**6. Effects of erbium transversal distribution profiles on EDFA performance**

Over the past years, Erbium-doped fiber amplifiers (EDFAs) have received great attention due to their characteristics of high gains, bandwidths, low noises and high efficiencies. As a key device, EDFA configures wavelength division multiplexing systems (WDMs) in optical telecommunications, finding a variety of applications in traveling-wave fiber amplifiers, nonlinear optical devices and optical switches. The EDFA uses a fiber whose core is doped with trivalent erbium ions as the gain medium to absorb light at pump wavelengths of 980 nm or 1480 nm and emit at a signal wavelength band around 1500 nm through stimulated

Doped Fiber Amplifier Characteristic Under Internal and External Perturbation 145

(a)

(b)

(c) Fig. 22. The Erbium distribution profile of EDFA (a) at different values of β when, θ=1 and δ=1.5 (b) at different values of ߠ when δ=1.5 and β=1. (c) at different values of δ when θ=1

and β =1.5.

emission. Theoretical study on optimization of rare-earth doped fibers, such as fiber length and pump power has grown along with their increased use and greater demand for more efficient amplifiers (Emamai et al., 2010). Previously, one of the most important issues in improving fiber optic amplifier performance is optimization of the rare-earth dopant distribution profile in the core of the fiber. Earlier approaches to numerical modeling of EDFA performance have assumed that the Erbium Transversal Distributions Profile (TDF) follow a step profile.

Only the portion of the optical mode which overlaps with the erbium ion distribution will stimulate absorption or emission from erbium transitions. The overlap factor equation is defined by (Desurvire, 1982):

$$
\Gamma(\mathcal{A}) = \frac{2\pi}{N\_T} \int\_0^\nu \Psi(r,\nu) \times n\_\tau(r) \times r \times dr \tag{20}
$$

Ψ(r, υ) is the LP01 fiber optic mode envelope, which is almost Gaussian and is defined as :

$$\Psi(r,\nu) = \begin{cases} j\_0^2(u\_k r/a) & r \le a \\ \frac{j\_0^2(u\_k)}{K\_0^2(w\_k)} K\_0^2(w\_k r/a) & r \ge a \end{cases} \tag{21}$$

where J0 and K0 are the respective Bessel and modified Bessel functions and uk and wk are the transverse propagation constants of the LP01 mode. NT is total dopant concentration per unit per length which is defined by:

$$N\_{\tau} = 2\pi \prod\_{0}^{\stackrel{\text{v}}{\sim}} n\_{\tau}(r) \times r \times dr \tag{22}$$

Various profiles of erbium transversal distributions can be used for describing mathematical function of EDFA. Two main requirement on choosing erbium transversal distribution functions are; flexibility to be adapted to a collection of profile as broad as possible and dependence on a number of the parameters as low as possible. The optimum transversal distribution function should be (Yun et al., 1999):

$$n\_{\boldsymbol{r}}\left(\boldsymbol{r}\right) = n\_{\boldsymbol{r}\_{\cdot,\max}} \exp\left\{-\left\|\left\lfloor\boldsymbol{r}-\boldsymbol{\delta}\right\rfloor/\theta\right\|^{\boldsymbol{\theta}}\right\}\tag{23}$$

where nT,maz is the value of the maximum erbium concentration per unit volume. β, θ and δ are distribution profile parameters which construct the profile shapes. θ and β are defined as dopant radius and the roll-off factor of the profile respectively. In practical, it would seem difficult to maintain a high concentration of Erbium in the center of the core, due to diffusion of erbium ions during the fabrication. Modifying the δ value, low ion concentration at the core center can be achieved. The Erbium distribution profiles of EDFA with different values β, θ and δ are depicted in Fig. 22. Figure 22(a) shows several of β values with fixed values of θ=1 and δ=1.5. Figure 22(b) shows the effect of θ values with fix values of δ=1.5 and β=1 while figure 22(c) shows several values of δ changes with fixed values of θ=1 and β =1.5.

emission. Theoretical study on optimization of rare-earth doped fibers, such as fiber length and pump power has grown along with their increased use and greater demand for more efficient amplifiers (Emamai et al., 2010). Previously, one of the most important issues in improving fiber optic amplifier performance is optimization of the rare-earth dopant distribution profile in the core of the fiber. Earlier approaches to numerical modeling of EDFA performance have assumed that the Erbium Transversal Distributions Profile (TDF)

Only the portion of the optical mode which overlaps with the erbium ion distribution will stimulate absorption or emission from erbium transitions. The overlap factor equation is

