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An effective numerical method for gain profile optimizations of multi pumped fiber Raman amplifiers
Optik 125 (2014) 2352–2355
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
An effective numerical method for gain profile optimizations of multi pumped fiber Raman amplifiers Kulwinder Singh ∗ , Manjeet Singh Patterh, Manjit Singh Bhamrah University College of Engineering, Punjabi University, Patiala, Punjab, India
a r t i c l e
i n f o
Article history: Received 20 May 2013 Accepted 14 October 2013 Keywords: Muti pump Fiber Raman amplifier Raman gain coefficient Pump power evolutions Average net gain Gain ripple
a b s t r a c t In this paper, we have solved propagation equations of multi-pump fiber Raman amplifier using Runge–Kutta (RK 4th order) numerical method and pump power evolutions along with the fiber length. They are used to calculate the net gain and gain ripple by varying the input signals powers for different fiber lengths. The pump powers are optimized by genetic algorithm and resulting net gain and gain ripple are reported graphically as well as in tabular form. The optimum minimum gain ripple is 0.26 dB for 1 mW input signal powers for 50 km fiber length. By increasing the fiber length gain ripple increases to 0.5 dB for 0.1 mW input signal power. In comparison to other methods reported in the literature, our method is simple to implement and efficient for numerical design of Raman amplification in optical communication systems. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Modern long haul lightwave system requires broad bandwidth optical amplifiers which can be provided by fiber Raman amplifiers (FRAs) or Raman/EDFA hybrid amplifiers. The gain spectrum of multi pumped FRAs is needed to be adjusted for its use in practical systems. Stimulated Raman scattering (SRS) is a fiber nonlinearity exploited to make fiber Raman amplifiers. A strong optical pump wave amplifies stoke shifted weak optical signal by SRS effect in an optical fiber. A broad bandwidth FRA often requires multiple pumps to generate composite gain spectrum. Generally multi pumped FRAs are designed through rigorous analysis of pump powers and wavelengths adjustments for optimum gain spectrum but strong Raman interactions of pump to pump, signal to signal, and pump to signal make the design somewhat difficult [1,7–11]. Moreover, it is a challenge for researchers to design multi pumped FRA for required gain and gain flatness with certain design constraints such as double Rayleigh backscattering noise and fiber nonlinear effects etc. The coupled differential equations of backward pumped FRAs are generally boundary value problems (BVPs), and are difficult to solve than initial value problems (IVPs) involving forwarding pumping [3]. It has been reported in [4] that forward pumping to FRAs improves the noise figure when used with backward propagating pump than purely backward pumping scheme.
In this paper, we have proposed a numerical algorithm to solve forward pumped Raman amplifier differential equations for signal and pump power evolutions along optical fiber length using Runge–Kutta (4th order) method and a simple genetic algorithm to adjust the average gain and gain flatness by using pump path power integration or effective area of pump power evolution along the fiber. Our work is based on the work reported in Ref. [2]. They had used Newton–Raphson method for gain spectrum adjustment by varying effective pump power combinations. We have used heuristic search method based on GA to optimize the pump power evolutions along the fiber. The optimized pumps are used to calculate the net gain and gain ripple by changing the input signals power for different fiber lengths. In comparison to Refs. [1,3,4] our proposed algorithm is easy to calculate the pump power evolutions, average gain and gain ripple, and effective gain profile optimization. The paper is organised so that Section 2, presents a theoretical model of multi-pump fiber Raman amplifier differential equations considering signal to signal, pump to signal, and pump to pump interactions. The solution of these differential equations is found by RK (4th order) numerical method and further average net gain and gain ripple is statistically calculated. In Section 3, pump power evolutions are optimized using genetic algorithm and results are plotted and discussed under different conditions. Finally, conclusions have been drawn in Section 4.
