1 Introduction

Optical amplifiers play an important and fundamental role in optical transmissions, allowing the transmitted signal to propagate along the fiber link over long distances (Amiri et al. 2020). The demand of high bandwidth services leads to the requirement to enhance the transmission capacity of dense wavelength division multiplexed (DWDM) optical communication systems (Obaid and Shahid 2018a). The performance of a DWDM system generally depends on the optical amplification method used. To broaden the DWDM bandwidth, optical amplifiers are essential components (Obaid and Shahid 2018b).

Raman optical amplifiers are an active area of research in the world of optical communications (Iqbal et al. 2019). Multi-pump configurations of the Raman amplifier make him attractive for DWDM applications. They are more appealing technology than other traditional optical amplifiers due to their broadband tunability (Obaid and Shahid 2020). Using proper pump wavelengths, Raman amplifiers can be designed to operate in the desired band. Additionally, they have advantages of high gain bandwidth, better gain flatness and low noise figure (NF) (Obaid and Shahid 2018c).

Different pumping configurations for Raman amplifier can be employed to improve overall gain for DWDM system. In the literature, various schemes meeting the high gain bandwidth requirements have been reported (Barth and Fisch 2018). Kidorf et al. (1999) used multiple pumps to design a Raman amplifier with a 100 nm bandwidth. They used eight 130 mW pump lasers and reported a low gain ripple of 1.1 dB. Singh et al. (2012) investigated the effect of counter propagating pumping in Raman amplifier. They used single, two and seven pumps and observe the resulting impacts on bandwidth and gain ripple. They reported that the gain ripple decreases by increasing the number of pumps from one to seven. Singh et al. (2019) investigated the gain spectrum evolutions of a dual/triple pumped fiber Raman amplifier by adjusting its design parameters. They reported a gain of greater than 15 dB when pumping the amplifier with three continuous wave lasers. Chen et al. (2006) reported better gain flatness and significant reduction in NF with multistage gain flattened Raman amplifiers using multiple counter-propagating pumps. Beshr and Aly (2020) introduced a new model for NF of Raman amplifier using three different pumping schemes. They reported that the NF increases exponentially with the fiber length and decreases exponentially with input signal power. Beshr et al. (2021) derived a model for carrier-to-noise ratio (CNR) of Raman amplifier using different pumping schemes. They reported that at 100 km fiber length, the CNR reaches its minimum value of 40 and 41 dB, in counter and bidirectional pumping respectively. Also, the co-pumping provides the lowest BER in contrast to the counter pumping. Pradhan and Mandloi (2018) discussed the performance of a 64-channel WDM system with backward multi-pump Raman amplifier. They optimized the gain variation without using any gain-flattening component. They reported a maximum gain of 8.6 dB with small gain ripple of 0.5 dB.

This paper presents three different pumping configurations of Raman amplifier: co-pumping, counter-pumping and bidirectional pumping. All schemes are simulated and investigated for a 50-channel DWDM system at reduced channel spacing of 0.8 nm. To achieve maximum gain with small ripple, pump powers are selected using multiparameter optimization algorithm. The paper is organized in five sections. After introduction in Sect. 1, the theoretical model is discussed in Sect. 2. The proposed setup is described in Sect. 3, preceded by the results in Sect. 4. Finally, Sect. 5 concludes the research.

2 Theory

The wave propagation in a multi-pump Raman amplifier is characterized by many physical effects (Obaid and Shahid 2019a). These effects include forward and backward spontaneous Raman emission, Rayleigh scattering components, stimulated Raman scattering (SRS), pump–pump interactions, pump–signal interactions and signal–signal interactions. The system incorporating all these effects is described by the following differential equation (Obaid and Shahid 2019a)

