Raman Amplifier Performance under New Wavelength Ranges

1 Introduction

Raman amplifier (RA) is one of the enabling technologies for high-capacity long-distance DWDM (dense wavelength division-multiplexed) transmission systems. RA provides wider amplification bandwidth, low-noise characteristics and simplicity. Multiwavelength pumping scheme is usually used to ensure gain bandwidth for high-capacity DWDM transmission. Raman gain bandwidth can be easily extended by adding pump wavelengths [1].

Broadband RAs for wavelength division multiplexing (WDM) have to be able to provide a flat gain response over their operational bandwidth. A promising option for achieving gain flatness without increasing the complexity of the amplifier by adding a large number of pumping sources is to make those pumps spectrally broader through the effect of fiber nonlinearity [2].

Nonlinear Continuous Wave (CW) pump broadening over non-standard transmission fiber is used for the first time to achieve improved gain flatness in a single-pump broadband RA[2].

Multiwavelength-pumped RAs have been widely implemented in ultra-long-haul transmission systems and high-capacity optical networks, thanks to their outstanding gain and noise performance. To date, intensive studies on optimal design of steady-state multiwavelength-pumped RAs have been reported [3]. However, broadband RAs with fixed working state are obviously not suitable for commercial transmission applications [3].

Dynamically control the gain spectra of broadband RAs by introducing a simple saturation factor, which has the following merits:

1. Very good robustness, more suitable for wide-range adjustment of broadband RAs (up to 23 dB dynamic range), even at very high gain, which has not been reported elsewhere, up to the best knowledge of the authors.

2. Can realize both DGSA and AGC functions with the same s value, and satisfying results can be achieved even for 90 nm deeply saturated RAs in short time.

3. Can be easily applied to different system configurations, such as different pumping schemes, fiber types and fiber length [3].

Rapid developments of WDM transmission systems have contributed a lot to the capability of components in networks, such as intensity of channels and signal bandwidth. As one of the enabling technologies for long-distance and high-capacity fiber optical transmission systems, RFA is a promising choice for extending the operational range of optical transmission systems to L- and S-bands, which are out of the bandwidth of erbium-doped fiber amplifiers (EDFAs). Especially with the progress in pump laser sources, higher power and wider operational wavelength range make RFAs more efficient and practical [6].

For most RFAs using dispersion-compensating fiber (DCF) and single pump, signal reflection and pump reusing are common techniques to enhance gain, and gain-clamping methods and flattening filters are used to flatten the gain [6].

Due to its low convert efficiency, RA which is one of the key components of the high-speed and high-capacity communications systems, can only assist EDFA but can be substituted in commercial operation [7]. Therefore, it is an ideal application to combine the RA with EDFA. During designing the hybrid amplifier of RA and EDFA, there is a question that how to configure the gain parameters of both amplifiers to get the optimum performance [7].

Raman fiber amplifiers (RFAs) have been studied intensively in recent years due to the itinerant advantages. The gain spectrum flattening is one of the most important issues in these studies. Generally speaking, there are two ways to approach this issue. One way is to use new media with inherently flat Raman gain efficiency coefficient. The other way is to use multiple pumps simultaneously with appropriate wavelengths and power levels [8]. In many practical situations the latter is the only reasonable choice. For example, when updating an old optical fiber communication system, if one does not want to replace the RFAs in whole, the only alternative left is to add several new pumps or to improve power levels of the existing pumps. In this circumstance the second approach is obviously more convenient and more economical than the first one. An efficient and reliable way to design RFAs using multiple pumps is therefore desirable. In such scheme, finding the appropriate power levels and wave- lengths for the pumps so that to achieve an optimized gain spectrum is a challenging task, because the involved coupled Raman amplification equations are complex and nonlinear [8].