2. Theoretical model and numerical algorithm ∗ Corresponding author. Phone and Fax: +911753046338. E-mail addresses: [email protected] (K. Singh), [email protected] (M.S. Patterh), manjitsingh [email protected] (M.S. Bhamrah). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.10.069
The major consideration for designing the FRA bandwidth are interactions of pump to pump, signal to signal, pump to signal, as
K. Singh et al. / Optik 125 (2014) 2352–2355
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well as the attenuation. In the steady state the FRA a set of coupled equations can be described as given below [6] ±dP(v) = f (z, vi ) = P ± (z, vi )F(z, vi ) dz
(1)
(i = 1, 2 . . .. . .. . .m)
i−1 gR (vj − vi )
F(z, vi ) = −˛(vi ) +
j=1
Aeff
−
m
vi
j=i+1 vj
×
gR (vi − vj ) Aeff
(2) Fig. 1. (a) Optical wavelength (nm) vs. fiber loss (dB/km), (b) Frequency shift (THz) vs. Raman gain coefficient (m/W) for standard single mode fiber.
where, Pi , vi , and ␣i are the power, frequency, and attenuation coefficient for the ith wave respectively. Aeff is the effective area of optical fiber, factor accounts for polarization randomization effects, the value of which lies between 1 and 2, gR (vj , vi ) the Raman gain coefficient from wave j to i. The frequency ratio vi/ vj describe vibrational losses. The plus and minus sign on the left hand side describes the backward and forward propagation waves respectively. The frequency vi are numerated in the decreasing order of frequency (i = 1, 2, . . .. . .. . ...m). The terms from j = 1 to j = i−1 and from j = i+1 to j = m cause amplification and attenuation of the channel at frequency vi respectively. The signal evolution along with the fiber can be expressed by the following nonlinearly coupled equation.
dP(z, vi ) gR (vj , vi ), P(z, vj ) = −˛(v)P(z, vi ) + P(z, vi ) dZ
where, Gnet = [G1 , G2 ,. . .. . .. . .,GS ] is the net gain of the signals, A = [␣1 ,␣2 ,....,␣s ]L is the fiber attenuation of the signals. Ggross = 4.343 g × H is the gross gain of the signals,
⎡
g11
g12
g1N
⎤
⎢g ⎥ ⎢ 21 g22 g2N ⎥ ⎥ ⎥ .. ⎣ ⎦ .
g=⎢ ⎢
gS1
gS2
(7)
gSN
is the Raman gain coefficient between the pumps and the signals where gij is the Raman gain coefficient between the ith signal and jth pump, and
N
H = [H1 , H2 , ...., HN ]
(3)
j=1
(8)
where
Integrating the Eq. (3) from z = 0 to z = L we can obtain
Hj =
L
(P(z, vp )dZ
(9)
0
L
P(L, vi ) (gR )(vj , vi ) = exp[−˛i L + P(0, vi ) N
(j=1)
P(z, vj )dZ]
Clearly Hj represents the area under the pump power evolution curve of the jth pump and we denote as effective pump area of the pump. For a given amplifier with given number of pumps and signals, A and g are constant matrices. For the gain profile adjustment pump power in Eq. (6) is varied to get optimum average gain and gain flatness by using genetic algorithm (GA). The main parts of GA include initialization, clustering, sharing, selection, crossover, mutation, and elitist replacement.
(4)
0
where, L is the length of the fiber. Small signal Raman gain from of the signal vi from Eq. (4) can be written as Gi = 10 × log10
= exp[−˛i L +
P(L, vi ) P(0, vi )
N
3. Results and discussion
L
(gR )(vj , vi )
(j=1)
(5)
Our proposed shooting algorithm employs Runge – Kutta (4th order) numerical method using fixed step size to solve the Raman amplifier differential Eqs. (1) and (2). It calculates the pump power distribution along fiber length. In the calculations following parameters are fixed: there are 36 signal channels launched having wavelength from 1543 (194.43 THz) to 1598 nm (187.73 THz) with input signal power varied 0.1, 0.5, and 1 mW per channel. Standard single mode fiber (SMF) is used with different lengths 50, 60, 70, and
P(z, vj )dZ] 0
For a Raman amplifier with N pumps and S signals the net gain of the signals can be expressed in a matrix form as follows: Gnet ∼ = 4.343(A + g × H) = 4.343A + Ggross
(6)
Table 1 Output pump powers for different fiber lengths under different signal launched powers. Pump wave
Output pump power (mW) Fiber length L = 50 km
L = 60 km
L = 80 km
No.