$$ \begin{aligned} \frac{{dP_{f} \left( {z,v} \right)}}{dz} & = - \alpha \left( v \right)P_{f} \left( {z,v} \right) + \gamma \left( v \right)P_{b} \left( {z,v} \right) + \mathop \smallint \limits_{\mu > v}^{ } \left\{ {\frac{{g_{R} \left( {v - \mu } \right)}}{{A_{eff} }}\left[ {P_{f} \left( {z,\mu } \right) + P_{b} \left( {z,\mu } \right)} \right]P_{f} \left( {z,v} \right)} \right. \\ & \quad \left. { + 2hv\frac{{g_{R} \left( {v - \mu } \right)}}{{A_{eff} }}\left[ {P_{f} \left( {z,\mu } \right) + P_{b} \left( {z,\mu } \right)} \right] \left[ {1 + \frac{1}{{e^{{h\left( {\mu - v} \right)/kT}} - 1}}} \right]} \right\}d\mu - \mathop \smallint \limits_{\mu < v}^{ } \left\{ {\frac{{g_{R} \left( {v - \mu } \right)}}{{A_{eff} }}\left[ {P_{f} \left( {z,\mu } \right) + P_{b} \left( {z,\mu } \right)} \right]P_{f} \left( {z,v} \right)} \right. \\ & \quad \left. { + 2hv\frac{{g_{R} \left( {v - \mu } \right)}}{{A_{eff} }}\left[ {P_{f} \left( {z,\mu } \right) + P_{b} \left( {z,\mu } \right)} \right] \left[ {1 + \frac{1}{{e^{{h\left( {v - \mu } \right)/kT}} - 1}}} \right]} \right\}d\mu \\ \end{aligned} $$
(1)

where Pf(z,v) and Pb(z,v) are the forward and backward power at frequency v respectively; α(v) is the attenuation and Aeff is the effective area of the fiber; γ(v) is Rayleigh scattering coefficient; gR(v‒µ) is the Raman gain coefficient between frequencies v and µ; T is temperature of the fiber; h is Planck’s constant and k is Boltzmann's constant.

Practically, the amplifier gain is not much affected by the noise effects related to spontaneous Raman scattering and Rayleigh back scattering and the terms corresponding to these effects can be ignored (Mahran 2015). Therefore, the wave propagation in a multi-pumped Raman amplifier can be described by the following coupled equation

$$ \pm \frac{{dP_{k} }}{dz} = \left[ { - \alpha_{k} + \mathop \sum \limits_{j = 1}^{k - 1} \frac{{g_{R} \left( {v_{j} - v_{k} } \right)}}{{A_{eff} }}P_{j} - \mathop \sum \limits_{j = k + 1}^{n + m} \frac{{v_{k} }}{{v_{j} }}\frac{{g_{R} \left( {v_{k} - v_{j} } \right)}}{{A_{eff} }}P_{j} } \right]P_{k} , \quad \left( {k = 1, 2, \ldots , n + m} \right) $$
(2)

The above equation can also be written as

$$ \pm \frac{{dP_{k} }}{dz} = - \alpha_{k} P_{k} + \mathop \sum \limits_{j = 1}^{n + m} g_{jk} P_{k} P_{j} ,\quad \left( {k = 1, 2, \ldots , n + m} \right) $$
(3)

In Eqs. (2) and (3), (k = 1, 2,…, n) and (k = n + 1,…, n + m) represent pump and signal waves respectively. The power, frequency and attenuation coefficient for the k-th wave are respectively denoted by Pk, vk and αk. “+” and “−” sign represent forward propagating signal and backward propagating pumps respectively. The boundary conditions for the fiber of length L are defined at z = L for pump waves and at z = 0 for signal waves. That is, we have

$$ P_{k} \left( L \right) = P_{ko} \left( {k = 1, 2, \ldots , n} \right)\quad {\text{and}}\quad P_{k} \left( 0 \right) = P_{ko} \left( {k = n + 1, \ldots , n + m} \right) $$
(4)

The Raman gain coefficients (gjk) in Eq. (3) are given by

$$ g_{jk} = sgn\left( {v_{j} - v_{k} } \right)\frac{1}{{A_{eff} }}\frac{{v_{k} }}{{v_{o} }}g_{R} \left( {\left| {v_{k} - v_{j} } \right|} \right) $$
(5)

where gR(vo‒v) is the Raman gain spectrum measured at a reference pump frequency vo.

