**4. Modelling of the macro-bent EDFA**

Macro-bending is defined as a smooth bend of fiber with a bending radius much larger than the fiber radius (Marcuse, 1982). Macro-bending modifies the field distribution in optical fibers and thus changes the spectrum of the wavelength dependent loss. Various mathematical models have been suggested to calculate the bending effects in optical waveguide. Earlier references for bending loss in single mode fibers with step index profiles was developed by Marcuse. According to Marcuse, the total loss of a macro bent fiber includes the pure bending loss and transition loss caused by mismatch between the quasimode of the bending fiber and the fundamental mode of the straight fiber (Marcuse, 1976). The analytical expression for a single meter fiber bend loss α can be expressed as follows (Marcuse, 1982):

$$\alpha(\nu) = \frac{\sqrt{\pi}k^{\frac{\nu}{2}} \exp\left[-\frac{2}{3} \left(\overset{\nu}{\underset{\nu}{\geqslant}} \overset{\nu}{\geqslant}\_{\text{s}}\right) \mathbb{R}\right]}{\mathrm{e}\_v \mathcal{I}^{\frac{\nu}{2}} V^{\frac{\nu}{2}} \sqrt{\mathbb{R}} K\_{v-1}(\gamma a) K\_{v+1}(\gamma a)}\tag{1}$$

where eν=2 , a is the radius of fiber core, R is the bending radius, βg is the propagation constant of the fundamental mode, K(υ-1)(γα) and K(υ+1)(γα) are the modified Bessel functions and V is the well-known normalized frequency, which is defined as (Agrawal, 1997):

$$V = \frac{2\,\text{mA}.NA}{\lambda} \tag{2}$$

The values of k and γ can be defined as follows (Gred & Keiser, 2000):

Doped Fiber Amplifier Characteristic Under Internal and External Perturbation 135

The stimulated absorption, emission rate and pumping rate are calculated respectively as

(9)

*s*

*s*

*Ahv <sup>W</sup>* )( <sup>21</sup> 

*R*

*Ahv <sup>W</sup>* )( <sup>12</sup> 

*ASES ASE*

*ssSA PPP*

*<sup>P</sup>*

*A SE se se ASE s se ASE*

 

 

(10)

*<sup>S</sup> ASE ASE*

*ssSE PPP*

where *σPA* is the *4I11/2 → 4I15/2* absorption cross sections of the 980 nm forward pumping. *σSA* and *σSE* are the stimulated absorption and the stimulated emission cross-section of input signal respectively. PASE is the amplified spontaneous emission (ASE) power and A is the effective area of the EDF. The light-wave propagation equations along the erbium-doped

*p PPPA P Ahv*

 )(

(13)

 *PEP PA <sup>P</sup> <sup>P</sup> <sup>P</sup> PPNN*

2 1 <sup>2</sup> ( )( ) ( )2 *ASE*

<sup>1</sup> )

)(( ) <sup>2</sup> <sup>1</sup>

 

*dP* )(( <sup>2</sup>

*dP N NP h N P*

 (14) Absorption and emission coefficient are essential parameters to know for any types of EDFA modelling. With aid of cutback method the absorption coefficient of fiber was measured experimentally (Hajireza, et al. 2010). For an EDF with uniform radial core doping it is preferred to use the MFD expression developed by (Myslinski et al.,1996). The absorption cross section and emission cross section in room temperature were calculated respectively as

*ses sa ss <sup>s</sup> PPNN*

*a e*

 

<sup>0</sup> ( ) ( )exp( )

 

a nt (15)

(16)

*B h E*

 is absorption Cross section that describes the chance of an erbium ion absorbing a photon at wavelength *λ*. Cross section is given in terms of area because it represents the area is occupied by each erbium ion ready to absorb. Multiplying this by the number of ions, *s*, gives the total area of the fiber cross section that has erbium ready to absorb. The overlapping factors between each radiation and the fiber fundamental mode, Г (λ) can be

