Journal of information and
communication convergence engineering
(J. Inf. Commun. Converg. Eng.)

The advanced hypertext-type communication traffic generated by the fourth industrial revolution requires a high-capacity backbone network [1]. Fiber optic networks have great potential to provide ultra-high capacity on the order of high Tb/s over long-haul distances of thousands of kilometers. In particular, wavelength division multiplexed (WDM) links have transformed the concept of multichannel transmission. The fulfillment of ultra-high capacity based on optical fibers such as WDM can be attributed to the compensation of optical signal distortion due to the chromatic dispersion and the nonlinear Kerr effect of a standard single-mode fiber (SSMF).

Dispersion management (DM) is a simple and effective technique to mitigate the chromatic dispersion of SSMF, compensating for dispersion by adding a dispersion-compensating fiber (DCF) with dispersion opposite of SSMF into an optical link consisting of SSMF [2-4]. Several studies have been published to mitigate fiber Kerr nonlinearity [5-8]. Among these, optical phase conjugation is more attractive than other methods because it generates the phase-conjugation of the distorted signal using an optical phase conjugator (OPC) near the middle of the link without requiring additional optical and electrical processes [9-11]. This configuration, in which the OPC is placed around the middle of the link, is referred to as mid-span spectral inversion (MSSI).

However, both the DM technique and the MSSI exhibit limitations for compensation. The DM approach can only compensate for distortion in optical signals due to chromatic dispersion and is ineffective in compensating for nonlinear impairment. In MSSI, the flexibility of the optical link configuration cannot be obtained owing to the OPC position. Fortunately, the application of OPC to the DM link can reduce the limitations of each compensation approach [12-14].

In the case of an optical transmission link consisting of several fiber spans, each fiber span includes one SSMF and one DCF, and compensation performance is affected by the residual dispersion per span (RDPS) and net residual dispersion (NRD). The RDPS and NRD are defined as the dispersion accumulated in each fiber span and the total fiber span, respectively, and are important factors in the DM link configuration.

In this paper, a new configuration for a DM link with a nonmidway OPC is proposed for transmitting 24-channel×40-Gb/s WDM signals. In the context of this study, the non-midway OPC means that the OPC is placed between the 6-th and 7-th fiber spans from a total of 20 fiber spans (this configuration is called the 6vs14 configuration) and between the 14-th and 15-th fiber spans (this configuration is called the 14vs6 configuration). For the proposed DM link, the RDPS in the former transmission section (FTS) and the RDPS in the latter transmission section (LTS) consisting of all fiber spans from the first span to the span before the OPC and all fiber spans from the span after the OPC to the final span, respectively, are selected independently from each other. In contrast, the same RDPS value in each transmission section is selected in conventional DM.

The WDM transmission system and the dispersion-managed optical link embedded in the OPC are shown in Fig. 1. We consider two cases related to the OPC position: six spans-OPC-14 spans (6vs14 configuration) and 14 spans-OPC-6 spans (14vs6 configuration). Because the number of fiber spans with respect to OPC is unequal, the NRD in each transmission section is unequal if the same RDPS is applied to every fiber span. In the 6vs14 configuration, if the RDPS of every fiber span in the FTS is set to 210 ps/nm, the RDPS of each fiber span in LTS should be set to 90 ps/nm to equalize the NRD of each transmission section. In the 14vs6 configuration, the RDPS values in the FTS and LTS should be swapped to achieve the same NRD.

Figure 1. The configuration of a dispersion-managed link with a non-midway OPC and 24-channel WDM system. EDFA: erbium doped fiber amplifier, SMF: singlemode fiber, DCF: dispersion compensating fiber, OPC: optical phase conjugator, DC: dispersion calibrator.

Various RDPS values for each transmission section were considered in this study, as shown in Table 1. These values were selected by the uniform deviation from the above-mentioned RDPS values: 210 ps/nm and 90 ps/nm. For a value of 210 ps/nm the deviation is to be ±20 ps/nm, and the deviation is to be ∓10 ps/nm for the reference of 90 ps/nm.

