1. Introduction

The Raman amplification has been proved to be an effective means of providing relative flat gains over ultra-wide bandwidth [1]. Moreover, it is attractive to incorporate the dispersion compensation along with loss compensation in a transmission fiber span. The dispersion compensating fiber (DCF) is a particular convenient Raman gain medium [2], which has Raman gain efficiency of 5 to 10 times larger than standard single mode fiber (SSMF) as well as the appropriate dispersion properties. By using a modest amount pump power, the discrete Raman amplifier (DRA) can be used to offset the loss of the dispersion compensation module and to extend new gain bandwidth such as S-band or L-band. When designing such amplifiers, many issues require thorough investigation such as nonlinear impairments and Rayleigh backscattering [3]. An optimum gain distribution of amplifier must be found and the improvements in pump efficiency are needed to make the discrete Raman amplifiers competitive with the performance of new types of EDFAs [4].

Traditionally, fiber Raman amplifiers are operated in the backward pumping geometry to minimize the pump-to-signal crosstalk and polarization-dependant gain. However, with the low-noise pump sources are available now, the co-pumping and bi-directional pumping schemes are feasible in practice [5]. In this paper, we report on the novel design of double-pass discrete Raman amplifier achieving high Raman gain with much better pump efficiency and low noise figure (NF) in which the DCF is used as the Raman gain medium and the high reflection FBG is used as the reflector. The signal experiences co- and counter-pumping in the same fiber and it will acquire double-gain neglecting the pump depletion. Although this equivalent bi-directional pumped Raman amplifier is superior to the typical counter-pumping amplifier in the ASE noise performance because of the partial co-pumping gain, we show that the multi-path interference (MPI) noise induced by Rayleigh backscattering is the limitation factor in double-pass system. In fact, the additional MPI caused by the reflector requires a careful consideration of the gain and the reflection coefficient of FBGs.

2. Raman gain and ASE noise

The configuration of proposed double-pass discrete Raman amplifier is shown in Fig. 1. The dropped signal from circulator can co-propagate with the pump power in the DCF and will be reflected to counter-propagate with the pump. Both narrow band FBG and chirped wideband FBG (Reflection ratio R>99%) can be used here.

 

Fig. 1. Double-pass discrete Raman amplifier configuration.

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At a stable state, there are three types of lightwaves traveling in the amplifier, the forward propagating signal, forward pump, and the reflected backward signal, respectively. The power evolution of lightwaves can be described by the following coupled equations [6, 7]:

Here, P_SK =P_Sf or P_Sb is the forward or backward signal power, and P_Pf is pump power, respectively. α_s or α_P is the signal or pump transmission loss. Z is the propagation distance from the fiber input end and g=g ₀/(A_eff ·K where g ₀ is the Raman gain coefficient between signal and pump, A_eff is the effective fiber area and K is the polarization scrambling factor between pump and signal light (K varies from 1 to 2 and k=2 for depolarized case). We don’t consider the temperature dependence because of the magnificent temperature stability of Raman amplifier [8]. The Rayleigh backscattering induced system noises can be included additionally (see below).

In this double-pass system, neglecting the pump depletion and using boundary condition P_Sf (L)=P_Sb (L), the forward and backward ON-OFF signal gain can be derived analytically as:

Where L is total fiber length. Thus the output signal will experience the total ON-OFF Raman gain of G_Rf (0, L)·G_Rb (0, L) (Note that G_Rb (z ₁, z ₂) is the Raman gain experienced from z ₂ to z ₁). With the same notation, the ASE noise spectral density of double pass system can be described as ±${\mathit{\text{dN}}}_{\mathit{\text{SK}}}^{\mathit{\text{ASE}}}$ /dz=-α_s$N_{\mathit{\text{SK}}}^{\mathit{\text{ASE}}}$ +g·($N_{\mathit{\text{SK}}}^{\mathit{\text{ASE}}}$+hυ)·P_pf . Using the Raman gain Eqs. (3), (4), the backward and forward ASE noise spectral density can be obtained:

Where P_Pf (x)=P_Pf (0)exp(-α_Px) is undepleted pump power approximation, T(z ₁, z ₂)=exp[-α_s (z ₂-z ₁)] is the passive fiber loss, thus the forward net gain G_f from distance z ₁ to z ₂ is T(z ₁, z ₂)G_Rf (z ₁, z ₂) and the backward net gain G_b from distance z ₂ to z ₁ is T(z ₁, z ₂)G_Rb (z ₁, z ₂).