Wave length (nm)
Input power (mW)
Signal input power (mW)
Signal input power (mW)
Signal input power (mW)
1 2 3 4 5
1434 1444 1454 1483 1498
45.0 45.0 50.0 100.0 100.0
(0.1) 44.9 44.0 49.6 99.7 99.8
(0.1) 44.9 44.4 49.5 99.7 99.7
(0.1) 44.9 44.2 49.3 99.6 99.6
(0.5) 44.6 42.5 47.8 98.6 96.9
(1) 44.0 39.9 45.3 96.7 96.9
(0.5) 44.5 42.1 47.3 98.3 98.4
(1) 43.8 38.9 44.3 96.1 96.3
(0.5) 44.3 41.1 46.3 97.7 97.8
(1) 43.4 36.9 42.4 94.7 95.1
2354
K. Singh et al. / Optik 125 (2014) 2352–2355
Fig. 2. Power evolutions along the fiber length at fixed input signal power = 0.1 mW for the pumps (a) first, second, and third (b) fourth and fifth, input signal power = 0.5 mW for the pumps (c) first, second, and third (d) fourth and fifth, input signal power = 1 mW for the pumps (e) first, second, and third (f) fourth and fifth.
80 km with effective area of 80 m2 and polarization factor is taken 2. The Raman gain coefficient and attenuation are taken from reference [1] with standard curve as shown in Fig. 1. We have used five forward pump waves. The optimum wavelengths of pump waves as shown in Table 1 are taken from ref. [5]. These pump waves are 1434, 1444, 1454, 1483, and 1498 nm and we have optimized their pump powers by genetic algorithm as 45, 45, 50, 100, and 100 mW respectively under the condition of minimum gain ripple. These pump powers are calculated by our proposed algorithm at the input and output end of the fiber are as shown in Table 1 using different input launched signals power as 0.1, 0.5 and 1 mW per channel with varying fiber lengths of 50, 60, 70, and 80 km. The pumps power evolution of first, second, and third pump at wavelength 1434, 1444, and 1454 nm are shown in Fig. 2. (a), (c), and (f), with input 45, 45, and 50 mW respectively under input launched signals power of 0.1, 0.5, and 1 mW per channel with fiber length 50 km. It is evident from Table 1, second pump wave at 1444 nm wavelength is maximum power depleted of 8.1 mW for 80 km fiber is with 1 mW input signal power and minimum depletion is 0.1 mW for first pump wave at 1434 nm with input signals power of 0.1 mW. Similarly fourth and fifth pump waves 1483 and 1498 nm wavelengths respectively, evolutions along fiber length are depicted in Fig. 2.(b), (d), and (f). It has been observed from figures that maximum pump power depletion is 5.3 mW at 1483 nm with input signals power of 1 mW and minimum is 0.2 mW at 1498 nm with input signals power of 0.1 mW.
Further pump power evolutions along with fiber are used to calculate the pump power path integrals using Eq. (9) and matrix H is computed for five pump wave and net Raman gain calculated by Eq. (6). We have optimized the pump powers using simple genetic algorithm. A fitness function is written to calculate pump power evolution along the fiber length by varying input signals powers and fiber lengths. This fitness function is used in the simple genetic algorithm to optimize the pump powers by calculating the standard deviations of net gain vector i.e., gain ripple. The optimized average gain and gain ripple is plotted in Fig. 3(a)–(c) and numerically computed values are shown in Table 2 with signals input power of 0.1, 0.5, and 1 mW for fiber length of 50, 60, 70, and 80 km. As it is observed from these plots and the table, that net gain increases and gain ripple decreases with increasing the fiber length from 50
Table 2 Average net gain and gain ripple for different fiber length by varying signal input powers. Fiber length (km)
Average net gain (dB)
Gain ripple (dB)
Signals input power (mW) 50 60 70 80
(0.1) 28.78 34.53 40.26 46.0
(0.5) 28.53 34.16 39.77 45.35
(1) 28.15 37.77 39.24 46.66
(0.1) 0.32 0.39 0.44 0.50
(0.5) 0.29 0.34 0.39 0.43
(1) 0.26 0.30 0.35 0.41
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Fig. 3. (a) Net gain vs. signal wavelengths for fiber lengths = 50, 60, 70, and 80 km when input signals power (a) 0.1 mW (b) 0.5 mW (c) 1 mW. (d) Fiber length (km) vs. gain ripple (dB).
