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Journal of information and communication convergence engineering 2023; 21(2): 103-109

Published online June 30, 2023

https://doi.org/10.56977/jicce.2023.21.2.103

© Korea Institute of Information and Communication Engineering

Dispersion-managed Optical Link Configured Antipodalsymmetric Dispersion Maps with Respect to Midway Optical Phase Conjugator

Jae-Pil Chung 1 and Seong-Real Lee2* , Member, KIICE

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1Department of Electronic Engineering, Gachon University, Seongnam 13120, Korea
2Division of Navigational Information System, Mokpo National Maritime University, Mokpo 58628, Korea

Correspondence to : Seong-Real Lee (E-mail: reallee@mmu.ac.kr)
Division of Navigational Information System, Mokpo National Maritime University, Mokpo 58628, Republic of Korea

Received: March 10, 2023; Revised: May 2, 2023; Accepted: May 2, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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We investigated the antipodal-symmetric dispersion maps of a dispersion-managed link with a midway optical phase conjugator to compensate for the distorted 960 Gb/s wavelength division multiplexed (WDM) signal caused by these effects. The proposed antipodal-symmetric dispersion map has various shapes depending on the detailed design scheme. We confirmed that the dispersion-managed link designed with the dispersion map of the antipodal-symmetric structure is more advantageous than the conventional uniform dispersion map for compensating WDM channels. It was also confirmed that among the antipodal-symmetric structures, the dispersion map configured with the S-1-profile, in which S is inverted up and down, was more effective for distortion compensation than the dispersion map configured with the S-profile. In particular, we confirmed that the S-1-profile can broaden the optical pulse width intensively at a short transmission distance, more effectively compensating for the distorted WDM channel. Because this structure makes the intensity of the optical pulse relatively weak, it can decrease the nonlinear Kerr effect.

Keywords Antipodal-symmetric dispersion map, Chromatic dispersion, Midway optical phase conjugator, Nonlinear Kerr effect, Split-step Fourier method

I. INTRODUCTION

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The hyper-connected era initiated by the Internet and accelerated with the technology of the 4th industrial revolution can break time and spatial restrictions based on a high-speed optical communication network [1]. For a hyper-connected society to develop daily, the optical network infrastructure must meet new requirements of ultra-low latency, high integration, and low power [2]. In addition, the flexibility of optical networks must be guaranteed to realize a hyperconnected society. Following this trend, optical network technology has been developed to reliably transmit ultrawide-bandwidth signals through wavelength division multiplexing (WDM) technology and reconfigurable optical add/drop multiplexing (ROADM) links.

It is necessary to compensate for the temporal spread of light pulses due to the chromatic dispersion inherent in standard single-mode fiber (SSMF) to realize ultralow latency in optical transmission networks [3]. A representative technique is dispersion management, in which the dispersion is eliminated or reduced by additionally configuring a dispersion-compensating fiber (DCF) with the opposite dispersion characteristic to the SSMF in each fiber span [4].

It is also necessary to mitigate or eliminate the spectral distortion of light pulses owing to the nonlinear Kerr effect of SSMF for transmitting ultrawide-band signals in optical transmission systems. Various techniques have been proposed and demonstrated to compensate for the nonlinear Kerr effect, such as digital back propagation [5,6], phase-conjugated twin waves [7], phase-sensitive amplification [8], optical soliton transmission [9], and optical phase conjugation [10-13]. Optical phase conjugation is a technology that can restore distorted signals similarly to the original signals by phase-conjugating the distorted optical signals through an optical phase conjugator (OPC) located at the midpoint of the entire transmission link and transmitting the phase-conjugated signals through the remaining section [14].

However, dispersion management is limited because it cannot completely compensate for the distortion caused by the nonlinear Kerr effect by itself. Meanwhile, optical phase conjugation is limited because it does not make the link configuration flexible, as the OPC must be in the middle or near the entire transmission link [15]. Furthermore, in the case of a WDM system, dispersion management has a problem that the wavelength of each channel is different, and as a result, it is difficult to compensate for the dispersion amount, which is accumulated differently depending on the wavelength of each channel [16]. Fortunately, if these two technologies are properly combined, the limitations of each can be overcome to a certain extent [17-21].

