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Gauss's Law: Planar Symmetry

Gauss's Law: Planar Symmetry

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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Related Experiment Video

Updated: Feb 18, 2026

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Published on: January 3, 2016

Compacted dimensions and singular plasmonic surfaces.

J B Pendry¹, Paloma Arroyo Huidobro², Yu Luo³

¹The Blackett Laboratory, Department of Physics, Imperial College London, London SW7 2AZ, UK. j.pendry@imperial.ac.uk.

Science (New York, N.Y.)

|November 18, 2017

Summary

This summary is machine-generated.

A novel model reveals a hidden spatial dimension in metallic metasurfaces, impacting surface plasmon excitations. This discovery offers new insights into extra dimensions beyond typical field theories.

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Last Updated: Feb 18, 2026

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Area of Science:

Condensed matter physics
Metamaterials science
Theoretical physics

Background:

Advanced field theories propose extra spatial dimensions beyond the observable four.
These dimensions are typically theorized as compactified and unobservable at everyday scales.
Metasurfaces offer potential platforms for exploring exotic physical phenomena.

Purpose of the Study:

To present a simple, field-theory-unconnected model for a compactified dimension.
To explore the realization of this compactified dimension in a metallic metasurface.
To investigate the characteristics of surface plasmon excitations in such a structure.

Main Methods:

Modeling a metallic metasurface with periodic singularities forming a grating.
Analyzing the properties of surface plasmon excitations within this model.
Proposing an experimental realization using a doped graphene layer.

Main Results:

A compactified dimension can be realized in a metallic metasurface grating.
The surface plasmon excitations exhibit three wave vectors instead of the usual two.
The extra dimension of the grating remains hidden.

Conclusions:

The proposed model provides a novel, non-field-theory approach to compactified dimensions.
Metallic metasurfaces, particularly in doped graphene, are promising for experimental verification.
This work could bridge theoretical concepts of extra dimensions with experimental condensed matter physics.