*K T* 

fiber can be established as follows (Parekhan et al., 1988):

*dz*

*dz dP*

(11)

(12)

follows (Desurvire et al., 1990) :

*dz*

follows:

 <sup>a</sup> 

expressed as (Desurvire, 1990):

$$k = \sqrt{n\_1^2 k^2 - \beta\_s^2} \tag{3}$$

$$
\gamma = \sqrt{\beta\_\text{g}^2 - n\_2^2 k^2} \tag{4}
$$

For an optical fiber with length L, bending loss (α) is obtained by: Equation (3) agrees well with our experimental results for macro-bent single-mode fiber. *<sup>L</sup> l* 68.8))2log(exp(10 *aL*

The macro-bent EDFA is modeled by considering the rate equations of a three level energy system. Fig.11 shows the absorption and emission transitions, respectively in the EDFA considering a three-level energy system with 980 nm pump. Level 1 is the ground level, level 2 is the metastable level characterized by a long lifetime, and level 3 the pump level (Armitage, 1988) . The main transition used for amplification is from the 4I13/2 to 4I15/2 energy levels. When the EDF is pumped with 980 nm laser, the ground state ions in the 4I15/2 energy level can be excited to the 4I11/2 energy level and then relaxed to the 4I13/2 energy level by non-radiative decay. The variables N1, N2 and N3 are used to represent population of ions in the 4I15/2, 4I13/2 and 4I11/2 energy levels respectively. According to Fig. 11 we can write the rate of population as follows (Desurvire, 1994):

$$\frac{dN\_1}{dz} = -R\_{13}N\_1 + R\_{31}N\_3 - W\_{12}N\_1 + W\_{21}N\_2 + {}^R A\_{21}N\_2 \tag{5}$$

$$\frac{dN\_2}{dt} = -W\_{12}N\_1 - W\_{21}N\_2 - \prescript{R}{}{A}\_{21}N\_2 + \prescript{NR}{}{A}\_{23}N\_3\tag{6}$$

$$\frac{dN\_3}{d\mathbf{z}} = R\_{13}N\_1 - R\_{31}N\_3 - {}^{\text{NR}}A\_{32}N\_3 \tag{7}$$

$$N\_T = N\_1 + N\_2 + N\_3 \tag{8}$$

where *R13* is the pumping rate from level 1 to level 3 and *R31* is the stimulated emission rate between level 3 and level 1. The radiative and non radiative decay from level *i* to *s* is represented by *RAij* and *NRAij*. The interaction of the electromagnetic field with the ions or the stimulated absorption and emission rate between level 1 and level 2 is represented by *W12* and *W21 .*

Fig. 11. Three level energy system of EDF pump absorption, and signal transitions.

222 <sup>1</sup> *<sup>g</sup> knk*

22 2 <sup>2</sup> *kn*

For an optical fiber with length L, bending loss (α) is obtained by:

*<sup>g</sup>*

The macro-bent EDFA is modeled by considering the rate equations of a three level energy system. Fig.11 shows the absorption and emission transitions, respectively in the EDFA considering a three-level energy system with 980 nm pump. Level 1 is the ground level, level 2 is the metastable level characterized by a long lifetime, and level 3 the pump level (Armitage, 1988) . The main transition used for amplification is from the 4I13/2 to 4I15/2 energy levels. When the EDF is pumped with 980 nm laser, the ground state ions in the 4I15/2 energy level can be excited to the 4I11/2 energy level and then relaxed to the 4I13/2 energy level by non-radiative decay. The variables N1, N2 and N3 are used to represent population of ions in the 4I15/2, 4I13/2 and 4I11/2 energy levels respectively. According to Fig. 11

(7)

*dN <sup>R</sup>*

*dN <sup>R</sup> NR*

221221112331113 <sup>1</sup> *NANWNWNRNR*

221221112 323 <sup>2</sup> *NANANWNW*

13 1 31 3 32 3 *dN NR <sup>R</sup> N RN AN dz*

where *R13* is the pumping rate from level 1 to level 3 and *R31* is the stimulated emission rate between level 3 and level 1. The radiative and non radiative decay from level *i* to *s* is represented by *RAij* and *NRAij*. The interaction of the electromagnetic field with the ions or the stimulated absorption and emission rate between level 1 and level 2 is represented by

*<sup>T</sup> NNNN* <sup>321</sup>

Fig. 11. Three level energy system of EDF pump absorption, and signal transitions.

