Tech Guide

Coherence (physics)


In physics, two waves sources are coherent if they have a constant phase difference and fixed frequency. It is an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference. It contains several distinct concepts, which are limit cases that never occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics. More generally, coherence describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets.

Interference is nothing more than the addition, in the mathematical sense, of wave functions. In quantum mechanics, a single wave can interfere with itself, but this is due to its quantum behavior and is still an addition of two waves (see Young's slits experiment). This implies that constructive or destructive interferences are limit cases, and that waves can always interfere, even if the result of the addition is complicated or not remarkable.

When interfering, two waves can add together to create a wave of greater amplitude than either one (constructive interference) or subtract from each other to create a wave of lesser amplitude than either one (destructive interference), depending on their relative phase. Two waves are said to be coherent if they have a constant relative phase. The degree of coherence is measured by the interference visibility, a measure of how perfectly the waves can cancel due to destructive interference.

Spatial coherence describes the correlation between waves at different points in space. Temporal coherence describes the correlation or predictable relationship between waves observed at different moments in time. Both are observed in the Michelson–Morley experiment and Young's interference experiment. Once the fringes are obtained in the Michelson–Morley experiment, when one of the mirrors is moved away gradually, the time for the beam to travel increases and the fringes become dull and finally are lost, showing temporal coherence. Similarly, if in Young's double slit experiment the space between the two slits is increased, the coherence dies gradually and finally the fringes disappear, showing spatial coherence.

Contents
Introduction
Mathematical definition
Coherence and correlation
Examples of wave-like states
Temporal coherence
The relationship between coherence time and bandwidth
Examples of temporal coherence
Measurement of temporal coherence
Spatial coherence
Examples of spatial coherence
Spectral coherence
Measurement of spectral coherence
Polarization coherence
Applications
Holography
Non-optical wave fields
Quantum coherence
See also
References
External links
IntroductionEdit

Coherence was originally conceived in connection with Thomas Young's double-slit experiment in optics but is now used in any field that involves waves, such as acoustics, electrical engineering, neuroscience, and quantum mechanics. The property of coherence is the basis for commercial applications such as holography, the Sagnac gyroscope, radio antenna arrays, optical coherence tomography and telescope interferometers (astronomical optical interferometers and radio telescopes).

Mathematical definitionEdit

Coherence and correlationEdit

The coherence of two waves follows from how well correlated the waves are as quantified by the cross-correlation function.[1][2][3][4][5] The cross-correlation quantifies the ability to predict the value of the second wave by knowing the value of the first. As an example, consider two waves perfectly correlated for all times. At any time, if the first wave changes, the second will change in the same way. If combined they can exhibit complete constructive interference/superposition at all times, then it follows that they are perfectly coherent. As will be discussed below, the second wave need not be a separate entity. It could be the first wave at a different time or position. In this case, the measure of correlation is the autocorrelation function (sometimes called self-coherence). Degree of correlation involves correlation functions.

Examples of wave-like statesEdit

These states are unified by the fact that their behavior is described by a wave equation or some generalization thereof.

Waves in a rope (up and down) or slinky (compression and expansion)
Surface waves in a liquid
Electric signals (fields) in transmission cables
Sound
Radio waves and Microwaves
Light waves (optics)
Electrons, atoms and any other object (such as a baseball, as described by quantum physics)
In most of these systems, one can measure the wave directly. Consequently, its correlation with another wave can simply be calculated. However, in optics one cannot measure the electric field directly as it oscillates much faster than any detector's time resolution.[6] Instead, we measure the intensity of the light. Most of the concepts involving coherence which will be introduced below were developed in the field of optics and then used in other fields. Therefore, many of the standard measurements of coherence are indirect measurements, even in fields where the wave can be measured directly.