to 80 km. Similarly, as depicted in Fig. 3(d) net Raman gain and gain ripple decreases by increasing input signals power from 0.1 to 1 mW. The minimum gain ripple is 0.26 dB for input signals power of 1 mW with fiber length of 50 Km. The maximum gain ripple is 0.50 for input signal powers of 0.1 mW with fiber length of 80 km. The maximum and minimum average net gain is 46.66 dB and 28.15 dB for fiber length of 80 and 50 km respectively for input signal power of 1 mW. The standard deviation and average value of net gain vector is reported as gain ripple or gain flatness and average net gain of the optical fiber Raman amplifier. As in [2] reference gain fluctuations is 0.33 and it depends upon the average net gain adjustment parameter but we have optimized the gain flatness 0.26 dB by optimizing effective pump power using genetic algorithm. So our numerical method has better gain fluctuation than [2] by optimization. Moreover, our proposed method can be used for backward and bidirectional pumping schemes. We have not considered noise figures analysis in our work, further extension can be done by comparing noise effects under different pumping techniques. 4. Conclusion We have proposed an algorithm using RK (4th order) numerical method to solve fiber Raman amplifier propagation equations and calculated the pump power evolutions along the fiber length. Further we have calculated the average net gain and gain ripple by optimized the pump powers for optimum gain ripple with multipump fiber Raman amplifier. In comparison to other methods [2,3], our method is simple to implement and efficient for gain flatness optimization. We have also compared the gain ripple and average net gain with different launched signal powers 0.1, 0.5, and 1 mW
by varying fiber length 50, 60, 70, and 80 km. The minimum optimized gain ripple is 0.26 dB for 1 mW input signal powers with 50 km fiber length and maximum 0.5 dB with 0.1 mW for 80 km fiber length. Similarly minimum and maximum average net gain are 28.15 and 46.66 dB with 1 mW input signal power for 50 and 80 km fiber lengths respectively. Further this work can be extended by optimizing pump wavelengths and other pumping schemes with noise figure analysis of multi-pump distributed fiber Raman amplifiers. References [1] X. Liu, et al., Optimizing the bandwidth and noise performance of distributed multi-pump Raman amplifiers, Opt. Commun. 230 (2004) 425–431. [2] Q. Han, et al., A novel method for muti-pumped fiber Raman amplifier gain adjustment, Chin. Phys. Lett. 22 (5) (2005) 1148. [3] N. Ji Ping, et al., A powerful simple shooting method for designing multipumped fiber Raman amplifiers, Chin. Phys. Lett. 21 (11) (2004) 2184. [4] X. Liu, et al., Optimizing gain profile and noise performance for distributed fiber Raman amplifiers, Opt. Express 12 (24) (29 November 2004) 6053. [5] Lali-D. Zohreh, et al., Numerical design of multipumped Raman fiber amplifiers, in: PHOTONICS-2008, International Conference on Fiber Optics and Photonics, IIT Delhi India, 13–17 December 2008, in press. [6] X. Liu, et al., An effective method for two-point boundary value problems in Raman amplifier propagation equations, Opt. Commun. 235 (2004) 75–82. [7] J. Bromage, Raman amplification for fiber communication systems, J. Light Wave Technol. 22 (1) (2004). [8] M.N. Islam, Raman amplification for telecommunications, IEEE J. Sel. Top. Quan. Electron. 8 (3) (2002). [9] V. Perlin, et al., Optimal design of flat-gain wide-band fiber Raman amplifiers, J. Light Wave Technol. 20 (2002) 250–254. [10] J. Hu, et al., Flat gain fiber Raman amplifiers using equally spaced pumps, J. Light Wave Technol. 22 (6) (2004) 1519–1522. [11] S. Tenenbaum, et al., On the impact of multi path interference noise in all Raman dispersion-compensated links, J. Light Wave Technol. 24 (12) (2006) 4850–4860.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
An effective numerical method for gain profile optimizations of multi pumped fiber Raman amplifiers Kulwinder Singh ∗ , Manjeet Singh Patterh, Manjit Singh Bhamrah University College of Engineering, Punjabi University, Patiala, Punjab, India
