# Coherence and Coherent Sources

In physics, two waves are said to be coherent if their frequencies and waveforms are identical, and the phase difference between them is constant.

Coherence is the property of a wave that causes stationary interference. Several distinct concepts explain coherence. These phenomena don't usually occur in reality but allow a brief understanding of waves. It has become an important concept in quantum physics.

Coherence describes the properties of the correlation between physical quantities of a single wave, several waves, or that of wave packets.

For instance, if two parallel slits are lighted by a single laser beam, then those slits can be classified as two coherent sources.

Coherence light is a type of light in which the photons are all in step. The change of phase for the light beam occurs at the same time. Also, no abrupt phase change occurs within the beam. The light produced by lasers is coherent and monochromatic (made up of single wavelength) in nature.

Incoherent sources emit light with random and frequent change in phase within the photons. For example, ordinary fluorescent tubes and tungsten filament lamps emit incoherent light.

Further, conventional lights are incoherent sources. The drift from one atomic energy level to the next is a random method & one cannot have control over it when atom losses its energy radiating all over.

Types of Coherence

Here you can find what are the two types of coherence. Well, there are two different types of coherent sources, temporal coherence, and spatial coherence. These two types of coherence are explained below.

1. Temporal Coherence

Temporal coherence is a measure of the average relationship between the value of a wave and the coherence itself, making a delay of τ, at any considerable pair of time. It measures how monochromatic a source of light is.

Its characteristic is that the wave can well interfere with it at different points of time. If the phase or amplitude is significant above the delay, the correlation also decreases significantly.

It is defined as the coherence time τc. Keeping a delay of τ = 0, the degree of coherence becomes ideal. If the delay is τ = τc, the degree of coherence drops significantly. The coherence length Lc is defined as the distance traveled by the wave in time τc.

The figure represents the amplitude of a single frequency wave over a function of time (in red) and the amplitude of the same wave delayed by τ (blue). Since it is perfectly correlated with itself for all delays in time τ, therefore coherence time of the wave is infinite.

2. Spatial Coherence

In light waves and water waves, it is found that the dimension of wave extends from one or two spaces. Spatial coherence is the ability of two points in the space of a wave that interferes. In simple words, spatial coherence is the cross-relation between two points of a wave.

A wave is said to be perfectly spatial coherence if it has a single amplitude value over an infinite length. The significant interference between the range of separation and two points can be used to define the diameter of the coherence area, Ac.

(A plane wave with an infinite coherence length)

(A wave with a wavefront and infinite coherence length)

(A wave with a wavefront and finite coherence length)

A wave with a finite coherence area is incident on a pinhole, and the wave will be diffracted out of the pinhole. The emerging spherical wavefronts are approximately flat, far from the pinhole. The coherence area becomes infinite, but the coherence length remains unchanged.

A wave with an infinite coherence area is combined with a spatially shifted copy of the same wave. Se sections of the wave interfere constructively and some destructively.

By averaging these sections with the help of a detector of length D, we can measure the reduced interference visibility.

An example of this is a misaligned Mach–Zehnder interferometer.

How to Produce Coherent Sources?

Methods of producing coherent source

Here are some of the methods to produce a coherent source of light.

a. By Dividing the Wavefront

A wavefront can be divided into several parts. It can be used by using different lenses, mirrors, and prisms are Young's double-slit experiment, Lloyd's mirror arrangement and Fresnel's biprism method are some of the techniques to do it.

b. By Dividing the Amplitude

If the amplitude of an incoming beam of light is divided, then a coherent source can be created. This can be done by the process of partial reflection or refraction. These divided parts further meet with each other to create interference.

Application of Coherence

Radiography is a technique that uses coherence of next-generation facility beam and makes it possible to break the usual barrier easily.

The X-ray beam has:

1. A high spatial coherence - In this the size and divergence of the beam are small

2. A good temporal coherence - It occurs after monochromatization.

These characteristics of the beam are because of its super brilliance. It allows new techniques to be developed in the X-ray field:

1. Phase-contrast, tomography, and imaging

2. Photon correlation spectroscopy

3. In-line holography.

Coherence also forms the basis of some other applications. Some of the applications are mentioned below:

i. Holography

It uses coherent superposition of optical waves, and its use is commonly found in credit cards.

ii. Non-optical Wavefield

The superposition of non-optical wave fields also occurs, which is opposite to holography. For example, a probability field related to a wave function is considered in quantum mechanics. Coherent waves also have applications in future technologies like quantum computing.

iii. Modal Analysis

Coherence is also used in the model analysis to maintain the quality of the transfer function.

Q1. Is Sun a Coherent Source?

Ans: Sun is an incoherent source of light. However, sunlight can impart a coherence speckle to the image of a microscope. Most of the light sources bother spatial coherence (related to angular size) and temporal coherence (related to wavelength).

Q2. Can Two Independent Sources be Coherent?

Ans: No, two independent sources of light can never be coherent. When individual atoms return to the ground state, light is emitted. Even the smallest light source cannot emit light waves of the same phase.

Q3. Can Two Independent Monochromatic Sources of Light be Coherent?

Ans: No, two independent monochromatic sources of light cannot be coherent. Since two sources of light have a different frequency, wavelength, and phase; so they cannot produce any interference.

Q4. Why is a Coherent Source Needed for Interference?

Ans: Coherent sources of light have the same frequency, wavelength, and are in the same phase. This is required to produce a sustained interference pattern. This is the new intensity of light.