Erbium doped fiber amplifier

Optical waveguides doped with certain rare earth elements are frequently used as the gain medium of a laser or optical amplifier that is close correlated to the modern human life [1,2]. For example, the erbium-doped fiber devices have been extraordinarily successful due to their low noise, high and broad optical gain, and would continue to dominate as part of the backbone of long-haul telecommunications networks [2].

A typical setup of a simple bi-directional pump EDFA is shown case below:

The energy diagram of the Er³⁺ doped system is presented in the following figure. The pumping process takes place between the ground level ⁴I_15/2 and the excited level ⁴I_13/2 (1480 pump) or ⁴I_11/2 (980 pump) with respective fractional populations n₁, n₂ and n₃.

Two critical parameters in the numerical solution of coupled rate and propagating equations are the absorption and emission cross sections. The Er cross section information can be loaded from a data file. The figure below shows the default absorption and emission cross section in the model.

Application example

In this section, we show case the example we used to reproduce the results from reference [1]. The results we reproduced are in good agreement with the ones in the reference book. The INTERCONNECT project file we used is edfa_becker_chapter_6_fiber_a.icp. Following is the schematic design in the file:

where "CWL_1" is the signal that to be amplified, "Pump 1" is the co-propagation pump and "Pump 2" is the counter-propagation pump. The key properties are set based on the following table:

Absorption parameters and emission parameters

The cross section information is loaded from the file er_cross_section.txt and the absorption and emission curves are plotted below:

Fig. 1

Signal Gain in a "Typical" Fiber

To calculate the EDFA gain as well as the forward and backward ASE spectral profiles, we will first consider a specific fiber length of 14 m and investigate in depth the mechanics of the gain process for this length. The signal and pump are taken to be copropagating and injected at z = 0. The gains at the two signal wavelengths of 1530 nm and 1550 nm are computed as a function of pump power. The injected signal power was taken to be a small signal value, -40 dBm. The two pump wavelengths considered were 980 nm and 1480 nm.

Fig. 2 shows gain (a) and population in the upper state (b) as a function of pump power for a 14 m length of erbium-doped Al-Ge silica fiber (fiber A) pumped at 980 nm and 1480 nm.

Fig. 2 (a)

Fig. 2 (b)

We then shift our attention to the distribution of other parameters and this will allow us to explore further the subtle interplay between pump, signal, forward and backward ASE, and the population inversion in the fiber.

Fig. 3 shows population in the upper state as a function of position along a 14 m length of erbium-doped Al-Ge silica fiber, pumped at 980 nm in one case (a) and 1480 nm in the other (b), for the pump powers indicated on the graphs.

Fig. 3(a)

Fig. 3(b)

Fig. 4 shows signal gain at 1530 nm (a) and 1550 nm (b) as a function of position along the fiber for a 14 m length of erbium-doped fiber, for injected pump powers at z = 0 of 4, 10, and 40 mW at 980 nm and an injected signal power of -40 dBm.

Fig. 4(a)

Fig. 4(b)

Fig. 5 shows forward- and backward-traveling ASE in a 14 m long erbium-doped fiber umped at 980 nm, for the two pump powers 10 mW and 40 mW.

Fig. 5(a)

Fig. 5(b)

ASE generation

A parameter sweep is used in simulation to get the ASE power exiting from the fiber end as the function of pump power. The two pump wavelengths considered were 980 nm and 1480 nm.

Fig. 6 shows the forward- and backward-traveling ASE in a 14 m long erbium-doped fiber as a function of pump power, for both 980 nm and 1480 nm pump wavelengths.

Fig. 6

Fig. 7 shows pump power as a function of position along the fiber for a 14 m length of erbium-doped fiber (fiber A), for injected pump powers at z = 0 of 4, 10, 20, and 40 mW at 980 nm, and with an injected signal of power -40 dBm at 1550 nm. At higher pump powers, the pump drops very rapidly, due to depletion of the pump by the backward ASE. At the output end, where the forward ASE is strong, the pump is again depleted.

Fig. 7

We then shift our attention to two other lengths, representing a "short" fiber of 8 m and a "long" fiber of 25 m. Fig. 8 shows signal gain (a) and upper-state population averaged along the fiber length (b) as a function of pump power for an 8 m length of erbium-doped Al-Ge silica fiber pumped at 980 nm and 1480 nm.

Fig. 8(a)

Fig. 8(b)

Fig. 9 shows signal gain (a) and upper-state population averaged along the fiber length (b) as a function of pump power for a 25 m length of erbium-doped Al-Ge silica fiber pumped at 980 nm and 1480 nm.

Fig. 9(a)

Fig. 9(b)

Fig. 10 shows pump absorption (a), signal gain (b), upper-state population (c) and forward and backward ASE (d) as a function of position in a 14 m erbium-doped fiber for 980 nm and 1480 nm pumping with a launched pump power of 20 mW. The signal is at 1550 nm with a launched power of -40 dBm.

