Related Experiment Video
Updated: Jun 22, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Generating a geometric mode for clarifying differences between an operator method and SU(2) wave representation
Optics Express
|June 25, 2009
Summary
Researchers investigated the unique VW mode in Nd:YVO4 lasers. Numerical and experimental analysis revealed specific generation conditions and propagation characteristics, clarifying theoretical model limitations.
Area of Science:
- Laser physics
- Quantum optics
- Geometric modes
Background:
- End-pumped lasers utilize specific cavity designs for mode control.
- Geometric modes offer unique properties in laser resonators.
- Nd:YVO4 lasers are widely used for various applications.
Purpose of the Study:
- To analyze the geometric VW mode in an end-pumped Nd:YVO4 laser.
- To compare numerical simulations with experimental results.
- To clarify the theoretical underpinnings and limitations of different analytical methods.
Main Methods:
- Numerical simulations using the operator method, SU(2) wave representation, and Fox-Li approach.
- Experimental investigation of mode patterns in a plano-concave cavity.
- Comparative analysis of theoretical predictions and observed experimental data.
Main Results:
- Identified peculiar generating conditions for the VW mode.
- Demonstrated the propagation characteristics of the VW mode.
- Found limitations in the operator method and SU(2) representation for certain transverse patterns.
Conclusions:
- The operator method requires extension to include reverse directional trajectories for geometric modes.
- The SU(2) coherent state representation is too specific for fringe patterns.
- Experimental validation is crucial for refining theoretical laser mode analysis.
Related Concept Videos
01:03Modes of Standing Waves - I
A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This phenomenon...
01:04Modes of Standing Waves: II
The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.
01:02Equations of Wave Motion
Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
01:13Graphing the Wave Function
Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.
01:20Graphical and Analytic Representation of Sinusoids
Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
01:17Standing Waves
Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...