Now, the signal gain for channel k is given by Kidorf et al. (1999); Obaid and Shahid 2019a)

$$ G_{Raman} = \frac{{P_{k} \left( L \right)}}{{P_{k} \left( 0 \right)}} = exp\left( { - \alpha_{k} L + \mathop \sum \limits_{j = n + 1}^{n + m} g_{jk} I_{j} } \right)exp\left( {\mathop \sum \limits_{j = 1}^{n} g_{jk} I_{j} } \right) ,\quad \left( {k = n + 1, \ldots , n + m} \right) $$
(6)

where \(I_{j} = \mathop \smallint \limits_{0}^{L} P_{j} \left( z \right) dz, j = 1, 2, \ldots , n + m\). First term describes the signal–signal Raman scattering and effects of fiber attenuation. The second term represents the pump–signal Raman gain experienced by the signal.

The NF of amplification stage in a transmission system can be approximately computed using the relation (Krzczanowicz et al. 2018)

$$ NF_{ } = \frac{{2P_{ASE} }}{{B_{o} hvG_{ } }} + \frac{1}{{G_{ } }} $$
(7)

where PASE is the amplified spontaneous emission (ASE) noise power, G is the gain, hv is the photon energy and Bo is optical resolution bandwidth.

The Q-factor and bit error rate (BER) are used as a measure of the transmission quality and degradation in a system. The Q-factor is defined as (Obaid and Shahid 2019b)

$$ Q = \frac{{I_{1} - I_{0} }}{{\sigma_{1} + \sigma_{0} }} $$
(8)

where 〈I1〉 and 〈I0〉 are the mean photocurrents for ones and zeros respectively. The parameters ‘σ1’ and ‘σ0’ are the respective standard deviations of the photocurrents. The BER can be obtained from the Q-factor using the relationship (Obaid and Shahid 2021)

$$ BER = \frac{1}{2}erfc\left( {\frac{Q}{\sqrt 2 }} \right) $$
(9)

where ‘erfc’ is the complementary error function.

3 Proposed setup

The performance of multi-pump Raman amplifier is analyzed using three different pumping configurations. The schematics of the proposed setup for backward, forward and bidirectional pumping are shown in Fig. 1a, b and c respectively. Setup consists of 50 DWDM channels with 0.8 nm spacing, covering the 1531 – 1571 nm wavelength range using continuous wave lasers. The channels are driven by the data stream from 100 Gb/s, NRZ modulated signals with input power of − 20 dBm each. The PIN photodetector with a responsivity of 0.9 A/W and dark current of 1 nA is used at the receiver side.

Fig. 1
figure 1

Schematic of proposed setup for a backward, b forward and c bi-Directional pumping configuration

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Simulations are performed in this study to obtain the global performance of proposed Raman amplifier configurations. Simulations and analysis are made by using OptiSystem and MATLAB respectively. Three pump laser diodes have been employed for each configuration and their powers have been selected using a multi-parameter optimization algorithm of OptiSystem 19.0 software for obtaining a high and flat gain (Ferreira et al. 2011). OptiSystem software provides a robust, powerful, multi-target and multi-parameter optimization algorithm (Singh et al. 2019). It is a global search optimization algorithm, where the solution is searched between large numbers of possibilities (Zhou et al. 2006). The schematic and the flow chart describing the sequence of the optimization algorithm are shown in Figs. 2 and 3 respectively. Firstly, the total number of iterations are selected and pump powers have been chosen as design parameters. Then, the starting values and ranges of pump powers are specified for optimization (Rocha and Nogueira 2014). Gain is selected as output parameter for all DWDM channels. At each iteration, the gain is evaluated and then combination of parameters is modified for obtaining better gain. This process is repeated iteratively and as the desired gain is obtained, further modification is not required (Neto et al. 2007). Finally selected pump powers and the corresponding wavelengths, along with the other Raman amplifier parameters used in evaluating the net gain are summarized in Table 1.