NRA32

4I15/2 N1

W21

R31 W12

RA21

we can write the rate of population as follows (Desurvire, 1994):

*dz*

4I13/2

R13

4I11/2

*dt*

3

macro-bent single-mode fiber.

*l* 68.8))2log(exp(10 *aL*

*<sup>L</sup>*

*W12* and *W21 .*

(3)

(4)

(5)

(8)

N2

NRA21

RA31 RA32

N3

(6)

Equation (3) agrees well with our experimental results for

The stimulated absorption, emission rate and pumping rate are calculated respectively as follows (Desurvire et al., 1990) :

$$W\_{12} = \frac{\sigma\_{sl}(\hat{\lambda}\_s)\Gamma\_s}{h\nu\_s A} \left[ P\_S + P\_{\text{ASE}}{}^\* + P\_{\text{ASE}}{}^- \right] \tag{9}$$

$$W\_{21} = \frac{\sigma\_{\rm SE}(\hat{\lambda}\_{\rm s}) \Gamma\_s}{h \nu\_s A} \left[ P\_S + P\_{\rm sSE} \stackrel{\ast}{\ } + P\_{\rm sSE} \stackrel{\cdots}{\ } \right] \tag{10}$$

$$R = \frac{\sigma\_{pA}(\mathcal{A}\_p)\Gamma\_p}{h\nu\_p A} \left[P\_p\right] \tag{11}$$

where *σPA* is the *4I11/2 → 4I15/2* absorption cross sections of the 980 nm forward pumping. *σSA* and *σSE* are the stimulated absorption and the stimulated emission cross-section of input signal respectively. PASE is the amplified spontaneous emission (ASE) power and A is the effective area of the EDF. The light-wave propagation equations along the erbium-doped fiber can be established as follows (Parekhan et al., 1988):

$$\frac{dP\_{ASE}^{\pm}}{dz} = \pm \Gamma(\mathcal{k}\_{ASE}) (\sigma\_{ss} N\_{\pm} - \sigma\_{ss} N\_{\pm}) \times P\_{ASE}^{\pm} \pm \Gamma(\mathcal{k}\_{\circ}) 2h\nu \Delta \,\nu \sigma\_{ss} N\_{\pm} \mp a P\_{ASE}^{\pm} \tag{12}$$

$$\frac{dP\_p^\*}{dz} = \Gamma(\mathcal{A}\_\rho)(\sigma\_{p\mathbb{R}} N\_2 - \sigma\_{p\mathbb{A}} N\_1) \times P\_p^\* - aP\_p^\* \tag{13}$$

$$\frac{dP\_s^{+}}{dz} = \Gamma(\lambda\_i)(\sigma\_{su}N\_2 - \sigma\_{su}N\_1) \times P\_s - aP\_s \tag{14}$$

