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Standing Waves in a Cavity

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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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Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

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Electromagnetic approach to laser resonator analysis.

Tuomas Vallius, Jani Tervo, Pasi Vahimaa

|June 6, 2009

Summary

A new rigorous electromagnetic method analyzes semiconductor laser cavities using diffraction theory. This approach accurately determines laser modes and eigenvalues for improved device design.

Area of Science:

Optics and Photonics
Computational Electromagnetics

Background:

Semiconductor lasers are crucial optoelectronic devices.
Analyzing their modal structure is key for performance optimization.
Existing methods may lack rigor for complex laser designs.

Purpose of the Study:

To introduce a rigorous electromagnetic method for analyzing semiconductor laser cavities.
To provide a numerical approach for determining modal properties.

Main Methods:

Utilizing rigorous diffraction theory of gratings.
Employing the Fourier Modal Method (FMM) and S-matrix algorithm.
Formulating an eigenvalue problem for numerical computation.

Main Results:

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The method rigorously analyzes infinitely periodic laser arrays.

It accurately determines the wave forms and eigenvalues of laser modes.

Adaptable for individual laser resonators using absorbing regions.

Conclusions:

The developed method offers a rigorous and accurate tool for semiconductor laser modal analysis.
It enables precise determination of mode characteristics, aiding in laser design and optimization.