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  1. De Broglie Relation

    Linked via "group velocity"

    The Matter Wave Concept
    The physical manifestation of the de Broglie relation is the matter wave. Unlike classical electromagnetic waves, matter waves are not simple sinusoidal disturbances in a field but are rather complex probability amplitudes described by the Schrödinger equation. The wave associated with a particle is often localized into a wave packet, whose [group veloci…

  2. Intermodal Dispersion

    Linked via "group velocities"

    Intermodal Dispersion is a phenomenon observed in optical waveguides, particularly Multi-Mode Fibers (MMF)], where pulses of light transmitted through the fiber broaden over distance due to the propagation of multiple spatial optical modes at slightly different group velocities. This temporal spreading effectively limits the usable bandwidth and transmission distance of the fiber link, contrasting sharply with the mode-ign…

  3. Longitudinal Wave

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    Phonons in Crystals
    In perfect crystalline solids, the collective atomic vibrations propagating as waves are quantized into quasiparticles called phonons. The acoustic branches of the dispersion relation correspond to mechanical oscillations. The branch where atomic displacements are parallel to the direction of propagation is the [Longitudinal Acoustic (LA) mode](/entries/longitudinal-…

  4. Modal Distortion

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    Theoretical Basis and Mode Coupling
    In any confined optical system, the allowed field solutions, or modes, are defined by boundary conditions. For a standard step-index fiber, the characteristic equation dictates the allowed propagation constants ($\betam$) for each mode $m$. Modal distortion occurs when the group velocity\ ($v{g,m}$) for mode $m$ differs substantially from that of adjacent modes:
    $$v{g,m} = \frac{c}{n{eff,m}}$$

  5. Optical Dispersion

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    Normal Dispersion
    Normal dispersion occurs when the refractive index decreases as the wavelength increases (i.e., shorter wavelengths bend more strongly). This is the typical behavior observed for transparent materials operating in the spectral region between the main UV absorption band and the infrared absorption bands. In this regime, the group velocity ($v_g$) is less than the [phase velocity](/entries/ph…