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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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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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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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A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
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Related Experiment Video

Updated: Jul 12, 2025

Optical Trapping of Nanoparticles
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Published on: January 15, 2013

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Trapped modes in particles with a negative refractive index.

V V Klimov, A R Bekirov, B S Luk'yanchuk

    Optics Letters
    |November 1, 2023
    PubMed
    Summary

    Natural oscillations in left-handed metamaterial particles are analyzed. These oscillations are shown to be trapped modes with finite energy due to unique electromagnetic properties.

    Area of Science:

    • Electromagnetism
    • Materials Science
    • Metamaterials

    Background:

    • Left-handed metamaterials exhibit negative permittivity and permeability.
    • Understanding electromagnetic field behavior in these materials is crucial.

    Purpose of the Study:

    • To investigate natural oscillations of the electromagnetic field within left-handed metamaterial particles.
    • To determine the nature and characteristics of these oscillations.

    Main Methods:

    • Exact solution of sourceless Maxwell equations.
    • Analysis of electromagnetic field behavior considering negative permittivity and permeability.

    Main Results:

    • Natural oscillations exhibit exponential decay at infinity.

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  • These oscillations are identified as trapped modes with finite energy.
  • Opposite phase and group velocities contribute to the trapped mode behavior.

    • Conclusions:

    • Left-handed metamaterial particles support trapped electromagnetic modes.
    • The findings offer insights into the unique electromagnetic properties of metamaterials.
    • Potential applications in experiments with Bessel beams are highlighted.