Gain and Noise Figure Performance of Erbium-Doped Fiber Amplifiers at 10 Gbps

Fiber loss is a fundamental limitation in realizing long haul point–to-point fiber optical communication links and optical networks. One of the advanced technologies achieved in recent years is the advent of erbium doped fiber amplifiers (EDFAs) that has enabled the optical signals in an optical fiber to be amplified directly in high bit rate systems beyond Tetra bits. In this paper, a simulation of an EDFA has been studied to characterize Gain, Noise Figure of a forward pumped EDFA operating in C band (1525-1565 nm) as functions of Er +3 fiber length, injected pump power, signal input power and Er +3 doping density. The simulation has been done by using Optisystem 5.0 software simulator (license product of a Canadian based company) at bit rate 10 Gbps.


Introduction
The erbium-doped fiber amplifier EDFA has made tremendous progress since its invention in 1986.It replaced the rather involved process of the fiber optic repeater station.It created a revolution in long distance optical communication systems.Simplicity and reliability of the repeater compartment are especially important when the optical fiber cable is used as a submarine cable [1].Erbium Doped Fiber Amplifiers (EDFA) made by doping the silica fiber with erbium ions can operate in a broad range within the 1550 nm window at which the attenuation of silica fiber is minimum and therefore it is ideal for the optical fiber communication systems operating at this wavelength range.According to the research performed in recent years, it is known that the pumping of erbium doped fiber at 980 nm or 1480nm is the most efficient way [2].High gain (30~50dB), large bandwidth (>90 nm), high output power (10~ 20 dBm )and low noise figure (NF=3~5 dB) can be obtained using an erbium doped fiber amplifier optimized for 1550 nm range [3].

Pumping Requirements
The structure of a typical EDFA is shown in figure1.
EDFAs consist of optical couplers to combine pump and signal lights injected to active fiber.The gain characteristics of EDFAs can be pumped at 980 nm or 1480 nm, and with different configurations: backward, forward or bidirectional.In forward pumping, both of the signal and pump lights propagate in the same direction through the fiber whereas in the backward pumping they propagate in the opposite direction.

Simulation Model
Where σ a (λ) and σ e (λ) are radially averaged absorption and emission cross sections of erbium ions, n t is the averaged erbium ion concentration, and Г (λ) is the overlap factor between the optical mode field and erbium ions, which can be determined from optical mode field and erbium ion distribution via the following equation.the fiber has a step index core with a radius of "a", the radially symmetric mode intensity field then is [4] 

Gain and Noise Figure
Gain of an erbium-doped fiber with a length of L is the ratio of signal power at the fiber output to the signal power injected at the fiber input as: Amplified Spontaneous Emission (ASE) noise generates during amplification process is added to the signal leading to decrease in signal to noise ratio(SNR) at the amplifier output.SNR reduction ratio from input to output of the amplifier is defined as Noise n 1 and n 2 are ionic population in two energy levels .

EDFA Simulation Program
This study focuses on the performance characteristics of the amplifier (gain and noise figure) assuming the fundamental LP 01 mode exciting at the pump wavelength (λ p = 980 nm).After entering the required parameters for a desired amplifier in main menu and sub menus of the program gain and noise figure can be obtained as a function of four fundamental fiber parameters namely: fiber length, pump power, signal input power and erbium doping density.
Thus, the required fiber parameters and signal/pump power values can be optimized for a desired EDFA gain-NF performance at 10Gbps.The main menu of the simulation programs are shown in table (1).

Gain Characteristics
The variation of gain with fiber length is shown in figure (2.a) for different pump powers having a constant signal input power and erbium doping density.The gain varies along the fiber length because of pump power variations.For a given amplifier length, the amplifier gain initially increases exponentially with the pump power and then goes to saturation after a certain level of pump power.For a given pump power the amplifier gain increases up to a certain length of fiber, and then begins to decrease after a maximum point.The physical considerations for the decrease in gain is insufficient population inversion due to excessive pump depletion and getting higher losses than the provided gain at the signal wavelength due to high total loss of Erbium doped fiber (fiber background loss+ Er absorption loss).
It is seen that the gain of EDFA sharply increases with the increasing pump power.After a certain level of gain, the increase in gain becomes smaller when the population inversion is provided for all the erbium ions in the fiber and therefore amplifier goes to saturation , in addition, a higher gain can be obtained if a longer erbium doped fiber is used with sufficient pumping.It is seen that EDFA gain decreases with the increasing signal input power.When signal power less than -30 dBm the amplifier works in smallsignal regime where the signal gain is independent of the input signal power indeed the signal power is very weak and the amplifier works in unsaturated gain regime.When the amplifier reaches the saturation the maximum gain dropped by 3 dB below its unsaturated value G max .
The physical meaning of this is the easier saturation of the EDFA at higher signal powers for a constant pump power.The gain variation as a function of erbium doping density is shown in figure 3.b for a 50m long fiber and a constant signal input power for three different pump powers (10mw, 50mw and 100mw).It can be seen that for sufficiently large pump power, the gain linearly increases with increasing erbium ion density and remains constant after a certain level then decreases.Once the amplifier reaches the population inversion, the variation in maximum gain is small despite a high increase in pump power.In the trace obtained for10mw pump power the gain reduces sharply in highly doped fiber due to insufficient pump.

Noise Figure (NF) Characteristics
The

Conclusion
In this study, the performance characteristic of EDFA operating in C band and pumped at 980nm simulated: Gain and noise figure variations were obtained as functions of fiber length, pump power, signal input power and erbium doping density in high bit rate 10Gbps.
According to our results, it was seen that the pump power applied to EDFA sharply reduces due to absorption in erbium doped fiber; in addition gain and NF is strongly dependent on the fiber length, pumping power, signal input power and erbium ion density.The gain varies along the fiber length because of pump power variations .When the EDFA is supplied with sufficient pump power, it was shown that EDFA could be operated in saturation regimes leading to maximum gain and minimum NF.
It was seen that the variation of gain and noise figure as functions of fiber length, pump power, signal input power and erbium doping density do not change when bit rate is increased from (2.5 to 10 Gbps).
An EDFA model based on work by Giles is used to find the amplifier performance at a high bit rate.Additional loss mechnisem such us pump Excited State Absorption ESA, and the effects of background loss are only considered during the Giles algorithm calculation.This EDFA model assumes radially symmetric optical mode and dopant distribution, and that erbium radial distribution is well approximated by an overlap factor.Measured Giles parameters, (α k )-absorption per unit length and (g k )-small signal gain per unit length are used for basic modeling parameters.Giles parameters can be related to absorption and emission cross-sections, overlap factor, and erbium concentration by following overlap integral.

r
is the normalized mode intensity distribution of the fundamental mode, and ion density.If we assume that functions, respectively.Parameters x and y are determined by the characteristics equation that satisfies the boundary conditions at fiber core/cladding interface .

Figure
Figure(NF),which is also used for electronic amplifier:

Figure 2 .
Figure 2.the variation of gain with a) fiber length and b) pump power

Figure 3 .
Figure 3.The variation of gain with a)signal input power and b) Erbium ion density figure from 8 m can b e clearly noticed.The reason for this increase is the decreasing gain with sharp pump depletion.

Figure 4 .
Figure 4.The variation of noise figure with a) fiber length and b) pump power

Table 1 : EDFA properties 6. Typical EDFA Characteristic Obtained With Simulation Program
(2)le(2)represents the typical EDFA parameters used in the simulation program.Cross sections parameters obtained form the shape of absorption and emission cross-section as a function of wavelength in the program [6].

Table 2 .
Typical EDFA parameters used in the simulation program