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We have theoretically investigated the transmission performance limits of all semiconductor optical amplifiers (SOA)-based 10 Gb/s wavelength division multiplexing (WDM) systems using in-line SOAs and an optical phase conjugator (OPC) based on four-wave mixing in SOAs as a mid-span spectral inversion technique. With a verified numerical model of SOAs, we have found that the crosstalk from SOAs in OPC is a dominant factor to limit the number of channels in WDM systems. In order to increase the available number of channels, we optimize the input optical power and the injection current to SOAs in OPC with using a reservoir channel in inline SOAs. All SOA-based 10 Gb/s WDM systems using the OPC can transmit 16 channel signals up to 240 km distance with a 3 dB power penalty.
©2006 Optical Society of America
1. Introduction
In order to increase a transmission distance in optical systems, compensations of the chromatic dispersion are important factors. Dispersion compensating fibers (DCF) with negative dispersion at each fiber span can be normally used for the dispersion compensation. Chirped fiber grating with inverse dispersion also have potential to do such a function. These two dispersion compensating techniques require the accurate information about dispersion of a span, channel wavelength, channel data rate, channel spacing and number of channels [1]. Dispersion tolerant modulation formats may be used for overcoming the dispersion [2]. [3]. Moreover, a mid-span spectral inversion (MSSI) technique has been recently attracted for an alternative for the dispersion compensation of competing in price for metro networks.
The MSSI technique enables the dispersion compensation by placing an optical phase conjugator (OPC) which inverts the spectrum and the phase of optical signals distorted by the chromatic dispersion at the middle of a complete transmission link. If phase conjugated optical signals pass through the same amount of dispersion to the end of the link, phase distortion can be recovered to their initial state as exactly the same as the transmitter output. Using the MSSI method, 40 Gb/s transmission is possible over 800 km for 16 channels of on-off-keyed [4] and phase-shifted-keyed signals [5]. Theoretically, the reduction of nonlinear impairments has been shown in [6]. Other experiments using a difference frequency generation in periodically poled LiNbO3, have been reported so far at 40 Gb/s data rate [7], [8].
Because there are no DCFs at each span in optical transmission systems using the MSSI technique, it reduces the number of amplifiers used in a link and then offers competitive price. However, if the four wave mixing (FWM) effect in semiconductor optical amplifiers (SOA) is used in OPC, the optimization of OPC characteristics is required to reduce the crosstalk between WDM signals. It is worthy to investigate the limitations of WDM transmissions using the MSSI technique based on FWM in SOAs for a low cost application such as metro networks. Cost-effective transmission systems also can be realized by using SOAs instead of erbium-doped fiber amplifiers as in-line amplifiers [9]. In this paper, we numerically examined the transmission performance limits of all SOA-based 10 Gb/s WDM systems using in-line SOAs and a MSSI technique, OPC based on the FWM in SOAs. We estimated the crosstalk due to OPC in WDM signals and found the optimum input optical power and the injection current into SOAs in the OPC to reduce the crosstalk and increase the conversion efficiency. Then we investigated the limitations of transmission performance for the WDM systems with increasing the number of WDM channels (N) and fiber spans (M).
The rest of the paper is organized as follows. In section 2, we describe the modeling of optical components such as OPC, transmitter, receiver and fiber. In section 3, we verify the modeling of optical phase conjugation in WDM channels and optimize the OPC characteristics based on FWM in SOAs. Section 4 shows the transmission performance limits of all SOAs-based 10 Gb/s WDM systems using in-line SOAs and an OPC. Finally, conclusions are given in Section V.
2. OPC, Transmitter, Receiver, and Fiber Models
2.1 OPC model
Fig. 1. Schematic of describing wave propagation on a SOA model based on the timedependent TMM. In every section, the complex pulse envelope was calculated.