Fig. 10(a)

Fig. 10(b)

Fig. 10(c)

Fig. 10(d)

Figure 11 shows the ASE output from the 8 m (a) and 25 m (b) fibers as a function of pump power, for both 980 nm and 1480 nm pumping.

Fig. 11(a)

Fig. 11(b)

Gain as a Function of Fiber Length

Finally, we can study the small signal gain obtained as the length of fiber is varied between a few meter to 40 m.

Fig. 12 shows the signal gain at 1530 nm and 1550 nm for 1480 nm and 980 nm pumping of fiber A, as a function of fiber amplifier length. The launched pump power is 40 mW and the launched signal power is -40 dBm.

Fig. 12

Fig.13 shows the signal gain at 1530 nm and 1550 nm for 1480 nm and 980 nm pumping of fiber A, as a function of fiber amplifier length. The launched pump power is 10 mW and the launched signal power is -40 dBm.

Fig. 13

Spectral Profile of the ASE

Fig.14 shows the forward (a) and backward (b) propagating ASE power spectra (1 nm resolution) for a 14 m length of fiber A. The pump powers are 4, 6, 8, 15, and 20 mW at 980 nm and are indicated on the figure.

Fig. 14(a)

Fig. 14(b)

Fig. 15 shows the forward (a) and backward (b) propagating ASE power spectra (1 nm resolution) for a 14 m length of fiber A. The pump powers are 4, 6, 8, 15, and 20 mW at 1480 nm and are indicated on the figure.

Fig. 15(a)

Fig. 15(b)

Saturation Modeling - Signal Gain and Noise Figure

The effects of gain saturation with signal power can also be modeled. Fig. 16 shows the gain (a) and noise figure (b) as a function of signal wavelength (signal power input -40 dBm), for the pump powers indicated on the graphs, for a 14 m length of erbium-doped fiber (fiber A) pumped at 980 nm.

Fig. 16(a)

Fig. 16(b)

Fig.17 shows the noise figure as a function of signal wavelength (signal power input -40 dBm), for the pump power values 4, 6, 8, 15, and 40 mW, for an 8 m length of erbiumdoped fiber (fiber A) pumped at 980 nm.

Fig. 17

Fig. 18 shows the gain (a) and noise figure (b) as a function of signal wavelength (signal power input -40 dBm), for the pump power values 6, 8, 15, and 40 mW, for a 14 m length of erbium-doped fiber (fiber A) pumped at 1480 nm.

Fig. 18(a)

Fig. 18(b)

Fig. 19 shows the gain as a function of signal output power for the three pump power values 15, 40, and 65 mW, for a 20 m length of fiber A pumped at 1480 nm with a signal at 1530 nm (a) and 1550 nm (b).

Fig. 19(a)

Fig. 19(b)

Fig. 20 shows the gain (a) and the noise figure (b) as a function of input signal power, for a 20 m length of fiber A with a signal input at 1550 nm, for 980 nm pumping with 40 mW of power.

Fig. 20(a)

Fig. 20(b)

Power Amplifier Modeling

The difference configurations including the copropagating and counterpropagating pump configurations can result in different performances of EDFA. Fig.21 shows the signal output power (a) and quantum conversion efficiency (b) as a function of pump power, for a signal input at 1550 nm with -20 dBm launched signal power, for a 14 m fiber pumped at 980 nm, with bidirectional (bi), copropagating (co), and counterpropagating (counter) pumping.

Fig. 21(a)

Fig. 21(b)

Fig. 22 shows the signal and ASE powers, and the upper-state population as a function of fiber position, for a 14 m fiber with a signal input at 1550 nm with -20 dBm and 75 mW of pump power at 980 nm, for a copropagating pump (a)(b) and a counterpropogating pump (c)(d).

Fig. 22(a)

Fig. 22(b)

Fig. 22(c)

Fig. 22(d)

Fig. 23 shows the signal output power, for a length optimized piece of fiber A with a signal input at 1530 nm with -10 dBm input and for a copropagating pump at either 1480 nm or 980 nm (a) and the corresponding optimal lengths (b).

Fig. 23(a)

Fig. 23(b)

References

1. E. Desurvire, Erbium-doped fiber amplifiers: principles and applications, Wiley-Interscience, 2002.

2. Jiang, C., Hu, W. and Zeng, Q., Numerical analysis of concentration quenching model of Er 3+-doped phosphate fiber amplifier. IEEE journal of quantum electronics 39, 266-1271, 2003.

3. P. Blixt et al., “Concentration-dependent upconversion in Er -doped fiber amplifiers: Experiments and modeling,” IEEE Photon. Technol. Lett., vol. 3, p. 996, 1991.

4. E. Delevaque et al., “Modeling of pair-induced quenching in erbium doped silicate fibers,” IEEE Photon. Technol. Lett., vol. 5, pp. 73–75, Jan. 1993

See also

Erbium-doped fiber