Since we use the narrow band FBG as the reflector, only the in-band ASE will be reflected into the DRA, thus the out-band forward ASE will be eliminated through the reflection process. The amplification efficiency can also be improved by the reduction of wideband ASE.

3. Impact induced by the Rayleigh backscattering

Unlike the white noise random process feature of ASE, the MPI noises induced by Rayleigh backscattering have the same color of signal. The contribution from signal-MPI beat noise is more serious in our system with the introduction of reflection. We will examine the Rayleigh-backscattered (RB) and double- Rayleigh-backscattered (DRB) light of forward and backward transmission signals as shown in Fig. 2.

 

Fig. 2. Signal and noise light (ASE and MPI) flows.

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The RB and DRB noise power can be given separately using above notations as:

Where P_Sb (L)=P_Sf (L)=P_Sf (0)G_f (0,L), G_f and G_b are net gain, r is the Rayleigh-backscattering coefficient. Since the Rayleigh scattered light is continuous in fiber, $P_{\mathit{\text{Sb}}}^{\mathit{\text{RB}}}$ (L) and $P_{\mathit{\text{Sf}}}^{\mathit{\text{DRB}}}$ (L) will be reflected by the FBG and experience Raman gain. Consider all these factors we can obtain a general expression of noise figure (NF) of the double-pass Raman amplifier in which ASE and MPI noises are generated simultaneously. In the beat noise limited detection, one can write the noise figure of DRA from [9] as:

Here G_ON-OFF is the overall ON-OFF Raman gain and P_RB (0) is the total MPI noise at the output port. B_e is the equivalent square bandwidth of the electrical filter and B_S is the equivalent square bandwidth of the optical signal. Notice that ASE light is randomly polarized but the degree of polarization of Rayleigh backscattered light is 5/9.

4. Simulation and experimental results

The double-pass discrete Raman amplifier is designed for compensating both the attenuation and dispersion of a 50 km SMF span (we don’t discuss the dispersion property in this paper). If the input signal power in SMF is -4 dBm, transmission loss of SMF at 1550 nm is 0.18 dB/Km, the input signal power in DCF is -13 dBm. The loss of DCF is measured as 0.49 dB/Km at 1550nm and 0.69 dB/Km at 1455nm. The Raman gain coefficient comes from the Ref. [2]. It is worth noting that the average total PMD value of our DCF is measured as 0.82 ps, and it is high enough to neglect the polarization dependence of the Raman gain [11]. It is possible to avoid the need for depolarization of the pump source and we will assume K=2 in our simulation.

Figure 3 shows the signal and pump power distributions along the DCF fiber for our double-pass configuration and the traditional backward pumping amplifier. Both cases were simulated to provide the same gain=16 dB. The double-pass amplifier is pumped by 452 mW and the backward pumping single-pass amplifier is pumped by 830 mW. Clearly, the double-pass configuration achieves the same gain with 45% less pump power and only half-length of single-pass amplifier. We also implemented the double-pass amplifier in experiments as in Fig. 1. The signal wavelength is 1556 nm that comes from the CW tunable laser. The 1455 nm Raman laser serves as the pumping source. Raman gain medium is 3.013 km DCF. The double pass is provided by the high reflection FBG that has the reflection peak at 1556 nm and the stop-bandwidth of 0.2 nm. Figure 4 shows the experimental and simulation results of ON-OFF Raman gain versus pump power (dBm). It is clear that in order to achieve 20 dB Raman gain, the pump power (26.9 dBm) needed in the double-pass system is almost half of that (29.6dBm) with single-pass system. Furthermore, the gain slope (rate), which defined as the increase of gain over the increase of pump power, is much faster at the double-pass configuration. The average gain slope for double-pass is 50.2 dB/W and 28 dB/W for single-pass.

 

Fig. 3. Signal and pump power along the 3-km DCF for double- and single-pass schemes.

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Fig. 4. Raman gain versus pump power at double- and single-pass configuration.

