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Related Concept Videos

Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.
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...
Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
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Standing Waves in a Cavity

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Plane Electromagnetic Waves I01:30

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
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The Wave Nature of Light02:12

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Related Experiment Video

Updated: Jun 22, 2026

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
11:08

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Published on: November 30, 2012

Causality and Kramers-Kronig relations for waveguides.

Magnus Haakestad, Johannes Skaar

    Optics Express
    |June 9, 2009
    PubMed
    Summary

    This study derives Kramers-Kronig relations for optical waveguides, demonstrating their existence for both hollow and dielectric types based on causal signal propagation. These relations link real and imaginary parts of mode indices, simplifying for weakly guiding waveguides.

    Area of Science:

    • Photonics and Waveguide Optics
    • Electromagnetism and Optics

    Background:

    • Optical signal propagation is fundamentally causal.
    • Understanding waveguide mode behavior is crucial for optical device design.
    • Existing Kramers-Kronig relations apply to bulk materials, not waveguides.

    Purpose of the Study:

    • To derive and investigate Kramers-Kronig relations for optical waveguides.
    • To establish the relationship between real and imaginary parts of waveguide mode indices.
    • To explore the implications for different waveguide types.

    Main Methods:

    • Derivation of Kramers-Kronig relations starting from the principle of causality for optical signals.
    • Analysis of mode propagation in hollow waveguides with perfectly conductive walls.

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  • Examination of dielectric waveguides, including guided and evanescent modes.
  • Simplification of relations for weakly guiding waveguides based on mode field profiles.

    • Main Results:

    • Kramers-Kronig relations are derived for optical waveguides.
    • Causal propagation in hollow waveguides leads to relations between real and imaginary mode indices.
    • A Kramers-Kronig type relation exists for dielectric waveguides between guided and evanescent modes.
    • Modal dispersion in weakly guiding waveguides is simplified and determined by mode field profiles.

    Conclusions:

    • Kramers-Kronig relations are a fundamental property of causal optical waveguide propagation.
    • These relations provide a new framework for analyzing waveguide dispersion and mode behavior.
    • The findings offer insights into the design and characterization of optical waveguide devices.