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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