Optical phase conjugation can be realized by the FWM effect in SOAs. Since the conventional transfer matrix method (TMM) can not estimate the dynamic characteristics but the static characteristics of the semiconductor optical devices, the time-dependent TMM has been proposed for simulating the dynamic characteristics [10], [11]. Figure 1 shows the schematic of illustrating the wave propagation on a large-signal dynamic SOA model based on the timedependent TMM. The nonlinear gain dynamics in SOAs, responsible for the process of FWM, are based on inter-and intraband effects. Interband effects refer to transitions of carrier between the conduction and the valence band. They change the carrier density due to stimulated emission, which is referred to carrier density pulsation (CDP). On the other hand, intraband effects are related to change the carrier distribution within one band. They are associated with two phenomena. Firstly, the stimulated emission burns a hole in the carrier distribution causing a deviation from the Fermi distribution. This phenomenon is called spectral-hole burning (SHB). Secondly, free carriers at low-energy levels are transferred to higher levels due to free carrier absorption. This is referred to as carrier heating (CH). The time-dependent TMM was used for solving the pulse propagation equation in the device. In every section, the complex pulse envelope was calculated by self-consistently solving the pulse propagation equations, the gain equation and the rate equation for the carrier density. The pulse propagation equations, including FWM, amplified spontaneous emission (ASE) noise, and backward traveling waves, could be derived in the followings:
where Ai and Bi are normalized slowly varying envelopes of forward and backward fields at section i and index p, s and c present pump, signal, and conjugate waves, respectively. Δω=ωp-ωs is the frequency detuning for pump and signal waves, ḡ is the net gain, g is the material gain, vg is the group velocity, PSat is the saturation power, εSHB is the spectral hole burning parameter, and εCH1 and εCH2 are the carrier heating parameters. The frequency response hy(Δω) (y=CDP, CH, and SHB) of the individual nonlinear processes are given by
where τ s is carrier life time,τ 1 is carrier heating lifetime, and τ 2 is hole burning lifetime. In order to model an asymmetric gain profile in SOAs, the gain spectrum was assumed to be cubic and the material gain was approximated to
where index i corresponds to different sections and index w refers to different optical waves. a 0,, a 1 and a 3 are gain constants, and λ N is the gain peak wavelength assumed to shift linearly with carrier density
The rate equation in each small section was solved as
where I is the injection current, V is the active volume, q is the electronic charge, and c 1, c 2, and c 3 are related to the recombination constants. The ASE noise was calculated from the gain equation and the spontaneous emission factor [12].
2.2 Transmitter model
The output electric field and the chirp parameter of a Mach-Zehnder (MZ) modulator were modeled using the peak voltages applied to two electrodes and the switching voltage of the modulator. The device was biased at the midpoint of its transfer characteristic curve and driven in a push-pull manner. For nonideal devices, the MZ modulator experienced residual chirp and finite extinction ratio [13].
2.3 Fiber model
The nonlinear Schrödinger equation should be solved in order to consider the nonlinearity, the dispersion, and the loss in a fiber. Because the nonlinear Schrödinger equation is a nonlinear partial differential equation that does not have analytic solutions generally, it was numerically solved using the split-step Fourier method [14].
2.4 Receiver model
At the receiver, optical pulses were filtered using a fifth-order Bessel-Thomson filter. To accurately calculate receiver sensitivities at the specific bit-error rates (BER), we included the intersymbol interference caused by nonlinear optical fibers and OPCs. Additionally we calculated the various noise components, such as shot noise, signal-spontaneous beat noise, spontaneous-spontaneous beat noise, and thermal noise. The decision threshold was adjusted for obtaining the best BER performance [15].
3. Verification of Models and Optimization of OPCs
Generally, the wavelength conversion based on the FWM in SOAs has a poor conversion efficiency and narrow conversion frequency range. In order to apply OPCs based on the FWM in SOAs as a MSSI technique to a WDM transmission link, it requires a high conversion efficiency and wide conversion frequency range. To improve the conversion efficiency and the frequency range of the FWM in SOAs for WDM signals, we used a SOA model with a 1.5 mm length and a 2.2 µm width of the active region [16]. Similar characteristics of wavelength conversion using a SOA are possible at 40 Gb/s transmissions [17]. Although long SOAs provide high conversion efficiency and wide conversion range, there is the crosstalk between signals due to the cross-gain modulation [18]–[20]. The crosstalk is strongly related to the pump-to-signal power ratio because the gain in one channel is influenced by the combined power of all the multiplexed channels. To verify our developed simulation model for the wavelength conversion based on the FWM in SOAs for WDM signals, we compared the eye diagrams of converted signals with changing the pump-to-signal power ratio from 12 to 22 dB as shown in Fig. 2. LiNbO3 modulators driven by distributed feedback lasers with a 100 GHz channel spacing were modulated at 10 Gb/s. The wavelength conversion of two channels having the NRZ format was done at a 2 nm detuning wavelength by the pump power of 13 dBm. In the case of large pump-to-signal power ratio (22 dB), the input signals do not saturate SOAs and eye closure does not happen. However, the optical signal-to-noise ratio (OSNR) of converted signals was smaller than that with small pump-to-signal power ratio (12 dB) due to the small input optical power to SOAs. There are tradeoffs between the crosstalk and the OSNR for the WDM wavelength conversion based on the FWM in SOAs. From these results, we confirmed that our SOA model described accurate dynamic characteristics in WDM signals. The same experimental results also could be found in other study [21].
