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Oscillations In An LC Circuit

Oscillations In An LC Circuit

An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by

Forced Oscillations

Forced Oscillations

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

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:

Damped Oscillations

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...

Oscillations about an Equilibrium Position

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...

Limits with Oscillating Discontinuities

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...

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Related Experiment Video

Updated: Mar 15, 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

Backscattering-induced oscillated breathing soliton microcomb.

Xinyu Wang, Xinlin Han, Shulan Yi

|March 13, 2026

Summary

Researchers developed a new method to create breathing solitons in microcavities, overcoming challenges posed by Rayleigh backscatter. This technique also allows for enhanced repetition rates in soliton microcombs.

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Area of Science:

Nonlinear optics
Photonics
Optical microcavities

Background:

Rayleigh backscatter and Kerr nonlinearity are key phenomena in nonlinear optics.
Strong Rayleigh backscatter can hinder the formation of soliton microcombs due to mode-splitting.
Understanding soliton dynamics is crucial for optical frequency comb generation.

Purpose of the Study:

To investigate the impact of Rayleigh backscatter on soliton microcomb formation.
To propose a novel method for generating breathing solitons in mode-splitting microcavities.
To explore methods for enhancing the repetition rate of soliton microcombs.

Main Methods:

Utilizing a local dispersion method to control soliton formation.
Analyzing the energy exchange between counter-propagating waves in the microcavity.
Implementing frequency locking to modulate the soliton repetition rate.

Main Results:

Successfully generated a breathing soliton in a mode-splitting microcavity.
Demonstrated the energy exchange dynamics between counter-propagating waves.
Showcased the potential to enhance soliton microcomb repetition rates via frequency locking.

Conclusions:

The local dispersion method effectively enables breathing soliton formation despite strong Rayleigh backscatter.
The study provides insights into soliton dynamics and energy transfer mechanisms.
A novel method for locking soliton microcombs is presented, offering potential for advanced optical applications.