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Gain clamped L-band EDFA with forward–backward pumping scheme using fiber Bragg grating
Optik 125 (2014) 2463–2465
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Gain clamped L-band EDFA with forward–backward pumping scheme using fiber Bragg grating Ricky Anthony a,∗ , Rini Lahiri b , Sambhunath Biswas a a b
Department of Electronics and Communication Engineering, Heritage Institute of Technology, Kolkata, India Department of Electronics and Communication Engineering, National Institute of Technology, Nagaland, India
a r t i c l e
i n f o
Article history: Received 24 May 2013 Accepted 24 October 2013 Keywords: Erbium doped fiber amplifier L-band amplification Fiber Bragg grating
a b s t r a c t The paper proposes a novel two stage L-band erbium doped fiber amplifier with forward–backward pumping scheme for transmission of 32 wavelength division multiplexed (WDM) channels. It is gain clamped with an in-line fiber Bragg grating (FBG) to provide flat gain over 45 nm by restricting and reutilizing amplified spontaneous emission (ASE). We demonstrate that it provides an efficient small signal gain with minimum noise figure of over 20 dB and 5.5 dB, respectively, in the L-band region (1565–1610 nm) by comparing with its forward and backward pumped counterparts with fixed Er3+ fiber length of 20 m for −30 dBm/channel input power. We also obtain the gain and noise figure dependence as a function of each of the Er3+ fiber lengths, pump power (both 1480 and 980 nm), and temperature. Hence a 10 nm region (1580–1590 nm) has been acknowledged where temperature variations become constricted for 30 ◦ C variations (15–45 ◦ C). © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Erbium doped fiber amplifiers (EDFAs) have become integral part of every wavelength division multiplexed (WDM) and dense wavelength division multiplexed (DWDM) system. EDFA operating band has been extended from the C-band to L-band (1570–1610 nm) and S-band (1480–1520 nm) [1,2]. Yet L-band amplification faces considerable hurdles in terms of absorption, scattering effects and efficiency. Even though two staged L-band EDFAs show better pump power conversion compared to its single stage counterpart [3], noise figure still remains a matter of concern. Literature survey demonstrates various configurations such as reutilization of ASE [4–6] using fiber Bragg gratings (FBG), Cband seed injection [7], polarization maintaining ring cavity [8], etc. This band being located away from the zero dispersion wavelengths in WDM/DWDM system makes it less susceptible to non-linear four-wave mixing (FWM), reducing inter-channel cross-talks, thus making it a potential candidate for communications. Authors have previously reported simultaneous amplification of optical signals in C- and L-band with a tunable tap [9], while others include use of Raman amplifier [10]. Such approaches, however, require additional components, generating unwarranted losses and cost.
∗ Corresponding author. Tel.: +353894031377. E-mail addresses: [email protected] (R. Anthony), [email protected] (R. Lahiri), [email protected] (S. Biswas). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.10.102
In the letter, the authors propose a simple L-band EDFA with a forward–backward pumping scheme. Firstly, we theoretically investigate the governing equation of EDFAs. Then we analyze the proposed EDFA in terms of pump powers and temperature with and without FBG. The design criterion is to obtain a gain above 20 dB at the output with noise figure close to 5 dB. We strategically introduce a FBG into the system to obtain a gain clamped result. 2. Theoretical model and configuration The L-band EDFA model with forward–backward pumping scheme assumes a three level system with homogeneous broadening with 980 nm pumps. Such a model is justified, since the erbium ion lifetime at the upper energy state is negligible compared to the metastable state, also ion–ion interaction is negligible with no upconversion from ground state (4 I11/2 ). The rate equation associated with the upper and lower state can be given by temporal ordinary differential equations for propagation along z direction: dn1 (z, t) n2 (z, t) = Re (z)n2 (z, t) + − Ra (z)n1 (z, t) − Rp (z)n1 (z, t) 21 dt + Rp n3 (z, t)
(1)
dn2 (z, t) n2 (z, t) − Ra (z)n1 (z, t) + Rp (z)n1 (z, t) = Re (z)n2 (z, t) + 21 dt + 32 n3
(2)
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R. Anthony et al. / Optik 125 (2014) 2463–2465
Fig. 1. L-band erbium doped fiber amplifier with (a) backward and (b) pumping scheme.