We introduce several definitions for a simple analysis of numerical simulation results. First, the difference between the NRD in FTS (NRD₁) and the NRD in LTS (NRD₂) is expressed by the symbol δ. For example, values of 210 ps/nm and 90 ps/nm were applied to every fiber span in FTS and LTS, respectively, and δ is consequently 0. The value of δ changes as the RDPS value is modified for each transmission section and increases as the deviation magnitude of the RDPS from the reference RDPS increases. However, the difference in δ between adjacent RDPSs remains constant because the deviation of RDPS is uniformly selected. The interval between adjacent δ values is expressed as G_δ. If the RDPS is selected from Table 1, G_δ = 260 ps/nm. The normalized value δ/G_δ is our second definition is denoted by the symbol Δ, represented as a positive or negative integer in Table 1.

To analyze the effect of the magnitude of the selected RDPS on the compensation performance, we use three additional reference RDPSs, except for the values in Table 1. The additional reference RDPS can be simply obtained as 210 ps/nm and 90 ps/nm multiplied by two, three, and four for both configurations. In addition, we multiply the deviations of RDPS by two, three, and four, respectively. For example, the reference RDPS, i.e., the RDPS corresponding with Δ = 0, is set to 420 ps/nm and 180 ps/nm when multiplied by two in 6vs14 configuration. In this case, the deviations were ±40 ps/nm and ∓20 ps/nm.

For the simplicity of demonstration, we call all RDPSs listed in Table 1 as the “basic” scheme. Each case of the RDPS arrays made up of the reference RDPS and the deviation in case of “basic” multiplied by two, three, and four are called as “double,” “triple,” and “quadruple,” respectively.

Table 1 .

6vs14						14vs6
RDPS1	RDPS2	NRD1	NRD2	δ	Δ	RDPS1	RDPS2	NRD1	NRD2	δ	Δ
570	-90	3420	-1260	4680	18	-90	570	-1260	3420	-4680	-18
550	-80	3300	-1120	4420	17	-80	550	-1120	3300	-4420	-17
⁝					⁝	⁝					⁝
250	70	1500	980	520	2	70	250	980	1500	-520	-2
230	80	1380	1120	260	1	80	230	1120	1380	-260	-1
210	90	1260	1260	0	0	90	210	1260	1260	0	0
190	100	1140	1400	-260	-1	100	190	1400	1140	260	1
170	110	1020	1540	-520	-2	110	170	1540	1020	520	2
150	120	900	1680	-780	-3	120	150	1680	900	780	3
130	130	780	1820	-1040	-4	130	130	1820	780	1040	4
⁝					⁝	⁝					⁝
-130	260	-780	3640	-4420	-17	260	-130	3640	-780	4420	17
-150	270	-900	3780	-4680	-18	270	-150	3780	-900	4680	18

*Subscripts 1 and 2 indicate the FTS and LTS, respectively..

The SSMFs in all fiber spans were characterized at 1,550 nm as follows: the length is 80 km, the dispersion coefficient is 17 ps/nm/km, the attenuation coefficient is 0.2 dB/km, and the nonlinear coefficient is γ_SMF = 1.41 W⁻¹ km⁻¹. The DCFs in all fiber spans were characterized at 1,550 nm as follows: dispersion coefficient is -100 ps/nm/km, the attenuation coefficient is 0.6 dB/km, and the nonlinear coefficient is 5.06 W⁻¹ km⁻¹. However, the DCF lengths from the 1-st to the 20-th fiber spans depend on the selected RDPS value according to the expression (l_SMF · D_SMF–RDPS)/|D_DCF|. For example, if the RDPS is selected to be 210 ps/nm in FTS, then the DCF length in FTS is determined to be 11.5 km.

In the DM link for “pseudo-linear” systems, when the total NRD should be maintained near 0 ps/nm rather than 0 ps/nm, the best compensation occurs [15]. Thus, the special fiber span must take the role in retain this condition, because in our simulation, 0 ps/nm cannot be simultaneously selected as the RDPS applied to FTS and LTS. We assign the fiber span front of #1 fiber span and the fiber span next to #20 fiber span as the special fiber span for this role, which are called the pre-dispersion calibrator (DC) and post-DC, respectively. However, only one of these two DCs plays the role of an NRD controller of FTS or LTS by varying its own length; on the other hand, the DCF length of the remaining DC should be fixed to make the NRD of LTS or FTS 0 ps/nm.

The feature of highly nonlinear dispersion-shifted fiber (HNL-DSF) as the nonlinear medium of the OPC shown in Fig. 1 is the same as in previous studies [13] and [14].