Absorption and emission coefficient are essential parameters to know for any types of EDFA modelling. With aid of cutback method the absorption coefficient of fiber was measured experimentally (Hajireza, et al. 2010). For an EDF with uniform radial core doping it is preferred to use the MFD expression developed by (Myslinski et al.,1996). The absorption cross section and emission cross section in room temperature were calculated respectively as follows:

$$a\left(\mathbb{A}\right) = \sigma \mathbf{a}\left(\mathbb{A}\right) \Gamma\left(\mathbb{A}\right) \text{nt} \tag{15}$$

$$
\sigma a(\nu) = \sigma e(\nu) \exp(\frac{h\nu - E\_0}{K\_B T}) \tag{16}
$$

 <sup>a</sup> is absorption Cross section that describes the chance of an erbium ion absorbing a photon at wavelength *λ*. Cross section is given in terms of area because it represents the area is occupied by each erbium ion ready to absorb. Multiplying this by the number of ions, *s*, gives the total area of the fiber cross section that has erbium ready to absorb. The overlapping factors between each radiation and the fiber fundamental mode, Г (λ) can be expressed as (Desurvire, 1990):

Doped Fiber Amplifier Characteristic Under Internal and External Perturbation 137

Parameter Unit Value

Doping density 1.6 [×1025 ions/m3]

The bending loss spectrum of the EDF is measured across the wavelength region from 1530 nm to 1570 nm. Fig. 14 illustrates the bending loss profile at bending radius of 4.5 mm, 5.5 mm and 6.5 mm, which clearly show an exponential relationship between the bending loss and wavelength, with strong dependencies on the fiber bending radius. Bending the EDF causes the guided modes to partially couple into the cladding layer, which in turn results in

Saturation paramter (typ) 7.985 [×1015 /ms]

Fig. 13. Bending loss spectral for different bending radius

Table 1. Numerical parameter used in the simulation

NA (typ) 0.22 λcut-off (typ) 935 [nm] dcore (typ) 3.3 [µm]

τ (Life time) 10 [ms]

λpump 980 [nm] MFDpump 3.7 [µm] A 1.633x10-11 m2 nclad 1.451 ncore 1.469 λsig 1550 [nm] MFDsig 5.3 [µm] Гsig 0.74 - Гpump 0.77 σSA(λs) 2.9105x10-25 m2 σSE(λs) 4.1188x10-25 m2 σ PA(λp) 2.78x10-25 m2 σ PE(λp) 0.81056x10-25 m2 Δν 3100 GHz

$$\Gamma(\mathcal{J}) = 1 - e^{\frac{2b^2}{\alpha\_0^2}} \tag{17}$$

$$a\_0 = a \left( 0.761 + \frac{1.237}{V^{1.5}} + \frac{1.429}{V^6} \right) \tag{18}$$

where ω0 is the mode field radius defined by equation (18), a is the core diameter, b is the Erbium ion-dopant radius and V is the normalized frequency. The absorption and emission cross section has shown in fig.12 (Michael & Digonnet, 1990). Background scattering loss and wavelength-dependent bending loss is represented by α (λ). Wavelength-dependent bending losses used in this numerical model for three different bending diameters as shown in Fig. 13. The bending loss spectral profile is obtained theoretically with help of Marcuse formula (Marcuse, 1982).. These bending radius values are chosen because significant bending losses can be observed in the L-band region. The bending loss profile indicates the total distributed loss for different bending radius associated with macro-bending at different EDF lengths. This information is important when choosing the appropriate bending radius to achieve sufficient suppression of the gain saturation effect in L-band region and reduces the energy transfer from C-band to the longer wavelength region (Giles & Digiovanni, 1990).

Fig. 12. Absorption and Emission Cross section.

In order to solve the population rate in steady state condition, the time derivatives of for pump and signal powers, equations are set to zero. All the equations are first order differential equations and the Runge-Kutta method is used to solve these equations. The variables used in the numerical calculation and their corresponding values are shown in Table 1.

(17)

1)(

*a*

> 

*b e* 

 (18) where ω0 is the mode field radius defined by equation (18), a is the core diameter, b is the Erbium ion-dopant radius and V is the normalized frequency. The absorption and emission cross section has shown in fig.12 (Michael & Digonnet, 1990). Background scattering loss and wavelength-dependent bending loss is represented by α (λ). Wavelength-dependent bending losses used in this numerical model for three different bending diameters as shown in Fig. 13. The bending loss spectral profile is obtained theoretically with help of Marcuse formula (Marcuse, 1982).. These bending radius values are chosen because significant bending losses can be observed in the L-band region. The bending loss profile indicates the total distributed loss for different bending radius associated with macro-bending at different EDF lengths. This information is important when choosing the appropriate bending radius to achieve sufficient suppression of the gain saturation effect in L-band region and reduces the energy transfer from C-band to the longer wavelength region (Giles & Digiovanni, 1990).