Optical phase conjugation performed intensively at the midpoint of the entire link is called midspan spectral inversion (MSSI). Our previous study demonstrated that the degree of compensation of a distorted WDM channel depends on the dispersion map when MSSI is applied to the dispersion-managed link [21]. The dispersion map is defined as the overall profile of the accumulated dispersion over the transmission distance. The shape of the distribution map is determined according to the specific method of applying the residual dispersion to each fiber. It was confirmed that the antipodal-symmetry structure is more advantageous for mitigating the distorted 960 Gb/s (= 40 Gb/s × 24 channels) WDM signals than the bilateral-symmetry structure in the MSSI system, in which the symmetry represents the dispersion distribution profile for the midpoint OPC [21].

In this paper, we propose and investigate various dispersion maps of antipodal-symmetry structures capable of compensating for the distorted WDM signal suffered through multifiber spans consisting of SSMF and DCF in an MSSI system, associated with our previous study [21]. More specifically, we analyzed the effect of the antipodal-symmetric distribution map of various structures, which were created by varying the magnitude and application pattern of the residual dispersion per span (RDPS) applied to each fiber span, on the compensation of the distorted 960 Gb/s WDM signals.

II. MODELING OF DISPERSION-MANAGED LINK WITH MSSI

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Fig. 1 shows 960 Gb/s WDM transmitters, receivers, the dispersion-managed link, and the midway OPC. The entire link consists of 50 fiber spans; thus, the former half section (FHS) and latter half section (LHS) with respect to midway OPC have the same 25 fiber spans. In dispersion management, the chromatic dispersion effect on the propagated WDM signals is controlled by inserting the DCF into SSMF for each fiber section. Furthermore, the deployment of each fiber should be opposite to each other about the midway OPC to increase the symmetry of the dispersion distribution, as shown in Fig. 1.

Fig. 1. Configuration of an optical link for transmitting 24-channel wavelength-division multiplexing (WDM). DFB-LD: distributed feedback laser diode, PRBS: pseudo random bit sequence, MOD: modulator, SMF: single-mode fiber, DCF: dispersion compensating fiber, EDFA: erbium doped fiber amplifier, OPC: optical phase conjugator, DC: dispersion calibrator, HNL-DSF: highly-nonlinear dispersion shifted fiber, OBPF: optical band pass filter, PD: photo detector.

The features of SSMF and DCF depend on the transmission wavelength. The transmission features of both fibers were chosen as the values at 1,550 nm. The detailed parameters and values of SSMF are as follows: the attenuation coefficient (αSMF) is 0.2 dB/km, dispersion coefficient (DSMF) is 17 ps/nm/km, and nonlinear coefficient (γSMF) is 1.41 W−1 km−1. The DCF has an attenuation coefficient (αDCF) of 0.6 dB/km, dispersion coefficient (DDCF) of -100 ps/nm/km, and nonlinear coefficient (γDCF) of 5.06 W−1 km−1. We assume that the length of SSMF (lSMF) in all fiber spans is 80 km, but the length of DCF (lDCF) varies depending on the RDPS according to the expression (lSMF · DSMF – RDPS)/│DDCF│, except for the first and last fiber spans. Moreover, RDPS is defined as the accumulated dispersion for a fiber span; thus, this is determined by the equation lSMF · DSMF – lDCF · DDCF.

We consider the two antipodal-symmetric dispersion map types illustrated in Fig. 2: S-profile and inverse S (S−1)-profile. This dispersion map can be obtained by artificially controlling the accumulated dispersion of each fiber span. As will be discussed later, the first and last fiber spans play roles other than forming a dispersion map profile. That is, 48 fiber spans are involved in the dispersion map profile.