In these equations, Re , Ra and Rp stimulated emission, absorption and pumping rates. 21 and 32 are the spontaneous emission lifetimes between the upper to lower levels. The total erbium ion concentration is given by nt (z, t) = n1 (z, t) + n2 (z, t) + n3 (z, t)
(3)
n1 and n2 are the erbium ion concentration in the ground and metastable states. Under steady state conditions, integrating Eq. (3) yields
P (z, t)˛i /hfi n2 |av(z, t) i i = nt |av(z, t) 1+ P (z, t)(˛i + gi∗ )/hfi i i
(4)
where is the saturation parameter, h is Planck’s constant, f representing the frequency of operation, and ˛ and g the absorption and gain cross-sections, respectively. The forward and backward propagation equation given below is solved in an iterative manner using Runge–Kutta of numerical analysis with fiber lengths from 0 to L for the two fibers individually [11]: dp± p dz
= ±[(tp )21 (tp )n2 (z, t) − (tp )12,13 (tp )n1 (z, t)Pp± (z, tp )
dps (z, ts ) = [(ts )12 (ts )n2 (z, t) − (ts )12 (ts )n1 (z)]Ps (z, ts ) dz dPASE±(z,t)
= ±2h(t)21 (t)n2 (z)
dz
(5) (6)
1 ± [(t)21 (t)n2 (z) tt
± − (t)12 (t)n1 (t)n1 (z)]PASE (z, t)
(7)
where (t) is the overlap integral between the mode field intensity |E (r, t)|2 and the erbium ion density distribution (r) and given by the expression:
R
(t) =
o
|E(r, t)|2 (r) dr
R o
|E(r, t)|2 r dr
Fig. 3. Gain and noise figure spectra of the proposed configuration with forward and backward pumping at different pump powers without fiber Bragg gratings.
979 nm.The in-line fiber Bragg grating (FBG) has a center wavelength of 1553.7 nm with effective index (eff ) and grating pitch of 1.47 nm and 528.4 nm, respectively. It reflects a portion of the Cband backward ASE back into the system. The resonance condition of the FBG is given by the expression: = 2eff
(9)
3. Results and discussions Configurations shown in Fig. 1(a) and (b) have shown gains close to 5 dB which is unacceptable for any communication system. However forward–backward pumped configurations (Fig. 2) shows excellent L-band gain above 30 dB (for 120 mW pump powers) for fixed Er3+ fiber lengths and signal powers of 20 m and −30 dBm, respectively. The input signal is maintained at −30 dBm/channel. As shown from the figure, the gain is nearly 35 dB which is attractive, but with a noise figure close to 15 dB for most of the channels which needs to reduced. Furthermore, as expected increase in pump power from 60 to 240 mW increases the overall gain. The increase in pump powers aids inversion and hence increases stimulated emission, but the fiber length remains critical (Fig. 3). Fig. 4 depicts the gain and noise figure after the inclusion of in-line FBG. The grating wavelength is fixed at 1565 nm. The FBG allows a small portion of ASE for amplification by the second 980 nm pump. This enhances the stimulated emission and increases pump efficiency. As observed, the gain variation is maintained less
(8)
Fig. 1a and b shows the forward and backward pumped erbium doped fiber amplifier. The modified and proposed system (shown in Fig. 2) provides a transmission of 32 channels with a spacing of 1.54 nm. The isolator restricts back-reflection of the spurious signal toward the source. DHB 1500TM and IsoGainTM EDF are selected as the two gain mediums. IsoGainTM EDF has a numerical aperture (NA) of 0.25, a cut-off frequency of 910 nm and absorption of 10 dB/m at 979 nm. While DHB 1500TM has a NA of 0.23, cut-off frequency of 930 nm and an absorption of 4.3 dB/m at
Fig. 2. L-band erbium doped fiber amplifier with forward–backward pumping scheme.
Fig. 4. Gain and noise figure spectra of the proposed configuration with and without fiber Bragg gratings.
