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Related Concept Videos

Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
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:
Effects of feedback01:24

Effects of feedback

Feedback in control systems plays a critical role in shaping various operational parameters, extending beyond simple error reduction to influence stability, bandwidth, gain, impedance, and sensitivity. Understanding these effects requires examining a basic feedback system characterized by defined input, output, error, and feedback signals.
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In most cases, excessive hormone production is prevented by negative feedback—a loop that starts with a stimulus inducing the release of a particular substance, like a hormone, to maintain a certain level before triggering a signal that results in a decrease in further release of the hormone.
Positive and Negative Feedback Loops01:18

Positive and Negative Feedback Loops

Animal organs and organ systems constantly adjust to internal and external changes through a process called homeostasis ("steady state"). Examples of these changes include regulation of the level of glucose or calcium in the blood or internal responses to external temperatures. Homeostasis requires  maintaining an internal dynamic equilibrium:

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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
07:42

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Published on: December 15, 2021

Vortex solitons in lasers with feedback.

P V Paulau1, D Gomila, P Colet

  • 1IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain. pavel@ifisc.uib-csic.es

Optics Express
|July 1, 2010
PubMed
Summary
This summary is machine-generated.

This study reveals stable two-dimensional self-localized vortices in a laser model with frequency-selective feedback. Researchers mapped vortex solutions and their complex dynamics, offering insights into laser behavior.

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Area of Science:

  • Physics
  • Optics
  • Nonlinear Dynamics

Background:

  • Broad area vertical cavity surface emitting lasers (VECSELs) are crucial for high-power applications.
  • Understanding spatiotemporal dynamics in VECSELs is essential for optimizing device performance.
  • Frequency-selective feedback influences laser dynamics and spatial pattern formation.

Purpose of the Study:

  • To investigate the existence, stability, and dynamics of two-dimensional self-localized vortices in a simplified laser model.
  • To construct the complete bifurcation diagram for vortex solutions.
  • To characterize the various dynamical regimes exhibited by these vortices.

Main Methods:

  • Development of a mathematical model coupling a laser rate equation with a linear equation for the feedback field.
  • Analysis of the model in the limit of zero delay for VECSELs with external frequency-selective feedback.
  • Construction of the bifurcation diagram to systematically map vortex solutions.

Main Results:

  • Demonstrated the existence of two-dimensional self-localized vortices with azimuthal numbers up to 4.
  • Characterized the stability and dynamical properties of these vortex solutions.
  • Identified and described different dynamical regimes within the bifurcation diagram.

Conclusions:

  • The model effectively describes the spatiotemporal dynamics of VECSELs with frequency-selective feedback.
  • Stable, self-localized vortices are a significant feature of this laser system.
  • The findings provide a foundation for understanding complex spatiotemporal patterns in lasers.