A numerical analysis is presented on the long-haul wavelength-division multiplexing (WDM) transmission system employing fiber-optic parametric amplifier (FOPA) cascades based on one-pump FOPA model with Raman Effect taken into account. The end-to-end equalization scheme is applied to optimize the system features in terms of proper output powers and signal-to-noise ratios (SNRs) in all the channels. The numerical results show that—through adjusting the fiber spans along with the number of FOPAs as well as the channel powers at the terminals in a prescribed way—the transmission distance and system performance can be optimized. By comparing the results generated by different lengths of fiber span, we come to the optimal span length to achieve the best transmission performance. Furthermore, we make a comparison among the long-haul WDM transmission systems employing different inline amplifiers, namely, FOPA, erbium-doped fiber amplifier (EDFA), and Fiber Raman Amplifier (FRA). FOPA demonstrates its advantage over the other two in terms of system features.

In recent years, Fiber-optical parametric amplifiers (FOPAs) are attracting widespread interest among researchers in fiber-optic field because of efficient broadband amplification [

Another major problem in implementing amplified WDM transmission systems is “gain equalization.” As the gain spectrum of FOPA is nonuniform and wavelength-dependent, each channel in a WDM system will experience different optical gain, which leads to unacceptable BER performance in certain channels of the long-haul transmission system. Therefore, considerable effort has been made in inventing components that equalize the output powers at each amplifier repeater in all channels. Various equalizer proposals have been presented, including “smoothing filters” such as Fabry-Perot or tunable Mach-Zehnder interferometers [

In this paper, we numerically analyze the one-pump FOPA model with Raman Effect. And then, a FOPA-based WDM transmission system using end-to-end equalization is designed, analyzed, and optimized.

The mathematical model of one-pump FOPA with Raman Effect is developed in Section

The one-pump case of FOPA is also called the degenerate case, whereas the two-pump case the nondegenerate case, which are both described and developed in [

When FOPA is operated phase-insensitively, a coherent-state input signal is injected at the Stokes (anti-Stokes) frequency while the input at the anti-Stokes (Stokes) frequency remains in the vacuum state. The NF is then defined as

The quantum-limited NF of a FOPA exceeds the standard 3 dB limit at high gains due to the Raman Effect [

We build a mathematical model for the one pump FOPA with Raman Effect, which will later be applied in the WDM transmission system. Figure

Gain (Solid curve) and NF (dotted curve) spectra of the FOPA made with 1 km DSF and pumped at 1537.6 nm with 1.5 W power. The zero-dispersion wavelength is 1537 nm, and the dispersion slope is 0.034 ps

Our major task is to design and numerically analyze a long-haul WDM optical transmission system employing FOPA cascades. The schematic configuration of the system is shown in Figure

The schematic configuration of long-haul WDM transmission system employing cascaded FOPAs. Eight channels are multiplexed (total power is −3 dBm before Mux) to transmit through spans of conventional fiber. Loss is compensated by FOPAs. A preamplifier is applied before the demultiplexer.

The system consists of eight 2.5 Gb/s externally modulated channels with 0.4 THz channel spacing (193.8–196.6 THz). Each transmitter consists of a Pseudo-Random Bit Sequence Generator, a NRZ Pulse Generator, a CW Laser, and a Mach-Zehnder Modulator. Total signal power is −3 dBm before multiplexing, that is, −12 dBm in each channel. The eight channels are then multiplexed, and the signals are transmitted over spans of conventional optical fiber with an attenuation factor of 0.2 dB/km. The fiber loss and excess losses in the system are compensated by FOPAs. The FOPAs are pumped by 1.5 W of 1537.6 nm pump light. The demultiplexer is preceded by a fiber preamplifier. The bit-error-rate (BER) calculations take into account intersymbol interference, signal-spontaneous beat noise, and postdetection Gaussian noise [

We tested the performance of FOPA module operating in simulation transmission system. Equal input signal powers of −12 dBm are used in all eight channels. Figure

Output features of FOPA (described in Figure

In [

To have the output powers equalized, we only need to adjust individual input signal powers with attenuators while keeping the total input power constant. The power in each channel is scaled by a factor inversely proportional to the gain in that channel. The new input signal power of the

A similar adjustment algorithm is needed to equalize SNR. The transmitter power for the

An analysis has been presented to predict the performance of WDM lightwave transmission systems using power and SNR end-to-end equalization [

In the long-haul transmission system we designed for numerical analysis, although the output powers can be easily equalized by power equalization, this might lead to unacceptable BER in some channels due to low SNR. Therefore, we apply both equalization techniques in the simulation and choose the one that leads to better system performance in every individual case.