R. Anthony et al. / Optik 125 (2014) 2463–2465
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For temperature dependence of the multichannel EDFA, 32 input signals in L-band with input signal power of −25.23 dBm/channel have been used (shown in Fig. 6). Authors have reported similar studies for C-band erbium doped fiber amplifiers [12]. The erbium doped fibers were assumed to have temperature dependent spectral characteristics, while other components were considered to have a fixed response. A gain flatness of was less than 1.5 dBm at 25 ◦ C over 45 nm. This can be attributed to the use of 980 nm pumps which have temperature resistant pump cross-sections compared to its 1480 nm counterparts. However, such fluctuations with temperature can lead to unnecessary channel gain reductions with sudden rise in bit error rates (BERs). 4. Conclusions
Fig. 5. Gain and gain variation (P–P) spectra of the proposed configuration with fiber Bragg grating at different input signal power. The minimum gain (P–P) variation is obtained at 4.0 W.
In this paper we have proposed a simple yet effective gain flattened dual stage L-band configuration with fiber Bragg gratings (FBGs) for 32 channels operating WDM mode. The configuration shows excellent gain nearly 30 and 20 dB with and without gain flattening filter and temperature resistance over 45 nm bandwidth. We also obtain flat gain for the entire channels at −25.23 dBm, beyond which gain cross-over is observed. Temperature variation from 15 to 45 ◦ C shows gain variation of 2.5 dB for all the signal channels and becomes flattened for 1580–1590 nm bandwidth. References
Fig. 6. Gain and noise figure spectra for system operating in different temperature regimes.
than 7.5 dB for 45 nm (1565–1610 nm) with noise figure close to 5.5 dB. The gain spectrum variation for different channels with varying input signal power has been compared in Fig. 5. The static gain clamping has been tested for 5 different channels (from 1570 to 1610 nm) with 10 nm difference. The saturation input powers for all the signal channels have been found to be −25.23 dBm. Hence, we identify it as the input signal power with the flat gain of 17 dB. Such a gain cross-over is characteristic to an EDFA system. Gain peak to peak (P–P) variation was found to be lowest in −25.23 dBm (3 W) to −23.97 dBm (4 W) region, which reaffirms −25.23 dBm as ideal input signal power.
[1] H. Ono, M. Yamada, M. Shimizu, S-band erbium doped fiber amplifier with a multistage configuration-design, characterization and gain tilt compensation, J. Lightwave Technol. 21 (2003) 2240–2246. [2] S.W. Harun, K. Dimyati, K.K. Jayapalan, H. Ahmad, An overview on S-band erbium doped fiber amplifier, Laser Phys. Lett. (2007) 10–15. [3] R. Gangwar, S.P. Singh, N. Singh, Gain optimization of an erbium-doped fiber amplifier and two stage gain flattened EDFA with 45 nm flat bandwidth in the L-band, Optik 121 (2010) 77–79. [4] N. MdSamsuri, S. Harun, H. Ahmad, Comparison of performances between partial double-pass and full double-pass systems in two-stage L-band EDFA, Laser Phys. Lett. 1 (2004) 610–612. [5] M.A. Mahdi, A.A.A. Bakar, M.H. Al-Mansoori, S.S. Shaari, A.K. Zamzuri, Single stage gain-clamped L-band EDFA with C-band ASE self-oscillating in ring cavity, Laser Phys. Lett. 5 (2008) 126–129. [6] A.A.A. Bakar, M.A. Mahdi, M.H. Al-Mansoori, S. Shaari, A.K. Zamzuri, Singlestage gain clamped L-band EDFA with C-band ASE saturation tone, Laser Phys. 19 (2009) 1026–1029. [7] M.A. Mahdi, F.R. Mahamd Adikan, S. Selvakennedy, W.Y. Chan, H. Ahmad, Longwavelength EDFA gain enhancement through 1550 nm band signal injection, Opt. Commun. 176 (2000) 125–129. [8] K.J. Zhou, W. Zheng, L-band erbium doped fiber laser with polarizationmaintaining ring cavity, Laser Phys. 20 (2010) 1631–1635. [9] R. Anthony, M. Biswas, S. Pain, R. Lahiri, S. Biswas, Modeling of wide-band optical signal amplification in an EDFA network using tunable tap, Photonics Lett. Pol. 4 (2012) 158–160. [10] J. Yuan, T. Liang, W. Wang, S. Gu, Impact analysis on performance optimization of the hybrid amplifier (RA+EDFA), Optik 122 (2011) 1565–1568. [11] M. Karasek, The design of L-band EDFA for multi-wavelength applications, J. Opt. A: Pure Appl. Opt. 3 (2001) 96–102. [12] R. Anthony, S. Biswas, Temperature dependent gain analysis of a cascaded Cband EDFA DWDM network, Procedia Technol. 4 (2012) 92–96.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Gain clamped L-band EDFA with forward–backward pumping scheme using fiber Bragg grating Ricky Anthony a,∗ , Rini Lahiri b , Sambhunath Biswas a a b
