Related Experiment Video
Updated: Aug 2, 2026
09:23
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Quantum chaos in optical systems: the annular billiard
Martina Hentschel1, Klaus Richter
1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
Summary
This study explores dielectric annular billiards as quantum chaotic micro-optical resonators. An S-matrix approach reveals key resonances for optical communications, highlighting the necessity of wave descriptions for quantitative accuracy.
Area of Science:
- Quantum chaos
- Micro-optical resonators
- Wave phenomena
Background:
- Conventional billiards have hard-wall boundaries.
- Dielectric annular billiards are partially open and contain two dielectric media.
- Interfaces cause reflection and transmission, leading to complex dynamics.
Purpose of the Study:
- To model micro-optical resonators using quantum chaotic dielectric annular billiards.
- To analyze ray propagation and wave phenomena in these systems.
- To develop an S-matrix approach for open optical cavities.
Main Methods:
- Poincaré surfaces of section for ray propagation analysis.
- Numerical solutions of wave equations.
- S-matrix approach for open optical cavities.
- Husimi representation for resonance characterization.
Main Results:
- Identified resonances of intermediate width crucial for optical communications.
- Established ray-wave correspondence in real and phase space.
- Demonstrated the limitations of ray pictures for quantitative analysis.
Conclusions:
- Dielectric annular billiards offer a rich model for quantum chaotic micro-optical resonators.
- The S-matrix approach is effective for identifying important resonances.
- Wave descriptions are essential for a quantitative understanding of these systems.
Related Concept Videos
02:18Interference and Diffraction
Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
02:18The Bohr Model
Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus...
02:32The de Broglie Wavelength
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
04:08The Uncertainty Principle
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
02:45The Quantum-Mechanical Model of an Atom
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
01:28Conservation of Linear Momentum for a System of Particles
In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...