Fig. 2. Dispersion maps of dispersion-managed link plotted in Fig. 1.

The S-profile dispersion map can be created by linearly decreasing and increasing the cumulative dispersion as the fiber span number increases in the front and rear parts of the FHS, respectively, while the increase and decrease in the linearly cumulative dispersion in the LHS are reversed compared to those in the FHS. Comparing Figs. 2(a) and 2(b), it can be seen that the S−1-profile can be obtained by applying the cumulative distribution method used in profile S, in reverse.

As shown in Figs. 2(a) and 2(b), various S-profiles and S−1-profiles can be obtained according to the number of fiber spans, for which the cumulative dispersion continuously increases or continuously decreases in each half section. We considered five specific profiles such as 04:20, 08:16, 12:12, 16:08, and 20:04 for S-profile and S−1-profile, which are based on the FHS.

Successive increases and decreases in the cumulative dispersion are determined by selecting and arranging the magnitudes and signs of the RDPSs. As shown in Fig. 2, the maximum and minimum cumulative dispersion amounts are designed to be the same for all dispersion map profiles. This scheme can only be achieved when the magnitude of each RDPS is set differently, as shown in Table 1.

Table 1 . RDPS distribution in FHS for S-profile dispersion maps for the case of │Dcum│

Profile typeFront part of FHSRear part of FHS
Span numberRDPS valueSpan numberRDPS value
S(04:20)#2 ~ #5-600 ps/nm#6 ~ #25120 ps/nm
S(08:16)#2 ~ #9-300 ps/nm#10 ~ #25150 ps/nm
S(12:12)#2 ~ #13-200 ps/nm#14 ~ #25200 ps/nm
S(16:08)#2 ~ #17-150 ps/nm#18 ~ #25300 ps/nm
S(20:04)#2 ~ #21-120 ps/nm#22 ~ #25600 ps/nm


Table 1 summarizes the detailed RDPS in each span constituting the FHS for only five types of S-profiles and for the maximum and minimum cumulative dispersion amounts of 2,400 ps/nm and -2,400 ps/nm, respectively. The absolute values of the maximum and minimum cumulative dispersion amounts are denoted as │Dcum│. The RDPS distribution on the LHS can be obtained by reversing the sign of the RDPS, as listed in Table 1. The RDPS distribution for the five types of S-1-profile can be obtained by exchanging the RDPS distributed for the S-profiles. We also investigated the case of │Dcum│= 4,800 ps/nm. This can be achieved by doubling all the RDPS magnitudes mentioned thus far.

In a pseudo-linear system, the net residual dispersion (NRD) is another factor that influences dispersion compensation [22]. The NRD is defined as the exact dispersion accumulated over all fiber links. According to [22], the optimal NRD should be near but not equal to 0 ps/nm. Referring to this fact, the arbitrary fiber span should play a role in adjusting the NRD to achieve the best compensation, because all the proposed dispersion map schemes have an NRD of 0 ps/nm in each half section. In this study, this role is played by the first fiber span (expressed as ‘pre-DC’ in Fig. 1) in FHS and the last fiber span (expressed as ‘post-DC’) in LHS, where DC is the dispersion calibrator. In other words, they ultimately decide the total dispersion accumulated over 24 fiber spans of FHS and LHS by adjusting the length of the corresponding DCF.

III. MODELING OF WDM SYSTEM AND MIDWAY OPC

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We assume intensity modulation (IM) as the transmission method for each WDM transmitter and use the direct detection (DD) method for the reception process of the WDM channels. In this study, the configurations of the WDM transmitter and receiver and parameter values for their modeling were the same as those used in [21].