Department of Electronics and Communication Engineering, Heritage Institute of Technology, Kolkata, India Department of Electronics and Communication Engineering, National Institute of Technology, Nagaland, India
a r t i c l e
i n f o
Article history: Received 24 May 2013 Accepted 24 October 2013 Keywords: Erbium doped fiber amplifier L-band amplification Fiber Bragg grating
a b s t r a c t The paper proposes a novel two stage L-band erbium doped fiber amplifier with forward–backward pumping scheme for transmission of 32 wavelength division multiplexed (WDM) channels. It is gain clamped with an in-line fiber Bragg grating (FBG) to provide flat gain over 45 nm by restricting and reutilizing amplified spontaneous emission (ASE). We demonstrate that it provides an efficient small signal gain with minimum noise figure of over 20 dB and 5.5 dB, respectively, in the L-band region (1565–1610 nm) by comparing with its forward and backward pumped counterparts with fixed Er3+ fiber length of 20 m for −30 dBm/channel input power. We also obtain the gain and noise figure dependence as a function of each of the Er3+ fiber lengths, pump power (both 1480 and 980 nm), and temperature. Hence a 10 nm region (1580–1590 nm) has been acknowledged where temperature variations become constricted for 30 ◦ C variations (15–45 ◦ C). © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Erbium doped fiber amplifiers (EDFAs) have become integral part of every wavelength division multiplexed (WDM) and dense wavelength division multiplexed (DWDM) system. EDFA operating band has been extended from the C-band to L-band (1570–1610 nm) and S-band (1480–1520 nm) [1,2]. Yet L-band amplification faces considerable hurdles in terms of absorption, scattering effects and efficiency. Even though two staged L-band EDFAs show better pump power conversion compared to its single stage counterpart [3], noise figure still remains a matter of concern. Literature survey demonstrates various configurations such as reutilization of ASE [4–6] using fiber Bragg gratings (FBG), Cband seed injection [7], polarization maintaining ring cavity [8], etc. This band being located away from the zero dispersion wavelengths in WDM/DWDM system makes it less susceptible to non-linear four-wave mixing (FWM), reducing inter-channel cross-talks, thus making it a potential candidate for communications. Authors have previously reported simultaneous amplification of optical signals in C- and L-band with a tunable tap [9], while others include use of Raman amplifier [10]. Such approaches, however, require additional components, generating unwarranted losses and cost.
∗ Corresponding author. Tel.: +353894031377. E-mail addresses: [email protected] (R. Anthony), [email protected] (R. Lahiri), [email protected] (S. Biswas). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.10.102
In the letter, the authors propose a simple L-band EDFA with a forward–backward pumping scheme. Firstly, we theoretically investigate the governing equation of EDFAs. Then we analyze the proposed EDFA in terms of pump powers and temperature with and without FBG. The design criterion is to obtain a gain above 20 dB at the output with noise figure close to 5 dB. We strategically introduce a FBG into the system to obtain a gain clamped result. 2. Theoretical model and configuration The L-band EDFA model with forward–backward pumping scheme assumes a three level system with homogeneous broadening with 980 nm pumps. Such a model is justified, since the erbium ion lifetime at the upper energy state is negligible compared to the metastable state, also ion–ion interaction is negligible with no upconversion from ground state (4 I11/2 ). The rate equation associated with the upper and lower state can be given by temporal ordinary differential equations for propagation along z direction: dn1 (z, t) n2 (z, t) = Re (z)n2 (z, t) + − Ra (z)n1 (z, t) − Rp (z)n1 (z, t) 21 dt + Rp n3 (z, t)
(1)
dn2 (z, t) n2 (z, t) − Ra (z)n1 (z, t) + Rp (z)n1 (z, t) = Re (z)n2 (z, t) + 21 dt + 32 n3
(2)
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R. Anthony et al. / Optik 125 (2014) 2463–2465
Fig. 1. L-band erbium doped fiber amplifier with (a) backward and (b) pumping scheme.