a r t i c l e
i n f o
Article history: Received 20 May 2013 Accepted 14 October 2013 Keywords: Muti pump Fiber Raman amplifier Raman gain coefficient Pump power evolutions Average net gain Gain ripple
a b s t r a c t In this paper, we have solved propagation equations of multi-pump fiber Raman amplifier using Runge–Kutta (RK 4th order) numerical method and pump power evolutions along with the fiber length. They are used to calculate the net gain and gain ripple by varying the input signals powers for different fiber lengths. The pump powers are optimized by genetic algorithm and resulting net gain and gain ripple are reported graphically as well as in tabular form. The optimum minimum gain ripple is 0.26 dB for 1 mW input signal powers for 50 km fiber length. By increasing the fiber length gain ripple increases to 0.5 dB for 0.1 mW input signal power. In comparison to other methods reported in the literature, our method is simple to implement and efficient for numerical design of Raman amplification in optical communication systems. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Modern long haul lightwave system requires broad bandwidth optical amplifiers which can be provided by fiber Raman amplifiers (FRAs) or Raman/EDFA hybrid amplifiers. The gain spectrum of multi pumped FRAs is needed to be adjusted for its use in practical systems. Stimulated Raman scattering (SRS) is a fiber nonlinearity exploited to make fiber Raman amplifiers. A strong optical pump wave amplifies stoke shifted weak optical signal by SRS effect in an optical fiber. A broad bandwidth FRA often requires multiple pumps to generate composite gain spectrum. Generally multi pumped FRAs are designed through rigorous analysis of pump powers and wavelengths adjustments for optimum gain spectrum but strong Raman interactions of pump to pump, signal to signal, and pump to signal make the design somewhat difficult [1,7–11]. Moreover, it is a challenge for researchers to design multi pumped FRA for required gain and gain flatness with certain design constraints such as double Rayleigh backscattering noise and fiber nonlinear effects etc. The coupled differential equations of backward pumped FRAs are generally boundary value problems (BVPs), and are difficult to solve than initial value problems (IVPs) involving forwarding pumping [3]. It has been reported in [4] that forward pumping to FRAs improves the noise figure when used with backward propagating pump than purely backward pumping scheme.
In this paper, we have proposed a numerical algorithm to solve forward pumped Raman amplifier differential equations for signal and pump power evolutions along optical fiber length using Runge–Kutta (4th order) method and a simple genetic algorithm to adjust the average gain and gain flatness by using pump path power integration or effective area of pump power evolution along the fiber. Our work is based on the work reported in Ref. [2]. They had used Newton–Raphson method for gain spectrum adjustment by varying effective pump power combinations. We have used heuristic search method based on GA to optimize the pump power evolutions along the fiber. The optimized pumps are used to calculate the net gain and gain ripple by changing the input signals power for different fiber lengths. In comparison to Refs. [1,3,4] our proposed algorithm is easy to calculate the pump power evolutions, average gain and gain ripple, and effective gain profile optimization. The paper is organised so that Section 2, presents a theoretical model of multi-pump fiber Raman amplifier differential equations considering signal to signal, pump to signal, and pump to pump interactions. The solution of these differential equations is found by RK (4th order) numerical method and further average net gain and gain ripple is statistically calculated. In Section 3, pump power evolutions are optimized using genetic algorithm and results are plotted and discussed under different conditions. Finally, conclusions have been drawn in Section 4.