In this paper, the distributed multipumping RA has been studied and analyzed by using N-cascaded RA units, N pumping signals are injected in a parallel processing at different pumping powers and wavelengths. The designed model of amplifier is considered to obtain the gain of maximum flatness, minimum losses and wider bandwidth. We processed the total gain coefficient and we show losses in the gain, and the bandwidth for all cases of distributed multi-RA with two different ways and then we have compared each other. Computer simulations are carried out using the MATLAB software package.

2 Mathematical model

Figure 1 shows an N-RA in a cascade form of special pumping powers Pr1, Pr2, Pr3, Pr4,…, PrN and corresponding pumping wavelengths λr1, λr2, λr3, λr4,…, λrN.

Figure 1:

The gain, g, of multi-pump Raman amplifier versus wavelength, λ.

The map of δ–g or λ–g is as shown in Figure 1, where δ is the Raman shift and g is the Raman differential gain coefficient; both were cast based on [9–13] as:

The general equations representing the Raman gain in the three regions are g1,i, g2,i and g3,i, respectively [13], where i denotes the order of amplifier unit in cascade:

where “i” is the number of cascaded units, λ_r is Raman pumping wavelength and λ_o≥1.35 μm. The symbol δo,i is the Raman shift that indicates the position of each ith amplifier unit:

With

With 1 cm^–1=30 GHz [14], where λ_o,i indicates the offset wavelength and λ_r,i indicates the pumping wavelength of each amplifier. These wavelengths are then used to indicate δ_o,i for each amplifier:

where go=7.4×10−14m/W is the differential Raman gain constant (of pure SiO₂ at λ= 1.34 μm), and

And

Δλ = λ₂ – λ₁=16 nm (fixed value for all units)

By changing the position δ_o,i, the total bandwidth and the flatness of the amplifier are changed.

We are interested in obtaining a large bandwidth with a wider flat gain by changing δ_o,i or λ_o,i. In this case, we can use either of two cases: δ_o=δ_r (i.e. λ_o=λ_r) or δ_o>δ_r (i.e. λ_o>λ_r), where λ_r is Raman pump wavelength and λ_o is the offset wavelength.

Raman differential gain constant, g, and the effective core area, A, are defined as [9]:

where ∆ is the refractive index difference, n₁ is the refractive index of the core and n₂ is the refractive index of the clad:

and

where W_s and W_r are the mode field radii of two light waves coupled with each other with W=W_s at λ=λ_s and W=W_r at λ=λ_r.

Neglecting the cross-coupling among the signal channels, one has the differential equation governing the signal propagation for N-channel Raman pumping [9]:

where, i=1,2,3,…N, M is the number of pumps, S_i is signal power and P_Rj is the jth unit pumping power.

Assume the RHS of eq. (12) equals g_ti, as:

The total (overall) gain coefficient, gti in m^–1 represents the total gain coefficient of the ith signal due to the N-pumping cascaded units. It is clear that gti is a function of a set of variables such as signal wavelength; fiber core radius; Raman wavelength; relative refractive index difference and Raman pumping power. The overall gain, gti, can be written in the form:

where the total differential gain, gdi, is

And by defining a total gain coefficient per watt (m/w), gci, as:

Then, the three gain coefficients, gdi, gci and gti, are functions of the propagation distance.

Losses calculations in the Raman gain are:

where L is losses in decibel and g is the total gain coefficient and this equation indicates the performance of the RA.

This equation uses to indicate the flatness in the gain.

3 Model examples and cases

In this paper, we investigated four model examples of cascaded RA; these examples are the fifth-order, eighth-order, eighth-order and fourth-order RA for four ranges, respectively. These example designs are obtained by using the following equation:

Firstly, we choose the offset wavelength of the first unit of the cascaded units consisting of the overall RA; we choose λ_o from the wavelength range. Then, we calculate λ₁ using eq. (20). After that, we assume the identical Raman units of individual bandwidth of λ₂– λ₁=16 nm. This is done for each amplifier unit.

Finally, we obtain the four design examples, whichare the fifth-order, eighth-order, eighth-order and fourth-order RA as shown in Tables 1–4, respectively. λ₂– λ₁=16 nm.