In these equations, Re , Ra and Rp stimulated emission, absorption and pumping rates. 21 and 32 are the spontaneous emission lifetimes between the upper to lower levels. The total erbium ion concentration is given by nt (z, t) = n1 (z, t) + n2 (z, t) + n3 (z, t)
(3)
n1 and n2 are the erbium ion concentration in the ground and metastable states. Under steady state conditions, integrating Eq. (3) yields
P (z, t)˛i /hfi n2 |av(z, t) i i = nt |av(z, t) 1+ P (z, t)(˛i + gi∗ )/hfi i i
(4)
where is the saturation parameter, h is Planck’s constant, f representing the frequency of operation, and ˛ and g the absorption and gain cross-sections, respectively. The forward and backward propagation equation given below is solved in an iterative manner using Runge–Kutta of numerical analysis with fiber lengths from 0 to L for the two fibers individually [11]: dp± p dz
= ±[(tp )21 (tp )n2 (z, t) − (tp )12,13 (tp )n1 (z, t)Pp± (z, tp )
dps (z, ts ) = [(ts )12 (ts )n2 (z, t) − (ts )12 (ts )n1 (z)]Ps (z, ts ) dz dPASE±(z,t)
= ±2h(t)21 (t)n2 (z)
dz
(5) (6)
1 ± [(t)21 (t)n2 (z) tt
± − (t)12 (t)n1 (t)n1 (z)]PASE (z, t)
(7)
where (t) is the overlap integral between the mode field intensity |E (r, t)|2 and the erbium ion density distribution (r) and given by the expression:
R
(t) =
o
|E(r, t)|2 (r) dr
R o
|E(r, t)|2 r dr
Fig. 3. Gain and noise figure spectra of the proposed configuration with forward and backward pumping at different pump powers without fiber Bragg gratings.
979 nm.The in-line fiber Bragg grating (FBG) has a center wavelength of 1553.7 nm with effective index (eff ) and grating pitch of 1.47 nm and 528.4 nm, respectively. It reflects a portion of the Cband backward ASE back into the system. The resonance condition of the FBG is given by the expression: = 2eff
(9)
3. Results and discussions Configurations shown in Fig. 1(a) and (b) have shown gains close to 5 dB which is unacceptable for any communication system. However forward–backward pumped configurations (Fig. 2) shows excellent L-band gain above 30 dB (for 120 mW pump powers) for fixed Er3+ fiber lengths and signal powers of 20 m and −30 dBm, respectively. The input signal is maintained at −30 dBm/channel. As shown from the figure, the gain is nearly 35 dB which is attractive, but with a noise figure close to 15 dB for most of the channels which needs to reduced. Furthermore, as expected increase in pump power from 60 to 240 mW increases the overall gain. The increase in pump powers aids inversion and hence increases stimulated emission, but the fiber length remains critical (Fig. 3). Fig. 4 depicts the gain and noise figure after the inclusion of in-line FBG. The grating wavelength is fixed at 1565 nm. The FBG allows a small portion of ASE for amplification by the second 980 nm pump. This enhances the stimulated emission and increases pump efficiency. As observed, the gain variation is maintained less
(8)
Fig. 1a and b shows the forward and backward pumped erbium doped fiber amplifier. The modified and proposed system (shown in Fig. 2) provides a transmission of 32 channels with a spacing of 1.54 nm. The isolator restricts back-reflection of the spurious signal toward the source. DHB 1500TM and IsoGainTM EDF are selected as the two gain mediums. IsoGainTM EDF has a numerical aperture (NA) of 0.25, a cut-off frequency of 910 nm and absorption of 10 dB/m at 979 nm. While DHB 1500TM has a NA of 0.23, cut-off frequency of 930 nm and an absorption of 4.3 dB/m at
Fig. 2. L-band erbium doped fiber amplifier with forward–backward pumping scheme.
Fig. 4. Gain and noise figure spectra of the proposed configuration with and without fiber Bragg gratings.
R. Anthony et al. / Optik 125 (2014) 2463–2465
2465
For temperature dependence of the multichannel EDFA, 32 input signals in L-band with input signal power of −25.23 dBm/channel have been used (shown in Fig. 6). Authors have reported similar studies for C-band erbium doped fiber amplifiers [12]. The erbium doped fibers were assumed to have temperature dependent spectral characteristics, while other components were considered to have a fixed response. A gain flatness of was less than 1.5 dBm at 25 ◦ C over 45 nm. This can be attributed to the use of 980 nm pumps which have temperature resistant pump cross-sections compared to its 1480 nm counterparts. However, such fluctuations with temperature can lead to unnecessary channel gain reductions with sudden rise in bit error rates (BERs). 4. Conclusions
Fig. 5. Gain and gain variation (P–P) spectra of the proposed configuration with fiber Bragg grating at different input signal power. The minimum gain (P–P) variation is obtained at 4.0 W.
