# Electromagnetic Waves

When the alternating current passes through a wire than it sets up an electromagnetic field that propagate away from the wire. As the name implies the electromagnetic field consist of an electric field and magnetic field. These fields are at right angles to each other & to the direction of propagation.

If the conventional rotation of x-y-z orthogonal coordinates system is used, than we take electric field in y-direction, magnetic field in x-direction and the propagation in z-direction. This type of field is called Transverse electromagnetic field & can be shown as

Since the wave is induced by a sinusoidal current so the field increases, decreases and reverses polarity with the time that is the field intensity sinusoidally with time.

In the figure above the line between t_{1} and t_{2} represents the distance between time t_{1} and t_{2} that the wave has traveled.

- In vacuum the propagation velocity of electron magnetic waves is 300 X 10
^{6}m/s and is denoted by ‘C’. This velocity is independent of frequency. The velocity of propagation in a medium rather than in vacuum depends on the particular material and is always less than C = 300 X 10^{6}m/s. - Most of the light consist of a group of frequencies rather than a wave with a single frequency e.g. visible light contains frequencies ranging from blue light (App: 0.6 X 10
^{15}Hz) to red (app: 0.4 X 10^{15}Hz) and lower. - The light consist of range/group of frequencies directly effects the performance of fiber optic system.
- The propagation velocity can be defined as “The velocity of a group of waves with different frequencies”.

### Wavelength:

The distance, the wave has traveled in time T is called the wavelength, denoted by λ. It’s units is meter. The λ is the distance a constant phase point on the wave front travels in one period. Now since the velocity of wave in free space is c so the distance (λ) traveled in time T is T X C.

Therefore

- λ = T X C but T = 1/f
- λ = c/f ------------(1)

### Phase:

The relative position of a signal in time T is called phase.

### Phase velocity:

The velocity of the constant phase point (p) on propagation wave is called phase velocity, denoted by Vp

Mathematically

V_{p} = λ x f ------------(2)

In free space Vp – C = 3 X 10^{3} m/s and so above eq(2) become same to eq(1) other than free space value of Vp is different than C = 3 X 10^{8} m/s.

## Refractive Index

We know that propagation velocity in vacuum is

C = 300 X 10^{6} m/s

Or

C = 3 X 10^{8} m/s

Now when light propagates through a material (not vacuum) than velocity decreases and therefore propagation velocity

V_{p} = C/n_{1}

N = c / V_{p} ----------------(1)

This n is the refractive index of material. Some times n is also called index of refraction. Thus from (1) we can define refractive index as:

“The ration of light speed in vacuum to that in the material”

n – (e X μ)^{1/2}

in vacuum V_{p} = C, therefore n_{1} = 1/1 =1

Since propagation velocity can never exceed C. therefore the n (refractive index) for any material is greater than 1.

The frequency of wave in vacuum or in material does not change, however refractive index of any material varies with wavelength. Therefore λ in material with refractive index n1 is related to λ in vacuum as

A λ_{1} = λ/n_{1 } ------------------(2)

Where λ = c/f = V_{p}n_{1}/f

To find out λ_{1} = V_{p}/f easily here is the table

Material |
Vp X 10 (velocity of light) |
Refractive index n |
---|---|---|

Vaccum |
300 |
1.0 |

Air, Ice |
299.9, 230.7 |
1.003, 1.3 |

Water |
225.56 |
1.36 |

Ethanol |
220.48 ---> 151 |
1.46 -----> 1.96 |

Glass |
205.48 ----> 151 |
1.46 ------> 1.96 |

Diamond |
123.97 |
2.42 |

### Coherence:

We know that different light sources produce a light waves consisting of line width (range of frequency) for example

The incandescent lamp covers a wide frequency range while typical laser produce a relatively narrow frequency/wavelength range, now

A source that produces a single or narrow range frequency is called coherent source and so this phenomenon is called coherence.

The different light wave from coherent source can interfere with each other or combined in space to produce sums and differences of electromagnetic waves.

Formal definition of coherence or degree of coherence is that “the ability of particular wave to produce interference patterns is called coherence/degree of coherence”.

### Temporal Coherence:

An electromagnetic wave of a narrow range of frequency is called temporal coherence. Ideally the temporal coherence is the single frequency or single wave length wave.

### Spatial coherence:

An electromagnetic wave with a fixed and non-random phase at a point in space is called spatial coherence.

## Electromagnetic spectrum

Spectrum is the range of an electromagnetic waves. The overall spectrum of electromagnetic waves runs from very low frequencies through the radio frequencies, light, x-rays etc.

The use of electromagnetic spectrum is controlled by government through federal communication commission.

It is important to note that as the frequency increases ( the wavelength decreases), the data rate that can be carried increases. Therefore the short light wavelength can potentially carry higher data rates, particularly in the coherent systems.

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