We consider two cases for the pumping wavelength λ_r;these two cases are considered for each model example.

1. Case A: λ_r ≠ λ_o

2. Case B: λ_r=λ_o

There are many parameters affecting the gain coefficients such as effective core area, relative refractive index difference, pumping wavelengths and pumping powers. So these parameters must be taken into account for any design.

And finally, we show the losses in the total gain coefficient of each model in two cases.

4 Simulation results and discussions

The bandwidth for distributed multipumping RA is investigated with the aim of obtaining maximum flat-gain amplifier with as wider bandwidth as possible. Bandwidth, ∆λ_r, can be evidently broadened by means of increasing the number of pumps (amplifier units) and by adjusting the position of these cascaded units.

As we said in Section 3, we have investigated the distributed multipumping RA by four model examples that are fifth-order, eighth-order, eighth-order and fourth-order amplifier for the four ranges of wavelengths. Each model example has been tested under two cases. That are: λ_r≠λ_o case and λ_r=λ_o.

4.1 Results of model 1

For the fifth-order RA, total gain coefficients gti are obtained through simulation results and depicted in the corresponding figures.

4.1.1 Model 1: Case A: λ_r ≠ λ_o

In this case we put the pumping wavelengths of the amplifier units not equal to the offset wavelengths.

The design structure of the fifth-order RA is obtained as shown in Table 1.

The following results will be demonstrated as follows:

Figure 2 displays the variation of the total gain coefficient with wavelength. In this case, a bandwidth of 70 nm is obtained. We note that the total gain coefficient starts to increase from the first pumping wavelength to reach the peak value at 1.41 μm; the gain starts to decrease exponentially tending to 1.45 μm. Gain in this case is affected by pumping powers, effective core area and relative index difference. This result demonstrates if the pumping power increases and the overall gain increases. So RAs are used to source with high pumping powers.

Figure 2:

Variation of total gain coefficient with wavelength λ_r≠λ_o.

4.1.2 Model 1: case B: λ_r=λ_o

In this case we put the pumping wavelengths equal to the offset wavelengths of the corresponding units.

The following results will be demonstrated as follows:

Figure 3 displays the variation of the total gain coefficient with wavelength. In this case, a bandwidth of 70 nm is obtained. We note the total gain coefficient starts to increase from the first pumping wavelength to reach the peak value at 1.41 μm; the gain starts to decrease exponentially tending to 1.45 μm. Gain in this case is affected by pumping powers, effective core area and relative index difference.

Figure 3:

Variation of total gain coefficient with wavelength λ_r=λ_o.

This result demonstrates if the pumping power increases, the overall gain increases. So RAs are used to source with high pumping powers.

4.2 Results of model 2

For the eighth-order Raman, total gain coefficients, gti, are obtained through simulation results and depicted in the corresponding figures.

4.2.1 Results of model 2: case A: λ_r ≠ λ_o

In this case we put the pumping wavelengths of the amplifier units not equal to the offset wavelengths.

The design structure of the 8th order RA is obtained as shown in Table 2.

Figure 4 displays the variation of the total gain coefficient with wavelength. In this case, a bandwidth of 120 nm is obtained. We note the total gain coefficient starts to increase from the first pumping wavelength to reach peak value at 1.56 μm, the gain starts to decrease exponentially tending to zero at 1.65 μm. Gain in this case is affected by pumping powers, effective core area and relative index difference.

Figure 4:

Variation of total gain coefficient with wavelength λ_r≠λ_o.

This result demonstrates if the pumping power increases, the overall gain increases. So RAs are used to source with high pumping powers.

4.2.2 Model 2:case B: λ_r=λ_o

In this case we put the pumping wavelengths equal to the offset wavelengths of the corresponding units.

Figure 5 displays the variation of the total gain coefficient with wavelength. In this case, a bandwidth of 120 nm is obtained. By similarity we note that the total gain coefficient is start to increase from the first pumping wavelength to reach peak value at 1.56 μm, the gain starts to decrease exponentially tending to zero at 1.65 μm. Gain in this case is affected by pumping powers, effective core area and relative index difference.