Fig. 2. Calculated eye diagrams of wavelength converted signals in SOAs with a) large (22dB) and b) small (12 dB) pump-to-probe ratio. In the case of 22 dB, the input signals do not saturate SOAs.
To obtain low crosstalk and high OSNR in transmission systems using the MSSI method, we calculated the receiver sensitivities at 10-9 BER of converted signals while changing the total input optical power and the injection current to an OPC. Figure 3 shows the contour plots of the receiver sensitivities of the worst channel for the total input optical power and the injection current to the OPC. The number of input channels was varied from 2 to 16 and the first wavelength of the converted channel was fixed to 1550.0 nm. For example, the 4 and 16 WDM signals were converted from 1556.4~1558.8 to 1550~1552.4 nm and from 1566~1578 to 1550~1562 nm, respectively. The channel spacing was equally set to 100 GHz. The pump wavelength was placed in a 2 nm wavelength from the last wavelength of the converted channel and the pump power was 13 dBm. Each input optical signal had unequal conversion efficiency, consequently, channels with a high conversion efficiency experienced more crosstalk. Therefore, we found the optimum conditions of the OPC for the channel having the worst receiver sensitivities. The optimum region of BER characteristics means that the phase conjugated signals have the lowest crosstalk and the highest OSNR. It needs to select the largest input power to the OPC in the optimum region to maintain high OSNR in transmission links. With the minimum current in the optimum region, the OPC generates low ASE noise levels. Because the OSNR dominantly affects the phase conjugated signals with the low signal power to SOAs, the optimum injection current increases while reducing signal power. From the contour plots, the optimum injection current and input optical power to the OPC for two channels are 300 mA and -9 dBm, respectively. Using the same procedure, we could find the optimum conditions and the power penalties of the OPC for 4, 8, and 16 channels and then summarized the results in Table 1. The SOA model as an OPC supported for 16 channels with a 1.7 dB power penalty in the worst case. For larger than 16 channels using the OPC, it was impossible to convert all channels without error floors.
Fig. 3. Contour plots of calculated receiver sensitivities for the injection current and total input optical power to OPC with a) 2, b) 4, c) 8, and d) 16 channels. The optimum region of BER characteristics means that the phase conjugated signals have the lowest crosstalk and the highest OSNR.
Table 1. Optimized parameters and power penalties of OPC with different total input optical power to in-line SOAs for different number of channels
Wavelength dependent conversion efficiency of OPCs based on the FWM in SOAs limits the available number of channels in WDM transmissions. We investigated conversion efficiency of the OPC for 16 channels as shown in Fig. 4. Input optical power to the OPC was varied from 0 to -6 dBm. Optimum injection current to the OPC for 16 channels was used (Table 1). Due to the saturation effect of SOAs, conversion efficiency in the case of high input power (0 dBm) is smaller than that of low input power (-6 dBm). Wavelength dependent conversion efficiency is 7 dB for 16 channels and this will limit the transmission performance of the WDM system using the MSSI technique.
Fig. 4. Conversion efficiency of the OPC for 16 channels. Input power to the OPC was changed from 0 dBm to -6 dBm.
4. Simulation Results
Figure 5 shows the simulation setup of 10 Gb/s WDM transmission using the MSSI technique. LiNbO3 modulators driven by distributed feedback lasers with a 100 GHz channel spacing were modulated at 10 Gb/s with NRZ bit stream of 27 length and each channel had a 5 bit delay. One span consisted of 60 km of the standard single mode fiber (SSMF) with a 13 dB loss and a SOA as an in-line amplifier. Attenuation, dispersion at 1550 nm, dispersion slope, nonlinear index and effective core area of SSMF were 0.22 dB/km, 17ps/nm·km, 0.05936 ps/nm2·km, 2.6×10-20 m2/W and 78 µ m2, respectively. Each SOA has approximately the noise figure of 8 dB and the gain of 19 dB from our model. There was only one OPC used in the middle of the total link to compensate the chromatic dispersion. Due to the wavelength dependent gain and partially destructive or constructive phase interference between the contributing FWM mechanisms such as carrier density pulsation, carrier heating, and spectral hole burning, we selected the down conversion in the OPC. After the demultiplexer, the received power of each channel was adjusted to be equal between channels. The desired WDM channel was selected by using the optical bandpass filter that had the super Gaussian shape with the 3 dB passband width of 0.3 nm. The electrical bandwidth of the receiver was 10 GHz. Additionally, a CW reservoir channel at 1546 nm is forward injected to the SOA after the multiplexer. Inducing more photon density in SOAs shortens the gain recovery time and increases the saturation output power.
