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Related Concept Videos

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Stability of Equilibrium Configuration01:23

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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
Propagation of Uncertainty from Random Error00:59

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Related Experiment Video

Updated: Jun 11, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Modulation instability of a coherent-incoherent mixture.

Dmitry V Dylov1, Jason W Fleischer

  • 1Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA.

Optics Letters
|July 3, 2010
PubMed
Summary

The nonlinear instability threshold is eliminated by any coherent light component, with the coherent fraction controlling pattern gain and period. This finding, confirmed by simulations and experiments, advances understanding of light beam interactions.

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Last Updated: Jun 11, 2026

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Area of Science:

  • Nonlinear optics
  • Wave propagation physics

Background:

  • Partially spatially incoherent beams exhibit complex nonlinear behaviors.
  • Understanding modulation instability is crucial for optical system design.

Purpose of the Study:

  • To investigate the nonlinear coupling and modulation instability of combined coherent and partially spatially incoherent beams.
  • To determine the influence of the coherent component on instability thresholds and pattern formation.

Main Methods:

  • Derivation of perturbation growth rates using a mutual coherence approach.
  • Theoretical analysis of nonlinear coupling dynamics.
  • Validation through numerical simulations and experimental observations in photorefractive crystals.

Main Results:

  • The presence of any coherent light component removes the nonlinear threshold for modulation instability.
  • The fraction of coherent light dictates the instability gain and characteristic period of emergent patterns.
  • Experimental and numerical results confirm theoretical predictions.

Conclusions:

  • Coherent light fundamentally alters the onset and characteristics of modulation instability in partially incoherent beams.
  • The findings provide a theoretical and experimental framework for controlling beam dynamics in nonlinear optical media.
  • This research has implications for optical communications and materials processing.