2. Theoretical model and numerical algorithm ∗ Corresponding author. Phone and Fax: +911753046338. E-mail addresses: [email protected] (K. Singh), [email protected] (M.S. Patterh), manjitsingh [email protected] (M.S. Bhamrah). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.10.069
The major consideration for designing the FRA bandwidth are interactions of pump to pump, signal to signal, pump to signal, as
K. Singh et al. / Optik 125 (2014) 2352–2355
2353
well as the attenuation. In the steady state the FRA a set of coupled equations can be described as given below [6] ±dP(v) = f (z, vi ) = P ± (z, vi )F(z, vi ) dz
(1)
(i = 1, 2 . . .. . .. . .m)
i−1 gR (vj − vi )
F(z, vi ) = −˛(vi ) +
j=1
Aeff
−
m
vi
j=i+1 vj
×
gR (vi − vj ) Aeff
(2) Fig. 1. (a) Optical wavelength (nm) vs. fiber loss (dB/km), (b) Frequency shift (THz) vs. Raman gain coefficient (m/W) for standard single mode fiber.
where, Pi , vi , and ␣i are the power, frequency, and attenuation coefficient for the ith wave respectively. Aeff is the effective area of optical fiber, factor accounts for polarization randomization effects, the value of which lies between 1 and 2, gR (vj , vi ) the Raman gain coefficient from wave j to i. The frequency ratio vi/ vj describe vibrational losses. The plus and minus sign on the left hand side describes the backward and forward propagation waves respectively. The frequency vi are numerated in the decreasing order of frequency (i = 1, 2, . . .. . .. . ...m). The terms from j = 1 to j = i−1 and from j = i+1 to j = m cause amplification and attenuation of the channel at frequency vi respectively. The signal evolution along with the fiber can be expressed by the following nonlinearly coupled equation.
dP(z, vi ) gR (vj , vi ), P(z, vj ) = −˛(v)P(z, vi ) + P(z, vi ) dZ
where, Gnet = [G1 , G2 ,. . .. . .. . .,GS ] is the net gain of the signals, A = [␣1 ,␣2 ,....,␣s ]L is the fiber attenuation of the signals. Ggross = 4.343 g × H is the gross gain of the signals,
⎡
g11
g12
g1N
⎤
⎢g ⎥ ⎢ 21 g22 g2N ⎥ ⎥ ⎥ .. ⎣ ⎦ .
g=⎢ ⎢
gS1
gS2
(7)
gSN
is the Raman gain coefficient between the pumps and the signals where gij is the Raman gain coefficient between the ith signal and jth pump, and
N
H = [H1 , H2 , ...., HN ]
(3)
j=1
(8)
where
Integrating the Eq. (3) from z = 0 to z = L we can obtain
Hj =
L
(P(z, vp )dZ
(9)
0
L
P(L, vi ) (gR )(vj , vi ) = exp[−˛i L + P(0, vi ) N
(j=1)
P(z, vj )dZ]
Clearly Hj represents the area under the pump power evolution curve of the jth pump and we denote as effective pump area of the pump. For a given amplifier with given number of pumps and signals, A and g are constant matrices. For the gain profile adjustment pump power in Eq. (6) is varied to get optimum average gain and gain flatness by using genetic algorithm (GA). The main parts of GA include initialization, clustering, sharing, selection, crossover, mutation, and elitist replacement.
(4)
0
where, L is the length of the fiber. Small signal Raman gain from of the signal vi from Eq. (4) can be written as Gi = 10 × log10
= exp[−˛i L +
P(L, vi ) P(0, vi )
N
3. Results and discussion
L
(gR )(vj , vi )
(j=1)
(5)
Our proposed shooting algorithm employs Runge – Kutta (4th order) numerical method using fixed step size to solve the Raman amplifier differential Eqs. (1) and (2). It calculates the pump power distribution along fiber length. In the calculations following parameters are fixed: there are 36 signal channels launched having wavelength from 1543 (194.43 THz) to 1598 nm (187.73 THz) with input signal power varied 0.1, 0.5, and 1 mW per channel. Standard single mode fiber (SMF) is used with different lengths 50, 60, 70, and
P(z, vj )dZ] 0
For a Raman amplifier with N pumps and S signals the net gain of the signals can be expressed in a matrix form as follows: Gnet ∼ = 4.343(A + g × H) = 4.343A + Ggross
(6)
Table 1 Output pump powers for different fiber lengths under different signal launched powers. Pump wave
Output pump power (mW) Fiber length L = 50 km
L = 60 km
L = 80 km
No.