The optimum conditions of the OPC characteristics provided low crosstalk and high OSNR in transmission systems using the MSSI technique as explained in the previous section. Because there are also tradeoffs between crosstalk and OSNR in transmission systems based on in-line SOAs, it should be found the optimum input optical power to in-line SOAs. We used variable attenuators to change the input optical power to each in-line SOA with the optimized conditions of the OPC characteristics to achieve the best transmission performance. We summarized the optimum input optical power to in-line SOAs for different number of channels in Table 1.
4.1 Eye diagrams after 120 km transmissions
Figure 6 shows the received eye diagrams for the first channel (1550.0 nm) at back-to-back, the first 60 km SSMF, the OPC and the second 60 km SSMF for two input channels. The chromatic dispersion distorts the pulse shape after the first 60 km transmission and the selfphase modulation (SPM) can be negligible due to the low fiber launching power of -10 dBm. The crosstalk between two input channels also affects the converted signals after the OPC. Full dispersion compensation can be obtained by transmitting through the second 60 km SSMF. After the total 120 km transmission, there are a residual distortion of the received eye diagrams due to the dynamic characteristics of SOAs as in-line amplifiers and an OPC.
Fig. 6. Calculated eye diagrams at a) back-to-back, b) first 60 km SMF, c) OPC, and d) second 60 km SMF for two channels. Full dispersion compensation is done after OPC and the second 60 km transmission.
If the difference between input wavelength and output wavelength of the OPC becomes large, the accurate length of the second fiber span should be used. The reason for using the same length of the first and second fiber spans in our paper is that it is difficult to precisely adjust the length of the second fiber spans in the real system design. In the case of large number of channels, the dominant impairment for WDM transmission is the OSNR of converted channels from SOAs.
4.2 Limits of transmission distance with different number of channels
We investigated the performance of transmission systems with in-line SOAs and an OPC as the MSSI technique with changing the number of channels and the transmission distance. Figure 7 shows the average receiver sensitivities at 10-9 BER as a function of transmission distance for different number of channels without using a reservoir channel. We used the optimum conditions of the OPC characteristics for the number of channels in each case. Because the gain profile of SOAs was not flat, we averaged the receiver sensitivities of all the channels at 10-9 BERs after transmissions. Simulations had been performed on systems with a length multiple of 120 km for different number of channels. For comparison, we added the receiver sensitivities of a channel with a 1550.0 nm wavelength. The receiver sensitivity in the back to back case without OPC was -20.52 dBm. As expected, the transmission performance was degraded as the number of channels and the transmission distance was increased. The possible transmission distance for 16 channels was up to 120 km with a 2 dB average power penalty. It was possible to transmit over 480 km for 4 channels with a 2.5 dB average power penalty. Because a reservoir channel was not used, the dominant factors of the transmission performance are OSNR and crosstalk. The OSNR degradation is unaviodable in optical transmission systems but the crosstalk from in-line SOAs and an OPC can be eliminated by injecting a reservoir channel [22].
Fig. 7. Contour plots of calculated receiver sensitivities for transmission distance and number of channels without using a reservoir channel. The possible transmission distance for 16 channels was up to 120 km with a 2 dB average power penalty.
The average receiver sensitivities at 10-9 BER as a function of transmission distance for different number of channels with using a reservoir channel are shown in Fig. 8. The power of the reservoir channel was optimized to obtain the best transmission performance. In the case of 16 channels with a reservoir channel, it was possible to transmit over 240 km with a 3 dB average power penalty. Without using a reservoir channel, it couldn’t transmit up to 240 km distance. In addition to 16 channels, all the channels using a reservoir channel improved the transmission performance. Up to 8 channels, the possible transmission distance was 480 km with a 2 dB average power penalty.
Fig. 8. Contour plots of calculated receiver sensitivities for transmission distance and number of channels with using a reservoir channel. It was possible to transmit over 240 km with 3 dB average power penalty.
5. Conclusion
We investigated the transmission limits of all SOA-based WDM systems using in-line SOAs and an OPC based on FWM in SOAs as a MSSI technique. The input optical power and injection current to the OPC were optimized in the worst channel and a 1.7 dB power penalty existed in the case of 16 input optical signals to the OPC. Using the developed simulation models, it was possible to compensate the chromatic dispersion using an OPC based on the FWM in SOAs as a MSSI technique. With and without using a reservoir channel, we calculated the receiver sensitivities at 10-9 BER of 10 Gb/s WDM signals transmitted over M×60 km for different number of channels. With using a reservoir channel, over 240 km transmission was possible for 16 channels with a 3 dB average power penalty. These results can suggest the possibility to implement the cost-effective optical transmission systems using all SOA-based in-line amplifiers and an OPC.
Acknowledgments
This work was supported in part by the National Research Laboratory Program of Ministry of Science & Technology in South Korea.
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