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The impact of fiber optic transmission in multiservices networks in rwanda

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par Théogène NIYITEGEKA
National university of Rwanda - Bachelor's degree in electronics and communication system engineering  2011
  

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2.2.3 Schrödinger wave equation

The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior, it is also often called the Schrödinger wave equation, and is a partial differential equation that describes how the wave function of a physical system evolves over time.[9]

The time-dependent one-dimensional Schrödinger equation is given by

2

2

2

~ ) ) ) 2 ~

where i is the imaginary unit, is the time-dependent wave function, is h-bar, V(x) is the potential, and is the Hamiltonian operator, However the equation can be separated into temporal and spatial parts using separation of variables to write

) ) ) 2 )

thus obtaining

2

2

~

2

) I 2 7)

Where E represent the system energy

Setting each part equal to a constant then gives the time independent Schrodinger equation for one dimension:

2 )1 ) ) (2.8)

where T(t) = e~
Ø(x,t) = (x)e~

2.2.4 Emission

The figure bellow shows the Emission block of fiber and LASER diode as the source

Figure 6 : Emission block of fiber optical signal and laser diodes as the source.

The most commonly used optical transmitters are semiconductor devices such as light-emitting diodes (LEDs) and LASER diodes, the difference between LEDs and LASER diodes is that LEDs produce incoherent light, while LASER diodes produce coherent light, for use in optical communications, semiconductor optical transmitters must be designed to be compact, efficient, reliable and directly modulated at high frequencies.

The power emitted by the LASER diode is calculated as follow: P=h(I-Is) for I>Is and I<Is ,P=0 (2.9)
Where:

I: Injected current in LASER

Is: Threshold current of LASER

h: Gain of LASER

In an emissive transition, the energy of the photon created in LED diode is given by the difference of the energy levels Ei (initial level of energy ) and Ef (final level of energy ).

hv=Ei - Ef (Electron-volt) 2.2.5 Reception

The main component of an optical receiver is a photo-detector which converts light into electricity using the photoelectric effect, the photo-detector is typically a semiconductor-based photodiode.

Figure 7 : Block scheme of fiber optic receiver

The significant parameters which characterize a photodiode are : sensitivity, obscurity current , the response time, we can remove obscurity current which circulates in the junction , in absence of illumination, thus that current is not provident by photons transmitted by the fiber ,they can have many sources like thermal generation in the intrinsic zone, currents of surface.

The expression of the total current in photodiode is given by the equation. Iph=S.Popt+Iobs (2.10)

Where:

Iph: Total current in photodiode

S: Sensitivity in photodiode

Popt :The optical power received by photodiode

Iobs:Obscurity current

2.2.6 TYPES OF FIBER OPTIC

According to the modes of propagations which they use, the optical fiber can be classified in three categories such as: [8]

> Single mode Optical Fiber.

> Multimode Step Index fiber optic.

> Multimode Graded Index fiber optic.

2.2.6.1 Single mode fiber optic

The diameter of fiber being smaller, it transmits the signal on only one luminous way, it is especially used for very long distances.

This type of fiber presents the greatest performances but its cost is relatively high compared to multimode fiber.

Diameter of core 5 with 10um, cladding 125um;Very high bandwidth and Very weak attenuation 0.5dB/km with 13um and 0.2dB/km with 1.5um very delicate connections.

Figure 8 : Single mode fiber optic

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