cherenkov radiation.
Examination of the interaction between solitons and single-mode dispersive waves.

Main Results:

A single-mode dispersive wave induces hysteresis in soliton spectral and temporal properties.
An operating point with enhanced repetition-rate stability is identified.
This stability arises from balancing dispersive-wave recoil and Raman-induced soliton-self-frequency shift.

Conclusions:

Single-mode dispersive waves offer a pathway to quiet states of soliton comb operation.
These stable states are highly beneficial for various applications.
The findings advance the understanding and application of nonlinear optical phenomena.