We use Optical Spectrum Analyzer (OSA) to display the modulated optical signal in the frequency domain and WDM Analyzer to monitor the numerical results of signal and the noise power at each optical signal channel. In amplified WDM systems, SNR and BER are routinely monitored as a measure of system performance. In most cases, BER below

The fiber span is firstly set to be 30-km long. We gradually increase the amplifiers to look for the largest number in the system while the BER and output power features are within acceptable levels. Figure

We find though BER features are good in all channels but some signal powers are overly high with an imbalance of 47 dB. We choose to apply power end-to-end equalization. Figure

When fiber span is set to 30-km long, the largest number of amplifiers we have found is 3. When we continue to increase to 4, though the SNR and BER are still good in all channels, but the signal powers remain 18 dBm after several iterations of end-to-end equalization algorithm.

We set fiber span from 30-km to 65-km long with an increment of 5 km, and repeat the simulation as above. The results of certain typical lengths are selected with graphs and data displayed as follows.

Output signal (red) and noise (green) powers after 90 km transmission using 30-km fiber span and equal input signal powers of −12 dBm. No equalization is applied. The list beside shows signal frequency, output signal powers, SNR and BER.

Same as Figure

When fiber span is set to be 40-km long, the largest amplifiers number we have found is 6. After applying power end-to-end equalization, the system is optimized with equalized output powers and good BER in all channels; see Figure

Output signal (red) and noise (green) powers after 240 km transmission using 40-km fiber span and employing power end-to-end equalization. The list beside shows signal frequency, output signal powers, SNR and BER.

When fiber span is 50-km long, we gradually increase the amplifiers number to 6. In this case, BER in channel 4 is found no longer good (only

Output signal (red) and noise (green) powers after 300 km transmission using 50-km fiber span and employing power end-to-end equalization. The list beside shows signal frequency, output signal powers, SNR and BER.

Output signal (red) and noise (green) powers after 350 km transmission using 50-km fiber span and employing 4 iterations of SNR equalization. The list beside shows signal frequency, output signal powers, SNR and BER.

We can increase the amplifiers number to 7 with 55-km long fiber spans, which is the largest number that we achieved with a group of fiber spans of different lengths. When the fiber length becomes longer, signals close to the pump frequency experience larger power loss which generates unacceptable BER. Figure

Output signal (red) and noise (green) powers after 385 km transmission using 55-km fiber span and employing 3 iterations of SNR equalization. The list beside shows signal frequency, output signal powers, SNR and BER.

In this section, we sum up the results and make a comparison based on the graphs below. Figure

(a) Maximum transmission distance achieved in the long-haul WDM transmission system employing cascaded FOPAs and end-to-end equalization versus length of fiber span. (b) Constraints on number of amplifiers (with end-to-end equalization) ensuring BER below

Figure

(a) Average BER (logarithmic scale) achieved in eight channels of the long-haul WDM transmission system employing the largest number of cascaded FOPAs versus length of fiber span. Note that for fiber span from 30 to 45 km, the logarithmic scale of BER is -inf. (b) Average SNR achieved in eight channels of the system versus length of fiber span. System and FOPA description are the same with Figure

We further display in Figure

SNR features in eight channels (from 193.8 to 196.6 THz with 0.4 THz spacing) after experiencing the achievable maximum transmission distance described in Figure

BER features (logarithmic scale) in eight channels (from 193.8 to 196.6 THz with 0.4 THz spacing) after experiencing the achievable maximum transmission distance described in Figure

Finally, we compare the optimal transmission system employing cascaded FOPAs with that employing cascaded EDFAs or FRAs. The transmission system configuration is ensured to remain the same other than using different inline amplifiers. Transmission distance is set to be 385 km by using seven spans of 55-km-long fibers. We gradually adjust the transmission powers in eight channels to obtain the corresponding BER features. To optimize the gain and SNR imbalance, end-to-end equalization is also applied in three long-haul systems employing FOPA, EDFA, or FRA so that BER in all channels are almost on the same level. Figure

Average BER (logarithmic scale) in eight channels (from 193.8 to 196.6 THz with 0.4 THz spacing) versus signal transmission powers.

We come to find and to achieve the same level of BER that is acceptable (less than

In this paper, we present a numerical analysis on the long-haul WDM transmission system employing FOPA cascades. FOPA is modeled as one-pump and with Raman Effect. End-to-end equalization scheme is applied to optimize the system features. The numerical results show that—through adjusting the fiber spans along with the number of FOPA, and the channel powers at the terminals in a prescribed way—the transmission distance and system performance can be optimized. In our project, the WDM system is operated at

This work was supported by the National Natural Science Foundation of China (Grant nos. 60377023 and 60672017) and New Century Excellent Talents Universities (NCET) Shanghai Optical Science and Technology project.