 <sup>0</sup> 5.1 <sup>6</sup> 429.1237.1 761.0 *VV*

In order to solve the population rate in steady state condition, the time derivatives of for pump and signal powers, equations are set to zero. All the equations are first order differential equations and the Runge-Kutta method is used to solve these equations. The variables used in the numerical calculation and their corresponding values are shown in

Fig. 12. Absorption and Emission Cross section.

Table 1.

Fig. 13. Bending loss spectral for different bending radius


Table 1. Numerical parameter used in the simulation

The bending loss spectrum of the EDF is measured across the wavelength region from 1530 nm to 1570 nm. Fig. 14 illustrates the bending loss profile at bending radius of 4.5 mm, 5.5 mm and 6.5 mm, which clearly show an exponential relationship between the bending loss and wavelength, with strong dependencies on the fiber bending radius. Bending the EDF causes the guided modes to partially couple into the cladding layer, which in turn results in

Doped Fiber Amplifier Characteristic Under Internal and External Perturbation 139

The gain spectrum of the EDFA is then investigated when the optimized length of high concentration EDF spooled in different radius. Fig. 16 shows the gain spectrum of the EDFA with 3m long EDF at different spooling radius. The result was also compared with straight EDF. The input signal power and pump power are fixed at -30dBm and 200 mW respectively in the experiment. As shown in the figure, the original shape of the gain spectrum is maintained in the whole C-band region with the gain decreases exponentially at wavelengths higher than 1560nm. Without bending, the peak gain of 28dB is obtained at 1530 nm which is the reference point to find the optimized length. When the EDF was spooled at a rod with 4.5mm and 5.5mm radius, the shape of gain spectra are totally changed. Finally after trying different radius, 6.5 mm was the optimized radius for this

Fig. 16. Gain profile of EDFA with and without macro bending at various input signal

As shown in Fig. 14, bending loss at radius of 6.5 mm is low especially at wavelengths shorter than 1560nm and therefore the gain spectrum maintains the original shape of the gain spectrum for un-spooled EDF. To achieve a flatten gain spectrum, the unbent EDFA must operate with insufficient 980nm pump, where the shorter wavelength ASE is absorbed by the un-pumped EDF to emit at the longer wavelength. This will shift the peak gain wavelength from 1530nm to around 1560nm. The macro-bending induces bending loss is dependent on wavelength with an exponential relationship and longer wavelength has a higher loss compared to the shorter wavelength. In relation to the EDFA, the macro-bending also increase the population inversion in C-band due to reduction of gain saturation effect in L-band. Since the L-band gain cannot improve more than a limited value due to exposure bending loss, less C band photons will be absorbed by un-pumped ions to emit at L-band. This effect reduced gain saturation in L-band, so the C-band gain will increase. This increment for peak is not more than the optimized C-band EDFA (3m) since at that level the inversion is in the maximum value. Full inversion for bent EDFA take place at longer length

amplifier.

power.(Experimental)

losses as earlier reported. The bending loss has a strong spectral variation because of the proportional changes of the mode field diameter with signal wavelength. As shown in Fig. 14, the bending loss dramatically increases at wavelengths above 1550 nm. This result shows that the distributed ASE filtering can be achieved by macro bending the EDF at an optimally chosen radius. It was important to analysis the bending loss in an optimized C-band amplifier before proceed to the next step. The results as shown in Fig. 15 indicate that 3 meter is optimized length for C- band amplifier. It was also seen that with decreasing length, S-band gain is increasing. This happened because of reduction of inversion in Cband region which allow a peak competition for S-band photons to increase. In general Cband always keeps the gain peak unless for longer lengths.