The 24 transmitters of WDM depicted in Fig. 1, in which the external intensity-modulator (MOD) simultaneously generates return-to-zero pulses through a 40-Gb/s 127(=2⁷ − 1) pseudorandom bit sequence (PRBS). The center wavelengths and the wavelength interval of 0.8 nm (100 GHz) are based on ITU-T recommendation G.694.1 [16]. The 24 receivers were designed using the direct detection method. All parameters of each transmitter and receiver were identical to those in previous studies [13] and [14].

(1)$$\frac{\partial A_j}{\partial z}=-\frac{\alpha }{2}{A}_j-\frac{i}{2}{B}_{2j}\frac{{\partial }^2{A}_j}{\partial T^2}+\frac{1}{6}{B}_{3j}\frac{{\partial }^3{A}_j}{\partial T^3}+i{\gamma }_j{\left|A_j\right|}^2{A}_j+2i{\gamma }_j{\left|A_k\right|}^2{A}_j$$

The nonlinear Schrödinger equation shown in (1) can express a slowly varying envelope of optical signals propagating through an attenuated, dispersive, and nonlinear medium [17]. In (1), for j, k = 1, 2,…, 24 (j ≠ k), A_j represents the complex amplitude of the signal of the j-th channel, z indicates the propagation distance, β_2j denotes the GVD, β_3j represents the third-order dispersion, γ_j denotes the nonlinear coefficient, and T = t − z/v_j refers to the time measured in a retarded frame. The numerical simulation of 24-channels of 40 Gb/s propagating through the optical link plotted in Fig. 1 was completed using the split-step Fourier (SSF) method [17] using MAT-LAB software. The performance of the compensated optical signals was then assessed using the eye-opening penalty (EOP) and timing jitter. For EOP assessment, we consider a 1-dB EOP as the system performance criterion as this value is equivalent to a bit error rate (BER) of 10^–12 [18].

In Fig. 2, subplots (a) and (b) show the EOP of the worst channel with a launch power of 0 dBm as a function of Δ in the 6vs14 and 14vs6 configurations, respectively. The NRD is fixed to 10 ps/nm by pre-DC in the 6vs14 configuration, and -10 ps/nm by post-DC in the 14vs6 configuration. In Fig. 2, the compensation characteristics depending upon Δ in the 6vs14 configuration are mirror images of those in the 14vs6 configuration, indicating that intrinsic features of optical phase conjugation are also presented in our research. Another major result confirmed by Fig. 2 is that excellent compensation is possible when Δ is near to but not equal to zero. As previously mentioned, Δ = 0 means that the NRD of all transmission sections are equal. This result in Fig. 2 proves that the modest asymmetry of the NRD of the sections is affected by the non-midway OPC position.

Another takeaway from Fig. 2 is that the compensation performance for double and triple is slightly improved compared to basic and quadruple. It is known from this fact that optimal compensation of the distorted WDM channels can be obtained by properly increasing the RDPS difference between two transmission sections.

To analyze the detailed compensation effect of the proposed DM link, the EOP contour generated by the launch power and Δ is shown in Fig. 3. In Fig. 3, the contours of the 6vs14 and 14vs6 configurations, in which the RDPS was selected with the double case, are revealed only as an extension of the results in Fig. 2. Moreover, each of them is classified into the best compensation for the 6vs14 and 14vs6 configurations, respectively. The number above each contour line represents the value of the EOP.

Figure 2. EOP as a function of ∆ in the worst case.

Comparing Fig. 3(a) and Fig. 3(b), the 6 vs 14 configuration is shown to be more advantageous for compensating the distorted WDM channels than the 14 vs 6 configuration. Specifically, excellent compensation can be achieved by transmitting WDM channels of the launch power from -4.5 dBm to -2 dBm into a 6vs14 configured DM link with a Δ of -4 ~ -1, i.e., RDPS₁ = 260 ~ 380 ps/nm and RDPS₂ = 260 ~ 200 ps/nm.