We assume that the conjugated wave of each channel is generated through a four-wave mixing (FWM) process between the incident signal wave and pump light of 1549.75 nm in highly nonlinear-dispersion shifted fiber (HNL-DSF). In the HNL-DSF, the attenuation coefficient is 0.61 dB/km, nonlinear coefficient is 20.4 W−1 km−1 , zero dispersion wavelength is 1,550.0 nm, dispersion slope is 0.032 ps/nm2/ km, and length is 0.75 km. For signal wavelengths of 1550.0 to 1568.4 nm (0.8 nm intervals), the wavelengths of the conjugated wave generated through FWM correspond to 1549.5 to 1531.1 nm (−0.8 nm intervals). The 3-dB bandwidth of the conversion efficiency in the midway OPC is 48 nm (1526 nm ~1574 nm). Therefore, both the signal and conjugate wavelengths of the 24 WDM channels belong to this 3dB bandwidth.

IV. NUMERICAL ANALYSIS AND PERFORMANCE ASSESSMENT

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To analyze the performance of the distorted WDM signal, the nonlinear Schrödinger equation (NLSE) should be applied to the optical link in Fig. 1. The NLSE describes the propagation mechanism of the optical signal through a dielectric medium, where losses, dispersion, and nonlinear Kerr effects dominate.

The performance evaluation of the optical fiber system is generally based on the eye diagram of the received signals. The eye opening penalty (EOP) and bit error rate (BER) were measured using the eye diagram. In this study, we used the EOP to assess compensated optical signals.

The EOP, as the measure of system performance used in this study, is obtained through the “eye opening” of the eye diagram. EOP was quantified (in dB) as EOP = 10 log10 (eye opening after transmission/eye opening before transmission). As the decision threshold is set at the center of the open portion of the eye, any reduction in eye opening indicates an increase in BER. In other words, the EOP is related to the BER. We take 1 dB as the performance criterion for the EOP of the worst channel, which corresponds to a BER of 10−12.

V. SIMULATION RESULTS AND DISCUSSION

Fig. 3 shows the NRD resulting in a 1-dB EOP as a function of the launch power of the WDM channel when the RDPS of all fiber spans in the dispersion-managed link in Fig. 1 is uniformly distributed at 0 ps/nm. The result of the uniform distribution in Fig. 3 is the subject of comparison to evaluate the performance of the antipodal-symmetric dispersion maps. This is because a uniform distribution is the most common dispersion-managed link configuration.

Fig. 3. Launch power versus allowable NRD in the uniform distribution of RDPSs.

Fig. 3 shows that the effective ranges of the launch power and NRD that can achieve 1-dB EOP results in a closed curve. In other words, effective compensation can be achieved by selecting NRD and launch power within the closed curve shown in Fig. 3. Through the launch power versus the allowable NRD curve shown in Fig. 3, the maximum and minimum effective launch powers and optimal NRD can be obtained simultaneously. That is, the optimal NRD in the link that adjusts the NRD by pre-DC in the uniform distribution is 10 ps/nm, and in this case, the minimum and maximum launch power are obtained as −7.71 dBm and 4.47 dBm, respectively. Meanwhile, the optimal NRD in the link controlled by post-DC is −10 ps/nm, and the minimum and maximum launch power are obtained as −7.2 dBm and 4.83 dBm, respectively.

Fig. 4 compares the two cases with the largest differences in launch power characteristics versus the allowable NRD among the proposed antipodal-symmetric dispersion maps. The results in Fig. 4 indicate that even in antipodal-symmetric configurations, the compensation characteristics can be different, and the link design conditions for the best compensation must be different depending on the specific antipodal-symmetric configuration.

Fig. 4. Launch power versus allowable NRD in several antipodal-symmetric dispersion maps.

For a clear analysis and comparison of the 12 cases specified by S-profiles and S−1-profiles, the DC method, and optimal NRD value, we now use the power margin, product of allowable NRD, and effective launch power, which are obtained secondarily from the launch power versus allowable NRD curve shown in Figs. 3 and 4.

