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Related Concept Videos

Oscillations about an Equilibrium Position01:04

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 because...
Damped Oscillations01:07

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 In An LC Circuit01:30

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
Standing Waves in a Cavity01:28

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 Waves01:07

Propagation of Waves

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.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Forced Oscillations01:06

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.

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Related Experiment Video

Updated: Jul 8, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Stable topological spatial solitons in optical parametric oscillators.

S Trillo, M Haelterman, A Sheppard

    Optics Letters
    |July 1, 1997
    PubMed
    Summary

    Nearly resonant optical parametric oscillators can support stable topological spatial solitons. This stability arises from the interaction between diffraction and parametric amplification within chi((2)) nonlinearities.

    Area of Science:

    • Nonlinear optics
    • Quantum optics
    • Photonics

    Background:

    • Optical parametric oscillators (OPOs) are crucial for generating light at new frequencies.
    • Spatial solitons are self-trapping beams of light that maintain their shape.
    • Topological structures in optics are of interest for robust information encoding.

    Purpose of the Study:

    • To investigate the possibility of stable topological spatial solitons in nearly resonant OPOs.
    • To understand the role of diffraction and parametric amplification in soliton formation.
    • To explore the influence of chi((2)) nonlinearities on soliton stability.

    Main Methods:

    • Theoretical prediction using models of nonlinear light propagation.
    • Analysis of the interplay between diffraction and parametric gain.

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  • Numerical simulations to observe soliton dynamics in two transverse dimensions.
  • Main Results:

    • Prediction of stable topological spatial solitons in nearly resonant OPOs.
    • Observation of robust soliton stripes in two transverse dimensions.
    • Demonstration that phase-sensitive parametric processes ensure soliton stability.

    Conclusions:

    • Nearly resonant OPOs are a viable platform for generating stable topological spatial solitons.
    • The interplay of diffraction and nonlinear parametric amplification is key to soliton formation and stability.
    • Phase sensitivity in the parametric process is critical for robust soliton propagation.