Fig. 2
figure 2

Schematic of the applied multi-parameter optimization algorithm

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Fig. 3
figure 3

Flow chart of the applied multi-parameter optimization algorithm

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Table 1 Parameters of Raman amplifier
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4 Results and discussion

The performance of proposed Raman configurations is determined in terms of gain, NF, Q-factor and BER at input power of − 20 dBm per channel. The fluctuations in gain and NF are also observed with changes in input power. The effects of changing the Raman length on gain, Q-factor and BER are also investigated.

4.1 Gain and noise figure

The gain spectra of proposed configurations as a function of channel wavelengths are shown in Fig. 4a. It is observed that high gain with lower gain variations is obtained. ASE noise and non-uniform variations in gain are due to the nonlinearities produced by the amplifier (Iqbal et al. 2017). A gain of > 20.67 dB is achieved at each wavelength for the backward pumping configuration, with a peak value at 1535.8 nm. Low gain ripple of 1.28 dB is obtained over the selected wavelength range. A gain of > 20.35 dB is obtained at each wavelength for the forward pumping configuration with gain ripple of 1.55 dB. For the bidirectional pumping configuration, highest gain of > 20.76 dB is achieved at each wavelength. Maximum gain is obtained at 1553.4 nm. Overall, lowest gain ripple (1.24 dB) is obtained for bidirectional pumping configuration. Average gain and gain ripple values for the proposed amplifying stages are shown in Fig. 4b, c.

Fig. 4
figure 4

a Gain spectra, b average gain and c gain ripple values of proposed amplifiers

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The gain of proposed configurations is also investigated at different input powers per channel and the resulting spectra for backward, forward and bidirectional pumping are shown in Fig. 5a, b and c respectively. As the input power increases, overall decrease in gain is observed. It is expected, because gain-saturation effects dominate at higher input powers. Gain ripple values are also calculated for the same input powers and plotted in Fig. 6. It can be seen that the minimum ripple is obtained at − 20 dBm optimum input power. For backward pumping, the gain ripple decreases from 1.4679 dB at − 30 dBm to 1.2803 dB at − 20 dBm. After − 20 dBm, the value of gain ripple rises again and at − 5 dBm, the calculated value of gain ripple is 2.6220 dB. For forward pumping, the gain ripple decreases from 1.6484 dB at − 30 dBm to 1.5540 dB at − 20 dBm. For bidirectional pumping, the gain ripple decreases from 1.4313 dB at − 30 dBm to 1.2459 dB at − 20 dBm. After − 20 dBm, gain ripple increases again and at − 5 dBm, the gain ripple is 1.9307 dB. Actually, low gain and large gain variations at higher input powers reduce the system performance due to increased fiber nonlinearities and amplifier saturation effects.

Fig. 5
figure 5

Gain spectra of a backward, b forward and c bidirectional pumping configurations at different per channel input powers

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Fig. 6
figure 6

Gain ripple variations with input power for a backward, b forward and c bidirectional pumping configurations

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The NF spectra of proposed configurations as a function of channel wavelengths are shown in Fig. 7a. Results show that lowest NF is obtained for forward pumping configuration. At each wavelength, NF is found to be less than 8.22 dB and 8.00 dB for backward and bi-directional pumping respectively. On the other hand, NF is determined to be less than 7.43 dB at each wavelength for forward pumping. Average NF and NF ripple values for the three configurations are shown in Fig. 7b and c respectively. Forward pumping configuration is found to have the lowest NF ripple of 0.53 dB. For backward and bi-directional pumping, the obtained NF ripple is 0.57 dB and 0.65 dB respectively. Resultantly, forward pumping configuration is found to have the lowest NF and NF ripple.

Fig. 7
figure 7

a NF spectra, b average NF and c NF ripple values of proposed amplifiers

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The NF is also evaluated at different input powers per channel and the resulting profiles for backward, forward and bidirectional pumping are shown in Fig. 8a, b and c respectively. It can be seen that NF increases with the increase in input power. Average NF increases from 7.87 dB at − 30 dBm to 8.39 dB at − 5 dBm for backward pumping, as shown in Fig. 9a. For bi-directional pumping, average NF increases from 7.63 dB at − 30 dBm to 7.93 dB at − 5 dBm. It is shown in Fig. 9c. For forward pumping, average NF increases from 7.16 dB at − 30 dBm to 7.21 dB at − 5 dBm. It is shown in Fig. 9b.

