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Related Concept Videos

Plane Electromagnetic Waves I01:30

Plane Electromagnetic Waves I

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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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Plane Electromagnetic Waves II01:29

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Consider a plane wavefront traveling in position x-direction with a constant speed. This wavefront can be utilized to obtain the relationship between electric and magnetic fields with the help of Faraday's law.
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Electromagnetic Wave Equation01:24

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Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
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Standing Waves in a Cavity01:28

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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:
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Modes of Standing Waves: II01:04

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The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
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Gauss's Law: Planar Symmetry01:27

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
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Spectral element method for optical planar waveguide modal analysis.

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    This study introduces a novel spectral element method for analyzing waveguide propagation constants. The technique efficiently handles complex structures and leaky waves, offering improved accuracy and convergence for diverse waveguide types.

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    Area of Science:

    • Computational electromagnetics
    • Waveguide theory
    • Numerical analysis

    Background:

    • Planar multilayer waveguides are crucial in photonics and optoelectronics.
    • Accurate determination of propagation constants for guided and leaky modes is essential for device design.
    • Existing methods face challenges with semi-infinite domains and leaky wave analysis.

    Purpose of the Study:

    • To develop an efficient and accurate spectral element method for analyzing guided and leaky modes in planar multilayer waveguides.
    • To introduce a novel combination of hierarchical basis functions and rational mapping for handling semi-infinite domains.
    • To extend the method for leaky wave analysis using complex coordinates and perfectly matched layers (PMLs).

    Main Methods:

    • A spectral element method utilizing a hierarchical basis of modified Legendre polynomials.
    • Rational mapping for efficient treatment of semi-infinite computational subdomains.
    • Extension of algebraic mapping to complex coordinates to implement perfectly matched layers (PMLs) for leaky waves.

    Main Results:

    • The method naturally enforces radiation conditions at infinity and boundary conditions at material interfaces.
    • Demonstrated improved convergence properties without additional constraints.
    • Validated efficiency and numerical precision through comparisons with literature data for various waveguide types.

    Conclusions:

    • The developed spectral element method provides an accurate and efficient tool for analyzing complex waveguide structures.
    • The novel combination of basis functions and mapping techniques effectively handles semi-infinite domains and leaky waves.
    • The method shows broad applicability to dielectric, plasmonic, ARROW, and quantum well waveguides.