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The history behind optic fibers and its invention

From 1985 when at Southampton University was proved a new techinque in the fabrication of optic fibers doped with rare materials which prezent few loses, the optic amplifiers with structure based on these fibers where identified as very important dispozitives in aplications of fiber optic amplifiers. In principle, this is due high efficiency, lower intrinsec sound, low dependence on ploarization and power conservation energy.

The first rare material used was neodymium, the best material for doping solid lasers. After satisfying results, other materials were used in the production of fibre amplifiers like ytterbium and erbium.

In 1986 the group from Southampton made the first Erbium Doped Fibre Amplifier.

Nowadays, erbium doped fiber amplifiers are the most used fiber amplifiers and most known because their amplifying spectrum is the same as the minimum loss in the silicate for 1550 nm.

In order to understand the usage of fiber amplifiers, it is necessary to present few words about optic fibers.

The main principle on which optic fibers are working is the total internal reflection. In the case that a beam of light passes from a dense optic medium into one less dense (for example, from water into air, from glass into air, from glass into water, etc. ) the refraction angle is always bigger than the incident angle and so it can reach the value of π2 for a certain value of the incidence angle θ1smaller than π2. For this value the angle of incidence is called critical angle (θ0). Further, for any other values bigger than the critical angle, the light can not pass into the second medium, instead it is being reflected back intro the first medium according to the laws of reflection. Thus, the separation surface between the two mediums is acting like a mirror. The total absence of light in the second medium and the reflection if it back into the first one, made this phenomena to be called total internal reflection.

After presenting the principle of total internal reflection, it is obvious how an optic fibre works. Thus, a simple glass rod can act similar to an optic fibre.

Although no light passes in the second medium, some electric field exists beyond the boundary line between the two mediums. This secondary wave created along the boundary is called the evanescent wave and its amplitude decreases exponentially as we go away from the line (exp(-x/x0) where x0 is the constant distance at which wave amplitude falls off and x is the distance from the interface). Because of this property, the evanescent wave does not carry any energy out from the first medium.  But if some other material is near the interface, the evanescent wave becomes a real wave and this means that some of the energy will be lost. This is a problem for optical fibres, but it is solved by the construction and design of them.

Optical fibres are made from few concentric layers. First, the core is made of silica glass, sometimes doped with another element in order to change its refractive index.

The core is surrounded by a cladding, which is a guide for the light waves, preventing them from escaping the core. Also, it keeps the light beam going in the proper direction, down the fibre to its destination. Finally, the coating surrounds the cladding with the role of protecting the system inside it.

Because of many different factors, a big part of the input signal is lost during the transmission through the optic fibre.  The phenomena is called attenuation which is defined by the loss of optical power as light travels along the fibre. It can be caused by absorption, scattering and bending losses.

Several years, the loss of information inside the optic fibre was a problem for the development of telecommunications.

Optical amplifiers are characterised by the fact that at their output, the number of photons is larger than at their input. A material that posses this characteristic must have a structure of energy levels in which a population inversion Ni>Nf can be produced (where Ni is the population of the excited state and Nf is the population of the lower lying state).

The most simple way to obtain the basic principle of the erbium doped amplifier is to consider a three-level atomic structure.

The first level is consider to be the ground level (1), the second level is the excitation state for the erbium ions (2) and the third level is the one in which energy is pumped. The population of these levels is labelled N1, N2 and  N3. In order to get the needed amplification, the population between state 1 and state 2 must be inverted. For this, because state 1 is the ground level, at least half of it's population must be excited to the second state.

This is one of the particular advantage of the erbium doped fibre amplifiers. The light fields are confined in a core of very small dimensions, thus over long distances the light intensities reached are very high, so population inversion can be done with small pump powers.

For simplicity, it will be assumed that the pump, the signal intensity and the erbium ion distribution are constant in the transverse dimensions over and affective cross-sectional area of the fibre. Therefore, in order to present the properties  of the erbium doped fibre amplifier mathematically, the fallowing quantities will be defined:

p will be the flux of the incident light intensity at the frequency corresponding to the transition from level 1 to level 3 and corresponds to the pump.

s is the incident flux at frequency corresponding to the 1 to 2 transition and corresponds to the signal field.

Γ32 is the transition probability from level 3 to level 2 and Γ21 is transition probability from level 2 to level 1. Γ21 is defined as

Γ21=1τ2

where τ2  is the lifetime of level 2.

σp is the absorption cross section for the 1 to 3 transition and σs  is the emission cross section for the 2 to 1 transition. It is assumed that the emission and absorption cross sections are equal.

The equation for the population changes are written as:

dN3dt=- Γ32N3+(N1-N3)pσp(1)

dN2dt=- Γ21N2+ Γ32N3-(N2-N1)sσs (2)

dN1dt= Γ21N2-(N1-N3)pσp + (N2-N1)sσs (3)

In an equilibrium state situation: dN3dt=dN2dt=dN1dt=0

and the entire population is given by N=N1+N2+N3.

 From the first equation we can derive:

N3=11+Γ32/pσpN1

When there is a fast decay from level 3 to level 2 (Γ32 is very large), N3 is very close to zero, so the population is mostly on the first and second levels.

Knowing the equation for N3, the population from the second level can be found:

N2=(pσp/Γ32)-Γ21Γ21+sσsN1

 Using this we can derive the population inversion formula:

N2-N1=pσp-Γ21Γ21+2sσs+pσpN

 The condition for population inversion is N2≥N1. Thus, the threshold it will be for N2=N1. Using this, we find the minimum pump flux required(at threshold):

th=Γ21σp

 In the case that Γ32  is very large, population inversion can be written as:

N2-N1N=p,-1p,+1

Where p,=pth.

Logically, if the inversion is negative, there are more absorptions than emissions so the signal has negative gain. Otherwise, if the inversion is positive is positive the signal has positive gain.

The pump intensity is expressed as Ip=hνpp. Thus, the threshold pump intensity will be given by Ith=hνpΓ21σp.

As it can be easily observed from the equation above, the conditions for a low pump threshold are: high absorption cross section and long lifetime of the metastable level.

For erbium, the advantage consists in the very long time of the metastable level which is approximatively 10 ms in silica glass. This property creates a very low threshold, which is one of the main advantages of erbium doped fibre amplifiers.

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