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In order to evaluate the noise performance of double-pass system, we plot the ASE and all of the RB/DRB noise powers versus Raman ON-OFF gain in Fig. 5 (measured value of r=9.14×10^-5 km ^-1). The ASE light power is integrated within the FBG stop-band of 0.2 nm. For comparison, we also plot the ASE noise power of traditional backward pumped 6-km DCF single-pass system. It is clear that the ASE noise of our double-pass system can be suppressed by the equivalent bi-directional pumping scheme. But the MPI noises due to the reflection play an important role in double-pass system. As shown here, the double-Rayleigh-backscattered light is quite small because of the short fiber length and very low input signal power. At the same time, the Rayleigh-backscattered light of signal induced by the reflection of FBG is a key component when considering the noise performance. The output RB noise of forward signal $P_{\mathit{\text{Sf}}}^{\mathit{\text{RB}}}$ (0) is at the same order as ASE, but the output RB noise of backward signal $P_{\mathit{\text{Sb}}}^{\mathit{\text{RB}}}$ (0)=$P_{\mathit{\text{Sb}}}^{\mathit{\text{RB}}}$ (L)G_b (0,L) increases with the Raman gain rapidly and overwhelm ASE power at the high gain region. That is, the MPI noise is the mainly limitation factor of the double-pass Raman amplifier.

 

Fig. 5. ASE and RB/DRB noise light power versus Raman gain.

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Fig. 6. Equivalent NF with/without considering the MPI noise.

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We compare the equivalent NF performance versus Raman ON-OFF gain with and without considering MPI noise contribution in Fig. 6. When calculating the NF, we use the optical signal bandwidth B_S =10 GHz and the receiver electrical bandwidth B_e =10 GHz [10]. The total NF of the double-pass system increases at the beginning, and then decreases with the increasing gain. But unlike the NF induced by ASE, the NF increases when the Raman gain exceeds 13 dB, which limits double-pass DRA in high gain usage. Since most of the Rayleigh-backscattering induced noise is due to the RB light of backward propagating signal, we can try to vary the reflection rate of FBG to control the reflected power of backward amplified signal and hence reduce the equivalent NF in high gain region. Figure 7 shows the equivalent NF for reflection rate R=1, 0.75, 0.5 of FBG, respectively. The less the reflection rate, the more the NF at the 0 gain point because of the additional insertion loss of FBG. By increasing the pump power and consequently, the ON-OFF Raman gain, we can see an NF reduction in high gain region and then, the minimum NF can be achieved at the higher gain. The minimum NF of R=0.75 or 0.5 can be obtained when the DRA operating at the ON-OFF gain of 14 or 16 dB. It is clear that we can achieve less NF and higher Raman gain operation by reducing the reflection ratio of FBG. Note that the pump power needed in this case increases as well (such as the input pump power at R=0.5 is 15% larger than that at R=1). Actually, if we set R=0 that is no reflector is used, signal will be received at the reflector end and the DRA is a typical single-pass amplifier system. The RB noise has no effect on the system noise but the advantages of double-gain and high pump efficiency are lost.

 

Fig. 7. Overall equivalent NF for different reflection ratio R.

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5. Conclusions and discussions

We have investigated the design of double-pass discrete Raman amplifier theoretically and experimentally. We developed an explicit model for the equivalent bi-directional Raman gain and the noise performance due to ASE and Rayleigh-backscattering. For the same length DCF, by using the high reflection ratio FBG, DRA can achieve the same Raman gain as single-pass system while just half-pump power is needed or DRA can operate at double-gain at the same pump power. That is low pump power can be used to achieve high enough Raman gain in DCF and the dispersion compensation is also enhanced twice. The double-pass system with very low signal light input can suppress the nonlinear distortion with low pump power operation although the thorough understanding of nonlinear impairments need further study because of the small-effective area DCF. Actually, high local dispersion in DCF can mitigate the interchannel effects such as FWM or XPM, but the self-phase modulation can still lead to the signal distortion. We also proved theoretically and numerically that MPI noise induced by the Rayleigh-backscattering is the dominating source of noise impairments. From the equivalent NF we can see that the MPI noises limit the usage of our double-pass DRA in a very high gain region. We then decrease the reflection ratio of reflector to minimize the contribution of RB noise. The results show that minimum equivalent NF will decrease and will be obtained at higher Raman gain operation. The expense of the reduction of NF is the increase of pump power. Hence a trade-off between high gain/efficiency and noise performance must be considered based on the system requirements.