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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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Parallel Resonance

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The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:

Series Resonance

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The RLC circuit impedance is defined as the ratio of the supply voltage to the circuit current. Resonance in such a circuit occurs when the imaginary part of this impedance equals zero. This specific condition means that the inductive reactance is exactly equal to the capacitive reactance. The frequency at which this happens is known as the resonant frequency. Mathematically, the resonant frequency is inversely proportional to the square root of the product of the inductance (L) and capacitance...

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Related Experiment Video

Updated: Jun 16, 2026

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

Published on: August 5, 2013

Resonator theory for hollow waveguide lasers.

R L Abrams, A N Chester

|February 6, 2010

Summary

This summary is machine-generated.

A new numerical method analyzes waveguide laser modes using diffraction integrals and characteristic modes. This technique simplifies complex matrix diagonalization for efficient single-mode operation analysis.

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Area of Science:

Optics and Photonics
Laser Physics
Computational Electromagnetics

Background:

Waveguide lasers are crucial for various applications.
Analyzing transverse modes in laser resonators is complex.
External mirrors introduce additional challenges in mode analysis.

Purpose of the Study:

To develop a numerical technique for analyzing transverse modes in waveguide lasers with external mirrors.
To simplify the complex mode analysis of waveguide resonators.
To identify optimal resonator parameters for single-mode operation.

Main Methods:

Utilizing the Fresnel-Kirchhoff diffraction integral for external propagation.
Decomposing fields into characteristic guide modes for internal propagation.
Reducing mode analysis to the diagonalization of small complex matrices (5x5 or 10x10).

Main Results:

Identified distinct classes of transverse modes (e.g., TE(0m), TM(0m), EH(1m)).
Demonstrated that guide modes form complete and orthogonal sets for basis vector description.
Analyzed guide losses, coupling losses, and mode shapes for Fresnel numbers 0.1-1.0.
Showcased specific resonator parameters advantageous for single-mode operation.

Conclusions:

The developed numerical technique effectively analyzes transverse modes in waveguide lasers with external mirrors.
The method simplifies complex resonator analysis through matrix diagonalization.
Optimal resonator parameters can be identified to achieve efficient single-mode laser operation.