In this paper we have proposed a simple yet effective gain flattened dual stage L-band configuration with fiber Bragg gratings (FBGs) for 32 channels operating WDM mode. The configuration shows excellent gain nearly 30 and 20 dB with and without gain flattening filter and temperature resistance over 45 nm bandwidth. We also obtain flat gain for the entire channels at −25.23 dBm, beyond which gain cross-over is observed. Temperature variation from 15 to 45 ◦ C shows gain variation of 2.5 dB for all the signal channels and becomes flattened for 1580–1590 nm bandwidth. References
Fig. 6. Gain and noise figure spectra for system operating in different temperature regimes.
than 7.5 dB for 45 nm (1565–1610 nm) with noise figure close to 5.5 dB. The gain spectrum variation for different channels with varying input signal power has been compared in Fig. 5. The static gain clamping has been tested for 5 different channels (from 1570 to 1610 nm) with 10 nm difference. The saturation input powers for all the signal channels have been found to be −25.23 dBm. Hence, we identify it as the input signal power with the flat gain of 17 dB. Such a gain cross-over is characteristic to an EDFA system. Gain peak to peak (P–P) variation was found to be lowest in −25.23 dBm (3 W) to −23.97 dBm (4 W) region, which reaffirms −25.23 dBm as ideal input signal power.
[1] H. Ono, M. Yamada, M. Shimizu, S-band erbium doped fiber amplifier with a multistage configuration-design, characterization and gain tilt compensation, J. Lightwave Technol. 21 (2003) 2240–2246. [2] S.W. Harun, K. Dimyati, K.K. Jayapalan, H. Ahmad, An overview on S-band erbium doped fiber amplifier, Laser Phys. Lett. (2007) 10–15. [3] R. Gangwar, S.P. Singh, N. Singh, Gain optimization of an erbium-doped fiber amplifier and two stage gain flattened EDFA with 45 nm flat bandwidth in the L-band, Optik 121 (2010) 77–79. [4] N. MdSamsuri, S. Harun, H. Ahmad, Comparison of performances between partial double-pass and full double-pass systems in two-stage L-band EDFA, Laser Phys. Lett. 1 (2004) 610–612. [5] M.A. Mahdi, A.A.A. Bakar, M.H. Al-Mansoori, S.S. Shaari, A.K. Zamzuri, Single stage gain-clamped L-band EDFA with C-band ASE self-oscillating in ring cavity, Laser Phys. Lett. 5 (2008) 126–129. [6] A.A.A. Bakar, M.A. Mahdi, M.H. Al-Mansoori, S. Shaari, A.K. Zamzuri, Singlestage gain clamped L-band EDFA with C-band ASE saturation tone, Laser Phys. 19 (2009) 1026–1029. [7] M.A. Mahdi, F.R. Mahamd Adikan, S. Selvakennedy, W.Y. Chan, H. Ahmad, Longwavelength EDFA gain enhancement through 1550 nm band signal injection, Opt. Commun. 176 (2000) 125–129. [8] K.J. Zhou, W. Zheng, L-band erbium doped fiber laser with polarizationmaintaining ring cavity, Laser Phys. 20 (2010) 1631–1635. [9] R. Anthony, M. Biswas, S. Pain, R. Lahiri, S. Biswas, Modeling of wide-band optical signal amplification in an EDFA network using tunable tap, Photonics Lett. Pol. 4 (2012) 158–160. [10] J. Yuan, T. Liang, W. Wang, S. Gu, Impact analysis on performance optimization of the hybrid amplifier (RA+EDFA), Optik 122 (2011) 1565–1568. [11] M. Karasek, The design of L-band EDFA for multi-wavelength applications, J. Opt. A: Pure Appl. Opt. 3 (2001) 96–102. [12] R. Anthony, S. Biswas, Temperature dependent gain analysis of a cascaded Cband EDFA DWDM network, Procedia Technol. 4 (2012) 92–96.