Ψ(r, υ) is the LP01 fiber optic mode envelope, which is almost Gaussian and is defined as :

*N <sup>T</sup>*

 )(),( <sup>2</sup> )( <sup>0</sup> 

*T*

  *wK uj*

0

2 0

 

),( <sup>2</sup>

*r*

where J0 and K0 are the respective Bessel and modified Bessel functions and uk and wk are the transverse propagation constants of the LP01 mode. NT is total dopant concentration per

*ararwK*

*k*

)/(

*k k*

2 0

)(

2 0

Various profiles of erbium transversal distributions can be used for describing mathematical function of EDFA. Two main requirement on choosing erbium transversal distribution functions are; flexibility to be adapted to a collection of profile as broad as possible and dependence on a number of the parameters as low as possible. The optimum transversal

*<sup>T</sup> <sup>T</sup> drrrnN* )(2 0 

 (23) where nT,maz is the value of the maximum erbium concentration per unit volume. β, θ and δ are distribution profile parameters which construct the profile shapes. θ and β are defined as dopant radius and the roll-off factor of the profile respectively. In practical, it would seem difficult to maintain a high concentration of Erbium in the center of the core, due to diffusion of erbium ions during the fabrication. Modifying the δ value, low ion concentration at the core center can be achieved. The Erbium distribution profiles of EDFA with different values β, θ and δ are depicted in Fig. 22. Figure 22(a) shows several of β values with fixed values of θ=1 and δ=1.5. Figure 22(b) shows the effect of θ values with fix values of δ=1.5 and β=1 while figure 22(c) shows several values of δ changes with fixed

,max ( ) exp{ [| | / ] } *T T nr n r*

*drrrnr*

*araruj*

*k*

)/( )(

 (20)

(21)

(22)

follow a step profile.

defined by (Desurvire, 1982):

unit per length which is defined by:

values of θ=1 and β =1.5.

distribution function should be (Yun et al., 1999):

Fig. 22. The Erbium distribution profile of EDFA (a) at different values of β when, θ=1 and δ=1.5 (b) at different values of ߠ when δ=1.5 and β=1. (c) at different values of δ when θ=1 and β =1.5.

Doped Fiber Amplifier Characteristic Under Internal and External Perturbation 147

Fig. 24. (a) Gain profile of EDFA at ߠ=2) b) Noise figure of EDFA ߠ=2

mW respectively.

The effect of Erbium transversal distribution profile on the performance of an EDFA is investigated. The EDFA uses a 14m long EDF as the gain medium, which is pumped by a 980 nm laser diode via a WDM coupler. An optical isolator is incorporated in both ends of optical amplifier to ensure unidirectional operation. Two types of EDF with the same fiber structure and doping concentration but different on distribution profile are used in the experiment. Fig. 25 shows the Erbium transversal distribution profile of both fibers, which have a doping radius of 2 μm and 4 μm as shown in Figs. 25(a) and (b), respectively. In the experiment, the input signal power and 980nm pump power are fixed at -30dBm and 100

Figs. 23(a) and (b) demonstrate the gain and noise figure trends of EDFA, respectively at different ߚ and ߠ values of fiber. The input signal power and input pump power is fixed at - 30 dBm and 100 mW respectively while the EDF length is fixed at 14m.

Fig. 23. (a) Gain profile of EDFA at ߚ=0) b) Noise figure of EDFA ߚ=0

Fig. 24 shows the gain trends of EDFA at different ߚ and δ values of fiber. The input signal power and input pump power is fixed -30 dBm and 100 mW respectively. The EDF length is 14m long. By comparison between overlap factor and gain results, it is intuitive that the gain result follows the overlap factor values of the fiber. In the low ߠ values of the fiber in the same EDF concentration the gain decrease by decreasing the ߠ as depicted on figure 24, this is the results of high erbium intensity at the core and the quenching effect on the fiber amplifier.

Figs. 23(a) and (b) demonstrate the gain and noise figure trends of EDFA, respectively at different ߚ and ߠ values of fiber. The input signal power and input pump power is fixed at -

(a)

(b)

Fig. 24 shows the gain trends of EDFA at different ߚ and δ values of fiber. The input signal power and input pump power is fixed -30 dBm and 100 mW respectively. The EDF length is 14m long. By comparison between overlap factor and gain results, it is intuitive that the gain result follows the overlap factor values of the fiber. In the low ߠ values of the fiber in the same EDF concentration the gain decrease by decreasing the ߠ as depicted on figure 24, this is the results of high erbium intensity at the core and the quenching effect on the fiber amplifier.

