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Related Concept Videos

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
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Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:
Propagation of Waves01:07

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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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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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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: Jun 19, 2026

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
14:18

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

Published on: February 28, 2016

Effect of third-order dispersion on passive mode locking.

H A Haus, J D Moores, L E Nelson

    Optics Letters
    |October 3, 2009
    PubMed
    Summary

    Third-order dispersion broadens mode-locked pulses by introducing chirp. Simulations reveal a resonant sideband that reduces gain, but reducing filter bandwidth can suppress this and narrow the pulse.

    Area of Science:

    • Optics and Photonics
    • Ultrafast Lasers
    • Nonlinear Optics

    Background:

    • Mode-locked lasers generate ultrashort pulses.
    • Third-order dispersion (TOD) is a critical parameter affecting pulse characteristics.
    • Understanding TOD effects is crucial for controlling pulse width and stability.

    Purpose of the Study:

    • To analytically and numerically investigate the impact of third-order dispersion on mode-locked pulse width.
    • To explore the underlying mechanisms, including chirp and gain effects.
    • To examine the influence of resonant sidebands and filter bandwidth.

    Main Methods:

    • Analytical derivations to model pulse evolution.
    • Numerical simulations to observe complex phenomena.
    • Parameter variation to study the effect of third-order dispersion and filter bandwidth.

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    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
    12:14

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

    Published on: August 12, 2013

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    Last Updated: Jun 19, 2026

    Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
    14:18

    Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

    Published on: February 28, 2016

    Low-cost Custom Fabrication and Mode-locked Operation of an All-normal-dispersion Femtosecond Fiber Laser for Multiphoton Microscopy
    08:48

    Low-cost Custom Fabrication and Mode-locked Operation of an All-normal-dispersion Femtosecond Fiber Laser for Multiphoton Microscopy

    Published on: November 22, 2019

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
    12:14

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

    Published on: August 12, 2013

    Main Results:

    • Pulse width increases monotonically with increasing third-order dispersion due to symmetric chirp.
    • Third-order dispersion broadens spectral bandwidth and reduces gain.
    • Simulations show a gain-taxing resonant sideband.
    • Reducing filter bandwidth suppresses the sideband and narrows the pulse.

    Conclusions:

    • Third-order dispersion is a primary factor limiting pulse width in mode-locked lasers.
    • Resonant sidebands represent an additional loss mechanism.
    • Filter bandwidth control offers a method to mitigate sideband effects and optimize pulse characteristics.