Figure 5:

Variation of total gain coefficient with wavelength λ_r=λ_o.

4.3 Results of model 3

For the eighth-order Raman, total gain coefficients, gti, are obtained through simulation results and depicted in the corresponding figures.

4.3.1 Results of model 3: case A: λ_r ≠ λ_o

In this case we put the pumping wavelengths of the amplifier units not equal the offset wavelengths.

The design structure of the 8th order RA is obtained as shown in Table 3.

Figure 6 displays the variation of the total gain coefficient with wavelength. In this case, a bandwidth of 110 nm is obtained.

Figure 6:

Variation of total gain coefficient with wavelength λ_r≠λ_o.

We note that the total gain coefficient starts to increase from the first pumping wavelength to reach the peak value at 1.68 μm; the gain starts to decrease exponentially tending to 1.75 μm. Gain in this case is affected by pumping powers, effective core area and relative index difference.

This result demonstrates if the pumping power increases, the overall gain increases. So RAs are used to source with high pumping powers.

4.3.2 Model 3:case B: λ_r = λ_o

In this case we put the pumping wavelengths equal to the offset wavelengths of the corresponding units.

Figure 7 displays the variation of the total gain coefficient with wavelength. In this case, a bandwidth of 110 nm is obtained.

Figure 7:

Variation of total gain coefficient with wavelength λ_r=λ_o.

We note the total gain coefficient starts to increase from the first pumping wavelength to reach the peak value at 1.65 μm; the gain starts to decrease exponentially tending to 1.75 μm. Gain in this case is affected by pumping powers, effective core area and relative index difference.

This result demonstrates if the pumping power increases, the overall gain increases. So RAs are used to source with high pumping powers.

4.4 Results of model 4: case A: λ_r ≠ λ_o

In this case we put the pumping wavelengths of the amplifier units not equal the offset wavelengths.

The design structure of the eighth-order RA is obtained as shown in Table 4.

Figure 8 displays the variation of the total gain coefficient with wavelength. In this case, a bandwidth of 150 nm is obtained.

Figure 8:

Variation of total gain coefficient with wavelength λ_r≠λ_o.

We note that the total gain coefficient starts to increase from the first pumping wavelength to reach the peak value at 1.61 μm; the gain starts to decrease exponentially tending to 1.7 μm. Gain in this case is affected by pumping powers, effective core area and relative index difference.

This result demonstrates if the pumping power increases, the overall gain increases. So RAs are used to source with high pumping powers.

4.5 Model 4:case B: λ_r = λ_o

In this case we put the pumping wavelengths equal to the offset wavelengths of the corresponding units.

Figure 9 displays the variation of the total gain coefficient with wavelength. In this case, a bandwidth of 150 nm is obtained.

Figure 9:

Variation of total gain coefficient with wavelength λ_r=λ_o.

We note the total gain coefficient starts to increase fromthe first pumping wavelength to reach the peak value at 1.61 μm, the gain starts to decrease exponentially tending to 1.7 μm. Gain in this case is affected by pumping powers, effective core area and relative index difference.

This result demonstrates if the pumping power increases, the overall gain increases. So RAs are used to source with high pumping powers.

4.6 Variation of total gain coefficient withlosses at different four ranges forλ_r ≠ λ_o

In this section we are showing variation of total gain coefficient with losses at different values of relative refractive index difference.

4.6.1 For relative refractive index difference, ∆=0.8%

Figure 10 displays the variations of the total gain coefficient with losses at different four ranges of wavelengths at relative refractive index difference, ∆=0.8%.

1. Data1: This result demonstrates the variations of the total gain coefficient with losses for the range from 1.4 to 1.45 µm.

2. Data2: This result demonstrates the variations of the total gain coefficient with losses for the range from 1.45 to 1.65 µm.

3. Data3: This result demonstrates the variations of the total gain coefficient with losses for the range from 1.65 to 1.75 µm.