After our analysis using Fig. 2 and Fig. 3, the suitable link configuration depending on the non-midway OPC was determined to be 6vs14 rather than 14vs6. The desirable values of Δ are near zero in all configurations, and the RDPS value applied to every fiber span has to be chosen to be neither too large or too small. To date, the NRD of the total spans was set to be 10 ps/nm or -10 ps/nm by pre-DC or post-DC during the simulation process of the proposed link with non-midway OPC. However, an EOP of 1 dB was also obtained for other NRD values. For this reason, the authors used the effective NRD range, defined as the range from the minimum to the maximum NRD value, which are resulting in 1 dB EOP, as the analyzing factor for the compensation characteristics. The effective NRD range as a function of the launch power in the 6vs14 configuration is shown in Fig. 4, in which the RDPSs are selected with Δ = -1 and the total NRD controlled by pre-DC. That is, the RDPS of FTS and LTS were 190 ps/nm and 100 ps/nm, respectively, for the basic scheme. These are multiplied by two, three, and four in the double, triple, and quadruple schemes, respectively. In Fig. 4, a result of Δ = 0 is obtained in the basic scheme, that is, when the RDPS is 210 ps/nm in FTS and 90 ps/nm in LTS, for comparison.

Figure 3. The contour of launch power and Δ in the “double” case.

Figure 4. Effective NRD range depends on the launch power in 6vs14 configuration with Δ = -1.

The effective NRD range also has a contour form. To analyze and compare the effective NRD range in every case depending on Δ, the various magnitudes of RDPS, and the non-midway OPC position, it is convenient to use the area of each contour. Consequently, the area of the contour is identical to the product of launch power and NRD (expressed as “P×NRD”).

The results of the P×NRD considered in this study are plotted in Fig. 5. It is first confirmed that the features of P×NRD in the 6vs14 configuration are mirror images of those in the 14vs6 configuration, as shown in Fig. 2. The most outstanding feature is that the variation of P×NRD depending on Δ in double, triple, and quadruple schemes is too similar in all these cases. However, in the basic scheme, the magnitudes of P×NRD are generally different, the maximum and the minimum values of P×NRD are smaller, and the Δ resulting from these two values deviates from the other schemes. It is also known that the optimal P×NRD is obtained by adopting the quadruple scheme. Consequently, to enhance the flexibility of the link design by increasing P×NRD, the magnitude of RDPS applied to two transmission sections must be large, and Δ becomes a value around zero.

Figure 5. Product of launch power and NRD.

The EOP versus the launch power and the timing jitter versus the launch power in the cases of best and worst compensation is illustrated in Fig. 6(a) and Fig. 6(b), respectively. The best compensation for the 6 vs 14 configuration occurs for RDPS₁ = 380 ps/nm and RDPS₂ = 200 ps/nm, i.e., Δ = -1 of double scheme in which the total NRD is set to be -10 ps/nm by pre-DC, and RDPS₁ = 400 ps/nm and RDPS₂ = 760 ps/nm, i.e., Δ = 1 for the triple scheme in which the total NRD is set to be -10 ps/nm by post-DC in the 14vs6 configuration. On the other hand, the worst compensation of the 6vs14 configuration occurs for RDPS₁ = 1170 ps/nm and RDPS₂ = 0 ps/nm, i.e., Δ = 9 for the triple scheme in which the total NRD is set to be 10 ps/nm by pre-DC, and with RDPS₁ = 20 ps/nm and RDPS₂ = 740 ps/nm, i.e., Δ = -8 for the double scheme in which the total NRD is set to be -10 ps/nm by post-DC in the 14vs6 configuration. From the results of Fig. 6, it is confirmed that the power margin based on 1 dB EOP is approximately 5 dB in the case of the same OPC position. Therefore, it can be concluded that the selection of RDPS, the NRD deviation between two transmission sections, and the NRD calibration are all significant for improving the compensation performance in the DM link with non-midway OPC.

Figure 6. The received performances of the best compensation and the worst compensation.

We have numerically demonstrated the compensation for 960 Gb/s wavelength-division multiplexed (WDM) signals distorted by chromatic dispersion and Kerr nonlinearity of fibers in the DM link combined with the non-midway OPC. The simulation results showed that the 6vs14 configuration is more effective in compensating for the deteriorated WDM signals than the 14vs6 configuration. In addition, when the NRD difference between each transmission section was small but not zero, compensation was further improved in both configurations. It was also confirmed that a large magnitude of RDPS applied to each fiber span was more appropriate to extend the flexibility of the DM link topology than a small magnitude of RDPS.

It is expected that the numerical results and investigations performed in this study will help configure the long-haul optical link for transmitting ultra-high capacity traffic while maintaining high quality.