Wave length (nm)
Input power (mW)
Signal input power (mW)
Signal input power (mW)
Signal input power (mW)
1 2 3 4 5
1434 1444 1454 1483 1498
45.0 45.0 50.0 100.0 100.0
(0.1) 44.9 44.0 49.6 99.7 99.8
(0.1) 44.9 44.4 49.5 99.7 99.7
(0.1) 44.9 44.2 49.3 99.6 99.6
(0.5) 44.6 42.5 47.8 98.6 96.9
(1) 44.0 39.9 45.3 96.7 96.9
(0.5) 44.5 42.1 47.3 98.3 98.4
(1) 43.8 38.9 44.3 96.1 96.3
(0.5) 44.3 41.1 46.3 97.7 97.8
(1) 43.4 36.9 42.4 94.7 95.1
2354
K. Singh et al. / Optik 125 (2014) 2352–2355
Fig. 2. Power evolutions along the fiber length at fixed input signal power = 0.1 mW for the pumps (a) first, second, and third (b) fourth and fifth, input signal power = 0.5 mW for the pumps (c) first, second, and third (d) fourth and fifth, input signal power = 1 mW for the pumps (e) first, second, and third (f) fourth and fifth.
80 km with effective area of 80 m2 and polarization factor is taken 2. The Raman gain coefficient and attenuation are taken from reference [1] with standard curve as shown in Fig. 1. We have used five forward pump waves. The optimum wavelengths of pump waves as shown in Table 1 are taken from ref. [5]. These pump waves are 1434, 1444, 1454, 1483, and 1498 nm and we have optimized their pump powers by genetic algorithm as 45, 45, 50, 100, and 100 mW respectively under the condition of minimum gain ripple. These pump powers are calculated by our proposed algorithm at the input and output end of the fiber are as shown in Table 1 using different input launched signals power as 0.1, 0.5 and 1 mW per channel with varying fiber lengths of 50, 60, 70, and 80 km. The pumps power evolution of first, second, and third pump at wavelength 1434, 1444, and 1454 nm are shown in Fig. 2. (a), (c), and (f), with input 45, 45, and 50 mW respectively under input launched signals power of 0.1, 0.5, and 1 mW per channel with fiber length 50 km. It is evident from Table 1, second pump wave at 1444 nm wavelength is maximum power depleted of 8.1 mW for 80 km fiber is with 1 mW input signal power and minimum depletion is 0.1 mW for first pump wave at 1434 nm with input signals power of 0.1 mW. Similarly fourth and fifth pump waves 1483 and 1498 nm wavelengths respectively, evolutions along fiber length are depicted in Fig. 2.(b), (d), and (f). It has been observed from figures that maximum pump power depletion is 5.3 mW at 1483 nm with input signals power of 1 mW and minimum is 0.2 mW at 1498 nm with input signals power of 0.1 mW.
Further pump power evolutions along with fiber are used to calculate the pump power path integrals using Eq. (9) and matrix H is computed for five pump wave and net Raman gain calculated by Eq. (6). We have optimized the pump powers using simple genetic algorithm. A fitness function is written to calculate pump power evolution along the fiber length by varying input signals powers and fiber lengths. This fitness function is used in the simple genetic algorithm to optimize the pump powers by calculating the standard deviations of net gain vector i.e., gain ripple. The optimized average gain and gain ripple is plotted in Fig. 3(a)–(c) and numerically computed values are shown in Table 2 with signals input power of 0.1, 0.5, and 1 mW for fiber length of 50, 60, 70, and 80 km. As it is observed from these plots and the table, that net gain increases and gain ripple decreases with increasing the fiber length from 50
Table 2 Average net gain and gain ripple for different fiber length by varying signal input powers. Fiber length (km)
Average net gain (dB)
Gain ripple (dB)
Signals input power (mW) 50 60 70 80
(0.1) 28.78 34.53 40.26 46.0
(0.5) 28.53 34.16 39.77 45.35
(1) 28.15 37.77 39.24 46.66
(0.1) 0.32 0.39 0.44 0.50
(0.5) 0.29 0.34 0.39 0.43
(1) 0.26 0.30 0.35 0.41
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Fig. 3. (a) Net gain vs. signal wavelengths for fiber lengths = 50, 60, 70, and 80 km when input signals power (a) 0.1 mW (b) 0.5 mW (c) 1 mW. (d) Fiber length (km) vs. gain ripple (dB).