4. Data4: This result demonstrates the variations of the total gain coefficient with losses for the range from 1.43 to 1.7 µm.

Figure 10:

Variation of total gain coefficient with losses at different four ranges for λ_r≠λ_o (at ∆=0.8%).

From the figure we get minimum losses at data 1, but the losses at data 2, data 3 and data 4 were approximately the same.

4.6.2 For relative refractive index difference, ∆=0.6%

Figure 11 displays the variations of the total gain coefficient with losses at different four ranges of wavelengths at relative refractive index difference, ∆=0.6%.

Figure 11:

Variation of total gain coefficient with losses at different four ranges for λ_r≠λ_o (at ∆ = 0.6%).

From the figure we get minimum losses at data 1, but the losses at data 2, data 3 and data 4 were approximately the same, but in this case the losses is higher than in case for relative refractive index difference, ∆=0.8%.

4.6.3 For relative refractive index difference, ∆ = 0.4%

Figure 12 displays the variations of the total gain coefficient with losses at different four ranges of wavelengths at relative refractive index difference, ∆=0.4%.

Figure 12:

Variation of total gain coefficient with Losses at different four Ranges for λ_r≠λ_o (at ∆ = 0.4%).

From the figure we get minimum losses at data 1, but the losses at data 2, data 3 and data 4 were approximately the same, but in this case the losses are higher than in case of relative refractive index difference ∆=0.8% and for ∆=0.6%.

4.7 Variation of total gain coefficient withlosses at different four ranges forλ_r=λ_o

Also, we are showing variation of total gain coefficient with losses at different values of relative refractive index difference.

4.7.1 For relative refractive index difference, ∆=0.8%

In Figures 13–15, we have obtained the similar results in Figures 10–12) but the losses in this case are very small due to putting the pumping wavelengths are equal to the offset wavelengths of the amplifiers.

Figure 13:

Variation of total gain coefficient with losses at different four ranges for λ_r=λ_o (at ∆ = 0.8%).

4.7.2 For relative refractive index difference, ∆ = 0.6%

Figure 14:

Variation of total gain coefficient with losses at different four ranges for λ_r=λ_o (at ∆ = 0.6%).

Figure 15:

Variation of total gain coefficient with losses at different four ranges for λ_r=λ_o (at ∆ = 0.4%).

4.7.3 For relative refractive index difference, ∆ = 0.4%

From simulation results which obtained in this paper at different ranges of wavelengths for distributed multi-RA we concluded that from previous comparison in Table5:

1. Raman gain increases with relative refractive index difference.

2. Bandwidth and flatness of the gain depend on the position of amplifiers corresponding to each other and on the number of amplifiers.

3. The flatness of the gain improved if the relative refractive index difference decreases, but the value of the total gain coefficient increases with the relative refractive index difference.

4. The total gain coefficient various with losses at different values of relative refractive index difference, where if relative refractive index difference increases the value of the losses in the total gain decreases, also we get at ∆ = 0.8% the value of the losses is less than that at ∆ = 0.6% and at ∆ = 0.4%, but the flatness of the gain is better in case of ∆ = 0.4% than ∆ = 0.6% and ∆ = 0.8%.

5. For case B in each model the gain is higher than in case A for the same model due to putting the pumping wavelengths is equal to the offset wavelengths of the amplifiers also, the losses in the gain in case B is less than in case A for the same model, then case B is better than case A.

6. Also, we get higher bandwidth at the ranges from 1.45 to 1.65 µm and from 1.43 to 1.7 µm.

Table 5:

Comparison between the different models in the different ranges of wavelengths by using two different cases.