Fig. 23. (a) Gain profile of EDFA at ߚ=0) b) Noise figure of EDFA ߚ=0

30 dBm and 100 mW respectively while the EDF length is fixed at 14m.

Fig. 24. (a) Gain profile of EDFA at ߠ=2) b) Noise figure of EDFA ߠ=2

The effect of Erbium transversal distribution profile on the performance of an EDFA is investigated. The EDFA uses a 14m long EDF as the gain medium, which is pumped by a 980 nm laser diode via a WDM coupler. An optical isolator is incorporated in both ends of optical amplifier to ensure unidirectional operation. Two types of EDF with the same fiber structure and doping concentration but different on distribution profile are used in the experiment. Fig. 25 shows the Erbium transversal distribution profile of both fibers, which have a doping radius of 2 μm and 4 μm as shown in Figs. 25(a) and (b), respectively. In the experiment, the input signal power and 980nm pump power are fixed at -30dBm and 100 mW respectively.

Doped Fiber Amplifier Characteristic Under Internal and External Perturbation 149

Fig. 26. Numerical and experimental gain comparison of 2μm and 4μm doping radius EDFA

In this reserch work a macro-bending approach is demonstrated to increase a gain and noise figure at a shorter wavelength region of EDFA. In the conventional double-pass EDFA configuration , macro-bending improves both gain and noise figure by approximately 6 dB and 3 dB, respectively. These improvements are due to the longer wavelength ASE suppression by the macro-bending effect in the EDF. A new approach is proposed at secound section to achieve flat gain in C-band EDFA with the assistance of macro-bending. The gain flatness is optimum when the bending radius and fiber length are 6.5 mm and 9 meter respectively. This simple approach is able to achieve ±1 dB gain flatness over 25 nm. This cost effective method, which improves the gain variation to gain ratio to 0.1, does not require any additional optical components to flatten the gain, thus reducing the system complexity. The proposed design achieves temperature insensitivity over a range of temperature variation. The gain flatness is optimized when the bending radius and fiber length are 6.5mm and 2.5m respectively. This simple approach is able to achieve 0*.*5 dB gain flatness over 35nm with no dependency on temperature variations. It is a cost effective method which needs 100mW pump power and does not require any additional optical components to flatten the gain, thus reducing the system complexity. At the end the effect of ETP on the performance of the EDFA is theoretically and experimentally investigated. The ETP can be used to optimize the overlap factor, which affects the absorption and emission dynamics of the EDFA and thus improves the gain and noise figure characteristics of the amplifier. It is experimentally observed that the 1550 nm gain is improved by 3 dB as the doping radius is reduced from 4μm to 2μm. This is attributed to the Erbium absorption

**7. Conclusion** 

Fig. 25. Erbium TDP. (a) 2μm doping radius (b) 4μm doping

Fig. 26 compares the experimental and numerical results on the gain characteristics for both EDFAs with the 2μm and 4μm doping radius. As expected from the theoretical analysis, the amplifier's gain is higher with 2μm doping radius compared to that of 4μm doping radius at the 1550 nm wavelength region. In the simulation, fiber distribution profile parameters are set as θ=2, β=1.5 and δ=0 for 2μm doping radius which for 4μm doping radius, fiber distribution profile parameters are set as θ=4, β=4 and δ=0.8. The numerical gain is observed to be slightly higher than the experimental one. This is most probably due to splicing or additional loss in the cavity, which reduces the attainable gain. In the case of 4 μm dopant radius, the overlap factor is higher since the overlap happens throughout the core region. However, the high overlap factor will affect the erbium absorption of both the pump and signal. If one considers the near Gaussian profile of the LP01 mode, the erbium in the outer radius of the core tend to be less excited due to the lower pump intensity. The remaining Erbium ions absorption capacity in the outer radius of the core will be channeled to absorbing the signal instead. In the case of 2 μm dopant radius, the overlap factor is lower since the overlap happens only in the central part of the core region. If one considers the near Gaussian profile of the LP01 mode, the erbium in the inner radius of the core tend to be more excited due to the higher pump intensity. Since the outer radius of the core is not doped with Erbium, the lower intensity pump in the outer radius will not be absorbed. The advantage of reduced doping region is that the Erbium absorption only takes place in the central part of the core. Since, the pump intensity is the highest here; the Erbium population can be totally inverted, thus contributing to higher gain. Furthermore, the signal in the outer radius will no longer be absorbed. Hence, the signal will receive a net emission from the erbium which then contributes to higher gain.

Fig. 26. Numerical and experimental gain comparison of 2μm and 4μm doping radius EDFA