to 80 km. Similarly, as depicted in Fig. 3(d) net Raman gain and gain ripple decreases by increasing input signals power from 0.1 to 1 mW. The minimum gain ripple is 0.26 dB for input signals power of 1 mW with fiber length of 50 Km. The maximum gain ripple is 0.50 for input signal powers of 0.1 mW with fiber length of 80 km. The maximum and minimum average net gain is 46.66 dB and 28.15 dB for fiber length of 80 and 50 km respectively for input signal power of 1 mW. The standard deviation and average value of net gain vector is reported as gain ripple or gain flatness and average net gain of the optical fiber Raman amplifier. As in [2] reference gain fluctuations is 0.33 and it depends upon the average net gain adjustment parameter but we have optimized the gain flatness 0.26 dB by optimizing effective pump power using genetic algorithm. So our numerical method has better gain fluctuation than [2] by optimization. Moreover, our proposed method can be used for backward and bidirectional pumping schemes. We have not considered noise figures analysis in our work, further extension can be done by comparing noise effects under different pumping techniques. 4. Conclusion We have proposed an algorithm using RK (4th order) numerical method to solve fiber Raman amplifier propagation equations and calculated the pump power evolutions along the fiber length. Further we have calculated the average net gain and gain ripple by optimized the pump powers for optimum gain ripple with multipump fiber Raman amplifier. In comparison to other methods [2,3], our method is simple to implement and efficient for gain flatness optimization. We have also compared the gain ripple and average net gain with different launched signal powers 0.1, 0.5, and 1 mW
by varying fiber length 50, 60, 70, and 80 km. The minimum optimized gain ripple is 0.26 dB for 1 mW input signal powers with 50 km fiber length and maximum 0.5 dB with 0.1 mW for 80 km fiber length. Similarly minimum and maximum average net gain are 28.15 and 46.66 dB with 1 mW input signal power for 50 and 80 km fiber lengths respectively. Further this work can be extended by optimizing pump wavelengths and other pumping schemes with noise figure analysis of multi-pump distributed fiber Raman amplifiers. References [1] X. Liu, et al., Optimizing the bandwidth and noise performance of distributed multi-pump Raman amplifiers, Opt. Commun. 230 (2004) 425–431. [2] Q. Han, et al., A novel method for muti-pumped fiber Raman amplifier gain adjustment, Chin. Phys. Lett. 22 (5) (2005) 1148. [3] N. Ji Ping, et al., A powerful simple shooting method for designing multipumped fiber Raman amplifiers, Chin. Phys. Lett. 21 (11) (2004) 2184. [4] X. Liu, et al., Optimizing gain profile and noise performance for distributed fiber Raman amplifiers, Opt. Express 12 (24) (29 November 2004) 6053. [5] Lali-D. Zohreh, et al., Numerical design of multipumped Raman fiber amplifiers, in: PHOTONICS-2008, International Conference on Fiber Optics and Photonics, IIT Delhi India, 13–17 December 2008, in press. [6] X. Liu, et al., An effective method for two-point boundary value problems in Raman amplifier propagation equations, Opt. Commun. 235 (2004) 75–82. [7] J. Bromage, Raman amplification for fiber communication systems, J. Light Wave Technol. 22 (1) (2004). [8] M.N. Islam, Raman amplification for telecommunications, IEEE J. Sel. Top. Quan. Electron. 8 (3) (2002). [9] V. Perlin, et al., Optimal design of flat-gain wide-band fiber Raman amplifiers, J. Light Wave Technol. 20 (2002) 250–254. [10] J. Hu, et al., Flat gain fiber Raman amplifiers using equally spaced pumps, J. Light Wave Technol. 22 (6) (2004) 1519–1522. [11] S. Tenenbaum, et al., On the impact of multi path interference noise in all Raman dispersion-compensated links, J. Light Wave Technol. 24 (12) (2006) 4850–4860.