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Electromagnetic Wave Equation

Electromagnetic Wave Equation

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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Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

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Method to map individual electromagnetic field components inside a photonic crystal.

T Denis¹, B Reijnders, J H H Lee

¹Laser Physics and Nonlinear Optics, MESA+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands. t.denis@utwente.nl

|October 6, 2012

Summary

We developed a new technique to measure electromagnetic field strength within photonic crystals. This method maps the electric field component Ez in a 2D photonic crystal slab using a scanned scatterer, showing excellent agreement with calculations.

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Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

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Published on: November 30, 2012

Area of Science:

Photonics and Electromagnetism
Materials Science

Background:

Photonic crystals offer unique light manipulation properties.
Precisely mapping electromagnetic fields inside these structures is crucial for device design and understanding.

Purpose of the Study:

To introduce and validate a novel method for determining the absolute electromagnetic field strength within photonic crystals.
To specifically map the dominant electric field component (Ez) in a two-dimensional photonic crystal slab at microwave frequencies.

Main Methods:

A two-dimensional photonic crystal slab was placed in a resonant cavity formed by two mirrors.
A subwavelength spherical scatterer was scanned within the cavity to probe the electromagnetic field.
The shift in resonant Bloch frequencies, measured via reflection and transmission spectra, was correlated with the electric field at the scatterer's position.

Main Results:

The method successfully mapped the electric field component Ez inside the photonic crystal slab.
Frequency shifts of the resonant Bloch modes directly corresponded to the local electric field strength.
Experimental measurements showed excellent agreement with theoretical calculations, validating the method without adjustable parameters.

Conclusions:

The presented method provides an accurate and direct way to map absolute electromagnetic field strengths in photonic crystals.
This technique is valuable for characterizing photonic devices and advancing the understanding of light-matter interactions in periodic structures.