Related Experiment Video
Updated: Jun 15, 2026

12:18
Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
Published on: August 5, 2013
Eigenvalues of a nonconfocal laser resonator with an output-coupling aperture
Applied Optics
|March 10, 2010
Summary
This study analyzes laser resonators with output coupling apertures using matrix eigenvalue techniques. The power loss for the TEM(00) mode stabilizes within a specific mirror Fresnel number range, allowing independent estimation of coupling loss.
Area of Science:
- Optics and Photonics
- Laser Physics
- Resonator Design
Background:
- Nonconfocal laser resonators are crucial for various laser applications.
- Output coupling apertures significantly influence resonator performance.
- Understanding mode behavior and loss mechanisms is essential for optimizing laser design.
Purpose of the Study:
- To analyze a nonconfocal laser resonator with output-coupling apertures.
- To investigate the impact of aperture coupling on resonator modes and losses.
- To develop a method for estimating coupling loss independently.
Main Methods:
- Utilized the matrix eigenvalue technique for resonator analysis.
- Performed numerical calculations of eigenvalues and eigenfunctions.
- Examined resonator behavior with varying mirror and coupling aperture Fresnel numbers.
Main Results:
- The power loss of the TEM(00) mode stabilizes in a finite range of the mirror Fresnel number.
- In this range, power coupling through the aperture becomes the dominant loss factor.
- Coupling loss can be accurately estimated independently of mirror edge spillover loss.
Conclusions:
- The matrix eigenvalue technique effectively analyzes nonconfocal resonators with coupling apertures.
- Aperture coupling plays a critical role in determining resonator power loss, especially for the fundamental mode.
- The findings enable better prediction and control of resonator losses for improved laser performance.
Related Concept Videos
Standing Waves in a Cavity
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:
Sound Waves: Resonance
Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
Parallel Resonance
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:
Characteristics of Series Resonant Circuit
Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:

