Modelling - Simulation and Gain Flattening Improvements for an Erbium Doped

Fiber Amplifier

Barış ALTINER Electric and Electronics Department

Yıldız Technical University Istanbul, Turkey

baris1297@gmail.com

N. Özlem ÜNVERDİ Electric and Electronics Department

Yıldız Technical University Istanbul, Turkey

unverdi@yildiz.edu.tr

This paper initially investigates the design parameters for an EDFA (Erbium Doped Fiber Amplifier) simulation perspective. Complex effects which occur during the gain and noise figure improvement operations of EDFA are researched and simulated with an optical environment design software tool named OptiSystem. A gain flattered EDFA is simulated with the expected results.

Keywords; EDFA, optiSystem, simulation

I. INTRODUCTION The new lightwave generation, with vastly improved

capacity and cost, is based on the recent development of EDFA’s. Undersea systems were the early beneficiaries, as EDFA repeaters replaced expensive and unreliable electronic regenerators. The use of Erbium doped fiber amplifiers is desirable in such systems to reduce the number of repeaters. An equally attractive feature of the EDFA is its wide gain bandwidth. Along with providing a gain at 1550nm, in the low-loss window of silicon fiber, it can provide a gain over a band that is more than 4000 GHz wide. With available WDM (Wavelength Division Multiplexing) technics and devices, commercial systems transport more than 16 channels on a single fiber; and the number is expected to reach 100. Thus, more than 250 optical channels with a channel spacing of 15 GHz (0.1 nm) can be multiplexed into a fiber communication link and amplified by optical amplifiers placed periodically. However, optical noise due to ASE (Amplified Spontaneous Emission) restricts the number of amplifiers and/or the amount of amplification. Hence, installed systems can be upgraded many fold without adding a new fiber, and new WDM systems can be built inexpensively with much greater capacity. This condition indicates the signifiance of gain and noise figure improvements for EDFA design [1]. In this study, initially design parameters for a three-level EDFA model will be investigated, then optimization of EDFA gain will be addressed in the third section.

II. EDFA DESIGN PARAMETERS CONTENT Most of the treatments of the Er-Doped fiber amplifier

starts out by considering a pure three-level atomic system. Most of the important characteristics of the amplifier can be obtained from that simple model and its underlying assumptions [2].

Figure 1. The three-level system used for an EDFA amplifier model.

The transition rates between levels 1 and 3 are proportional to the populations in those levels and to the product of the pump flux ϕp and pump cross-section σp. The transition rates between level 1 and 2 are proportional to the populations in those levels and to the product of the signal flux ϕs and signal cross section σs. The spontaneous transition rates of the ion are given by Γ32 and Γ21.

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We consider a three-level system in Figure 1, with a ground state denoted by 1, an intermediate state labeled 3 (into which energy is pumped), and state 2. State 2 often has a long lifetime in the case of a good amplifier. State 2 is the upper level of the amplifying transition and state 1 is the lower level. The populations of the level are labeled N1, N2 and N3. This three-level system is intended to represent part of the energy level structure of Er+3 that is relevant to the amplification process. To obtain amplification, we need a population inversion between states 1 and 2, and since state 1 is also the ground state, at least half of the total population of erbium ions need to be excited to level 2 to have population inversion. This raises the threshold pump power needed for amplification [3].

The incident light intensity flux at the frequency corresponding to the 1-to-3 transition (in number of photons per unit time per unit area ) is denoted by ϕp (absorption cross-section) and corresponds to the pump. The incident flux at the frequency corresponding to the 1-to-2 transition (in number of photons per unit time per unit area ) is denoted by ϕs (emission cross-section) and corresponds to the signal field. In particular, transition probability from level 3 -> level 2 can be written as Γ32 and the transition probability from level 2 -> level 1 can be written as Γ21. In the case of the Er+3 level 2 -> level 1 transition Γ21 is mostly non-radiative. This is due to the fact that there are no intermediate states between levels 1 and 2 to which ions excited to level 2 can relax for Er+3.

The rate equations for the population changes are written as [1];

ppNNNdt

dN σϕ)( 313323 −+Γ−= (1)

ssNNNNdt

dNσϕ)( 12332221

2 −−Γ+Γ−= (2)

sspp NNNNNdt

dNσϕσϕ )()( 1231221

1 −+−+Γ= (3)

In a steady-state condition, time derivatives will all

be zero,

0321 ===dt

dNdt

dNdt

dN (4)

and the total population N is given by,

321 NNNN ++= (5)

We can write the N3 population as;

132

3

1

1 NN

ppσφΓ

+= (6)

According to these equations, for example below the pump threshold inversion is negative, above the pump threshold it is positive. When the negative inversion occurs, there are more absorptive transitions than emissive transitions at the wavelength, the signal gain is negative as shown below Figure 2:

Figure 2. Fractional population inversion in a three-level system.

III. OPTIMIZING EDFA GAIN FOR WDM SYSTEMS AND RESULTS

The gain of EDFA will be flattened by optimizing the fiber length and pump power. One difficulty in implementing a WDM system including EDFA’s is that the EDFA gain spectrum is wavelength dependent. This effect results in a SNR (Signal-to-Noise Ratio) differential between channels after passing through a cascade of EDFA’s. Several methods to correct this non-uniformity of the gain are suggested, for example using internal or external filters or thermally decreasing the homogeneous line broadening of the amplifier. These methods require either extra components or are complicated. Project layout is based on optimizing the EDFA itself by controlling the fiber length and pump power for a given input power and desired output power. Figure 3 project layout shows how to the gain of EDFA can be flattened by using this technique [4].

The inputs to EDFA are equalized wavelength multiplexed signals in the wavelength band of 12 nm (1546 – 1558nm) with 0.8nm separations. Power of each channel is -26 dBm. Default fiber parameters are used in this case. The desired gain is 23 dB. We also want an output power of more than 8.5 dBm and a gain flatness of less than 0.5 dB.

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Figure 3. Layout of the EDFA gain flattening project

Fiber length and power are selected as parameters to be optimized to achieve the desired gain under the output power and gain flatness constraints. The Dual Port WDM Analyzer measures gain and flatness, whereas the Optical Power Meter measures the output power. Initial parameter values are as follows: Pump power is 100 mW; fiber length is 4m. The pump power is bound between 0 and 160mW. The fiber length is bound between 1 and 40m. Parameter termination tolerance is 1, results and constraints termination tolerance is 0.1 .

Figure 4. Signal and noise spectrum of an un-optimized EDFA

Pump power and fiber length are selected as 100 mW and 4m. In this case, even though the average gain is about 30 dB, gain flatness is about 2.24 dB as shown in Figure 4, which is much higher than required.

Figure 5. Signal and noise spectrum of an optimized EDFA.

Optimum pump power and fiber length are found to be 24.13 mW and approximately 5.22 m. At these values, an average gain of 23 dB and a gain flatness of 0.29 dB are achieved and shown in Figure 5. The output signal power is about 8mW.

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IV. CONCLUSIONS In this study, EDFA parameters have been investigated to

realize a optimized EDFA. After numerical calculations, pump power, fiber flattened gain and length are optimized to achieve the desired targets for an EDFA with Optisystem 7.0 optical environment simulation tool. In this simulation the gain flattening improvement results satisfied the condition of not repeating the optical signal in WDM Network. Gain flattening improvement is achieved at expected power levels and noise power level is acceptable to design a high level efficient EDFA.

REFERENCES [1] P. C. Becker, “Erbium-Doped Fiber Amplifiers Fundamentals and

Technology”, Academic Press, San Diego, USA, 1999. [2] S. F. Su, “Flattening of Erbium-doped fiber amplifier gain spectrum

using an acousto-optic tunable filter”, Electronics Letters. p29, 477, Toronto, 1993.

[3] E. L. Goldstein, “Inhomogeneously broadened fiber amplifier cascade for transparent multiwavelength lightwave networks”, J.Light Tech, Electronic Letter. p13, 782, Boston, 1995.

[4] B. ALTINER, “EDFA Modelling & Gain, Noise Figure Optimization Analysis for WDM Networks”, M. Sc. Thesis, Yıldız Technical University, İstanbul, 2009.

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