Fig. 14. Different length of unspooled EDFA for -30dBm input signal

Fig. 15. Efficient length of EDF (3m) in different bending radius for -30dBm input signal (Experimental).

losses as earlier reported. The bending loss has a strong spectral variation because of the proportional changes of the mode field diameter with signal wavelength. As shown in Fig. 14, the bending loss dramatically increases at wavelengths above 1550 nm. This result shows that the distributed ASE filtering can be achieved by macro bending the EDF at an optimally chosen radius. It was important to analysis the bending loss in an optimized C-band amplifier before proceed to the next step. The results as shown in Fig. 15 indicate that 3 meter is optimized length for C- band amplifier. It was also seen that with decreasing length, S-band gain is increasing. This happened because of reduction of inversion in Cband region which allow a peak competition for S-band photons to increase. In general C-

band always keeps the gain peak unless for longer lengths.

Fig. 14. Different length of unspooled EDFA for -30dBm input signal

Fig. 15. Efficient length of EDF (3m) in different bending radius for -30dBm input signal

(Experimental).

The gain spectrum of the EDFA is then investigated when the optimized length of high concentration EDF spooled in different radius. Fig. 16 shows the gain spectrum of the EDFA with 3m long EDF at different spooling radius. The result was also compared with straight EDF. The input signal power and pump power are fixed at -30dBm and 200 mW respectively in the experiment. As shown in the figure, the original shape of the gain spectrum is maintained in the whole C-band region with the gain decreases exponentially at wavelengths higher than 1560nm. Without bending, the peak gain of 28dB is obtained at 1530 nm which is the reference point to find the optimized length. When the EDF was spooled at a rod with 4.5mm and 5.5mm radius, the shape of gain spectra are totally changed. Finally after trying different radius, 6.5 mm was the optimized radius for this amplifier.

Fig. 16. Gain profile of EDFA with and without macro bending at various input signal power.(Experimental)

As shown in Fig. 14, bending loss at radius of 6.5 mm is low especially at wavelengths shorter than 1560nm and therefore the gain spectrum maintains the original shape of the gain spectrum for un-spooled EDF. To achieve a flatten gain spectrum, the unbent EDFA must operate with insufficient 980nm pump, where the shorter wavelength ASE is absorbed by the un-pumped EDF to emit at the longer wavelength. This will shift the peak gain wavelength from 1530nm to around 1560nm. The macro-bending induces bending loss is dependent on wavelength with an exponential relationship and longer wavelength has a higher loss compared to the shorter wavelength. In relation to the EDFA, the macro-bending also increase the population inversion in C-band due to reduction of gain saturation effect in L-band. Since the L-band gain cannot improve more than a limited value due to exposure bending loss, less C band photons will be absorbed by un-pumped ions to emit at L-band. This effect reduced gain saturation in L-band, so the C-band gain will increase. This increment for peak is not more than the optimized C-band EDFA (3m) since at that level the inversion is in the maximum value. Full inversion for bent EDFA take place at longer length

Doped Fiber Amplifier Characteristic Under Internal and External Perturbation 141

Fig. 19. Comparison of the standard C-band EDFA with the flattened gain EDFA for -30 dB

Recently, macro-bent EDF is used to achieve amplification in S-band region. In this paper, a gain-flattened C-band EDFA is proposed using a macro-bent EDF. This technique is able to compensate the EDFA gain spectrum to achieve a flat and broad gain characteristic based on distributed filtering using a simple and low cost method. This technique is also capable to compensate the fluctuation in operating temperatures due to proportional temperature sensitivity of absorption cross section and bending loss of the aluminosilicate EDF. This new approach can be used to design a temperature insensitive EDFA for application in a real

**5. Temperature insensitive broad and flat gain EDFA based on macro-**

Fig. 18. Amplified Spontaneous emission (Simulation)

input power(Experimental)

optical communication (Hajireza, et al. 2010).