Case A: λr ≠ λo
	No. of optical amplifiers and range
	N = 5, from 1.4 to 1.45 µm
∆, %	0.8	0.6	0.4
Totalgaincoefficient (max.)	0.2909	0.1636	0.0727
Average gain	0.2194	0.1234	0.0548
Deviation from the maximum	0.0715	0.0402	0.0179
Losses (dB)	5.36	7.86	11.38
BW (nm)	70	70	70
	No. of optical amplifiers and range
	N = 8, from 1.45 to 1.65 µm
∆, %	0.8	0.6	0.4
Total gain coefficient (max.)	0.1600	0.0900	0.0400
Average gain	0.144	0.081	0.036
Deviation from the maximum	0.016	0.009	0.004
Losses (dB)	7.96	10.46	13.98
BW (nm)	120	120	120
Follow of case A: λr ≠ λo
	No. of optical amplifiers and range
	N = 8, from 1.65 to 1.75 µm
∆, %	0.8	0.6	0.4
Total gain coefficient (max.)	0.1904	0.1071	0.0476
Average gain	0.1692	0.0951	0.0423
Deviation from the maximum	0.0212	0.012	0.0053
Losses (dB)	7.20	9.70	13.2
BW (nm)	110	110	110
	No. of optical amplifiers and range
	N = 4, from 1.43 to 1.7 µm
∆, %	0.8	0.6	0.4
Total gain coefficient (max.)	0.1510	0.0849	0.0374
Average gain	0.1302	0.0733	0.0322
Deviation from the maximum	0.0208	0.0116	0.0052
Losses (dB)	8.21	10.71	0.1427
BW (nm)	150	150	150
	No. of optical amplifiers and range
	N = 5, from 1.4 to 1.45 µm
∆, %	0.8	0.6	0.4
Total gain coefficient (max.)	0.2960	0.1665	0.0740
Average gain	0.227	0.1253	0.0557
Deviation from the maximum	0.0733	0.0412	0.0183
Losses (dB)	5.29	7.79	11.31
BW (nm)	70	70	70
	No. of optical amplifiers and range
	N = 8, from 1.45 to 1.65 µm
∆, %	0.8	0.6	0.4
Total gain coefficient (max.)	0.1676	0.0943	0.0419
Average gain	0.1503	0.0846	0.0376
Deviation from the maximum	0.0173	0.0097	0.0043
Losses (dB)	7.76	10.25	13.78
BW (nm)	120	120	120
Follow of case B: λr = λo
	No. of optical amplifiers and range
	N = 8, from 1.65 to 1.75 µm
∆, %	0.8	0.6	0.4
Total gain coefficient (max.)	0.1922	0.1081	0.0481
Average gain	0.1707	0.0960	0.0427
Deviation from the maximum	0.0215	0.0121	0.0054
Losses (dB)	7.16	9.66	13.18
BW (nm)	110	110	110
	No. of optical amplifiers and range
	N = 4, from 1.43 to 1.7 µm
∆, %	0.8	0.6	0.4
Total gain coefficient (max.)	0.1655	0.0931	0.0410
Average gain	0.1404	0.0789	0.0347
Deviation from the maximum	0.0251	0.0142	0.0063
Losses (dB)	7.81	10.31	13.87
BW (nm)	150	150	150

5 Conclusions

By using N-cascaded RA units, N pumping signals are injected in a parallel processing at different pumping powers and wavelengths, we have obtained the following simulation results:

1. The overall gain of RA is increased due to putting the pumping wavelengths equal to the offset wavelengths of the amplifier units.

2. The bandwidth and/or the flatness of the gain depends on the position of the amplifier units (wavelength value of the cascaded units) corresponding to each other and on the number of amplifier units.

3. For the range from 1.4 to 1.45 µm we get low losses but the bandwidth is very small and number of units N = 5, for the range from 1.45 to 1.65 µm we get the losses are high but the bandwidth is large = 120 nm and number of units N = 8, for the range from 1.65 to 1.75 µm we get bandwidth = 110 nm and number of units N = 8 and for the range from 1.43 to 1.7 µm we get higher bandwidth = 150 nm, but the losses is high and number of units N = 4.

4. Then concluded that we can use any designed model in the different four ranges, which are suitable for any application according to the number of units, the losses in the gain and bandwidth.