Fig. 8
figure 8

NF spectra of a backward, b forward and c bidirectional pumping configurations at different per channel input powers

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Fig. 9
figure 9

Average NF versus input power for a backward, b forward and c bidirectional pumping configurations

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4.2 Investigation of the effects of Raman length on gain

The effects of changing the Raman length on gain is investigated for the proposed amplifiers and the optimized length for Raman fiber is determined for obtaining large gain with minimum ripple. Raman length is increased from 15 to 35 km, and the gain is investigated for the three configurations. The other Raman amplifier parameters remain same as given in Table 1. The average gain at various Raman lengths is calculated and the results for backward, forward and bidirectional pumping are shown in Fig. 10a, b and c respectively. As can be seen, the gain increases from 16.38 dB at 15 km to 23.28 dB at 35 km in the backward pumping configuration. For forward pumping, increase in gain from 16.21 dB to 23.29 dB is observed. Highest average gain is obtained for bi-directional pumping. It increases from 16.52 dB at 15 km to 23.34 dB at 35 km. The resulting gain spectra of proposed amplifiers at different Raman lengths are shown in Fig. 11. High gain is observed at increased lengths, with the maximum gain obtained at 35 km. However, the corresponding gain ripple values plotted in Fig. 12 shows that, the minimum ripple is obtained at 25 km Raman length for all configurations. For backward pumping, the gain ripple decreases from 1.65 dB at 15 km to 1.28 dB at 25 km. Beyond 25 km, the ripple increases again and it is calculated to be 1.96 dB at 35 km. Similarly, the gain ripple decreases from 1.81 dB at 15 km to 1.55 dB at 25 km for forward pumping. On the other hand, the gain ripple for bi-directional pumping decreases from 1.45 dB at 15 km to 1.24 dB at 25 km. After 25 km, the value of gain ripple rises again and it is found to be 1.76 dB at 35 km. Hence, the finally selected Raman length in the simulation of the proposed amplifiers is 25 km.

Fig. 10
figure 10

Average Raman gain as a function of Raman length for a backward, b forward and c bidirectional pumping configurations

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Fig. 11
figure 11

Gain spectra at different Raman lengths for a backward, b forward and c bidirectional pumping configurations

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Fig. 12
figure 12

Gain ripple values at different Raman lengths for a backward, b forward and c bidirectional pumping configurations

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4.3 Q-factor and BER performance

The Q-factor and BER performance of the system is directly affected by the induced crosstalk. The crosstalk effects arise because of the nonlinearities produced by optical amplifiers (Noor et al. 2022). The Q-factor and BER of received electrical signals as a function of channel wavelengths for proposed amplifiers are shown in Figs. 13 and 14 respectively. An acceptable Q-factor (> 12 dB) and BER (< 10−14) is achieved at each wavelength for all pumping configurations. The nonlinearities induced in Raman amplifier and inter-channel cross-talk at narrow channel spacing as well as high input powers produce fluctuations in Q-factor and BER results.

Fig. 13
figure 13

Q-factor as a function of channel wavelengths for a backward, b forward and c bidirectional pumping configurations

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Fig. 14
figure 14

BER as a function of channel wavelengths for a backward, b forward and c bidirectional pumping configurations

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5 Conclusion

The Raman amplifier, using three different pumping configurations, is designed and investigated for 50 × 100 Gbps DWDM system at channel spacing of 0.8 nm. System operates at an optimum input power of − 20 dBm per channel and Raman pump powers are selected using multiparameter optimization algorithm to achieve maximum gain with minimum ripple. Highest average gain of 21.42 dB is obtained with lowest gain ripple of 1.24 dB for bidirectional pumping configuration. The fluctuations in gain and NF are also observed with changes in input power. An acceptable Q-factor and BER is achieved at each wavelength for all pumping configurations. The achieved high and flat gain confirms the feasibility of proposed amplifiers for broad band long-haul DWDM applications.