**bending** 

due to limited energy transfer to longer wavelength. On the other hand, the L-band gain will reduce due to the suppression of L-band stimulated emission induced by macrobending. The net effect of both phenomena will result in a flattened gain profile.

Fig. 17. Noise figure profile of EDFA with and with-out macro bending at various input signal power(Experimental)

Fig. 17 compares the gain spectrum of with and with-out macro bending EDF at various input signal power. The input signal power is varied for -10 dBm to -30 dBm. The input pump power is fixed at 200 mW. The EDF length and bending radius is fixed at 9 meter and 6.5 mm respectively. As shown in the figure, increasing the input signal power decreases the gain but improves the gain flatness. The macro bending also reduces the noise figure of EDFA at wavelength shorter than 1550 as shown in Fig. 18. Since keeping the amount of noise low depends on a high population inversion in the input end of the erbium-doped fiber (EDF), the backward ASE power P –ASE is reduced by the bending loss. Consecutively, the forward ASE power P +ASE can be reduced when the pump power P is large at this part of the EDF which is especially undesirable. This is attributed can be described numerically by the following equation (Harun et al., 2010)

$$NF = \frac{1}{G} + \frac{2P\_{ASE}}{Gh\nu} \tag{19}$$

where G is the amplifier's gain, PASE is the ASE power and hν is the photon energy.

Fig 19 indicates the simulation of ASE for standard C-band EDFA (3m) and optimized gain flattened C-band EDFA (9m) after and before bending. ASE here represents population inversion. It clearly explains the gain shifting from longer wavelength to the shorter wavelength due to length increment. Besides effect of bending on gain flattening is explained. Fig 10 is the comparison between standard C-band EDFA with the flattened gain EDFA. We observe a gain variation within ±1 dB over 25 nm bandwidth in C-band region.

due to limited energy transfer to longer wavelength. On the other hand, the L-band gain will reduce due to the suppression of L-band stimulated emission induced by macro-

Fig. 17. Noise figure profile of EDFA with and with-out macro bending at various input

Fig. 17 compares the gain spectrum of with and with-out macro bending EDF at various input signal power. The input signal power is varied for -10 dBm to -30 dBm. The input pump power is fixed at 200 mW. The EDF length and bending radius is fixed at 9 meter and 6.5 mm respectively. As shown in the figure, increasing the input signal power decreases the gain but improves the gain flatness. The macro bending also reduces the noise figure of EDFA at wavelength shorter than 1550 as shown in Fig. 18. Since keeping the amount of noise low depends on a high population inversion in the input end of the erbium-doped fiber (EDF), the backward ASE power P –ASE is reduced by the bending loss. Consecutively, the forward ASE power P +ASE can be reduced when the pump power P is large at this part of the EDF which is especially undesirable. This is attributed can be described numerically

> 1 2 *PASE NF G Gh*

Fig 19 indicates the simulation of ASE for standard C-band EDFA (3m) and optimized gain flattened C-band EDFA (9m) after and before bending. ASE here represents population inversion. It clearly explains the gain shifting from longer wavelength to the shorter wavelength due to length increment. Besides effect of bending on gain flattening is explained. Fig 10 is the comparison between standard C-band EDFA with the flattened gain EDFA. We observe a gain variation within ±1 dB over 25 nm bandwidth in C-band region.

where G is the amplifier's gain, PASE is the ASE power and hν is the photon energy.

(19)

signal power(Experimental)

by the following equation (Harun et al., 2010)

bending. The net effect of both phenomena will result in a flattened gain profile.

Fig. 18. Amplified Spontaneous emission (Simulation)

Fig. 19. Comparison of the standard C-band EDFA with the flattened gain EDFA for -30 dB input power(Experimental)