A notable result from the analysis thus far is that the best NRDs determined by the pre- and post-DC are 10 ps/nm and -10 ps/nm, respectively, regardless of the dispersion map shape. Thus, we performed a compensation analysis on antipodal-symmetric dispersion maps with the NRD set to 10 ps/ nm pre-DC and -10 ps/nm post-DC. In Figs. 3 and 4, the difference between the maximum and minimum values of the effective launch power can be considered as the power margin applied to the corresponding link. Fig. 5 shows the power margin when five specific antipodal-symmetric dispersion maps are applied to the dispersion-managed link in Fig. 1.

Fig. 5. Power margins of the antipodal-symmetric dispersion maps.

From Fig. 5, it can be determined that the antipodal-symmetry dispersion maps that increase the power margin of the uniform distribution are S−1 (04:20), S−1 (08:16), S (16:08), and S (20:04). In other words, when the point where the cumulative dispersion reversal occurs is closer to the transmitter and receiver (i.e., (04:20) or (08:16)), the S−1-profiles are advantageous for compensation, whereas if the reversal point is closer to the OPC (i.e., (16:08) or (20:04)), effective compensation will be obtained by applying the S-profile rather than the S−1-profiles.

For the power margin of the system, it is also confirmed that when the antipodal-symmetric dispersion map of the S−1 (04:20) profile is applied, excellent compensation can be achieved, regardless of the DC method, optimal NRD value, and value of │Dcum│. A notable fact is that the maximum power margin is obtained when │Dcum│ of the dispersion-managed link is set to 4,800 ps/nm and the NRD is set to 10 ps/nm by pre-DC by applying the S−1(04:20) profile.

The larger the area of the closed curve shown in Figs. 3 and 4, the wider the diversity of the launch power and NRD selection for good compensation. In other words, the flexibility of the link design increases as the area of the closed curve widens. Therefore, to evaluate the design flexibility of the proposed antipodal-symmetric dispersion maps, the area of the closed curve obtained from each dispersion map was analyzed. The area of the closed curve formed by the effective NRD and launch power is equivalent to the product of the effective NRD and (launch) power.

Figs. 6(a) and 6(b) show the product of the effective NRD and power (hereinafter, referred to as “the product”) for a dispersion-managed link designed with a │Dcum│ of 2,400 and 4,800 ps/nm, respectively. The square- and round-ended bars are the products in the NRD controlled by pre-DC and post-DC, respectively. It can be confirmed that the dispersion calibration method, which is a method for determining the NRD, does not significantly affect the product. This product provides flexibility in the design of dispersion maps.

Fig. 6. Product of NRD and power.

As with the previous results, it is known that the flexibility of the dispersion map configured with the S−1-profiles is generally better than that with S-profiles; this feature is particularly noticeable in dispersion-managed links with large │Dcum│. In terms of design flexibility, it can also be confirmed that the dispersion map configured with S−1 (04:20) is the most advantageous for compensating distorted WDM channels compared to other dispersion maps.

VI. CONCLUSIONS

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Up to now, we have examined the compensation characteristics of 40 Gb/s × 24 channel WDM signals deteriorated by the combined effect of the nonlinear Kerr effect and chromatic dispersion by applying various types of antipodal-symmetric dispersion maps to midway OPC-applied dispersion-managed links. Computer simulations confirmed that the compensation in all the proposed antipodal-symmetric dispersion maps was superior to that in the conventional dispersion map configured with uniformly distributed RDPSs.

The antipodal-symmetric structure investigated in this study is largely divided into an S-profile and S−1-profile. The S-profile is a structure in which the overall shape of the cumulative dispersion across the entire transmission link is in the form of an S. If the dispersion map of the dispersion-managed link takes the form of the S-profile, in the FHS (i.e., front of the midway OPC), the cumulative dispersion is overall negative; thus, it compresses the optical pulse width, whereas in the LHS, the cumulative dispersion is overall positive; thus, it increasing the optical pulse width. The shape of the cumulative dispersion distribution of the S−1profile is opposite to that of the S-profile, and the fluctuation of the optical pulse width in this configuration is also opposite to that for the S-profile.

Various simulation results confirmed that the distorted WDM channel compensation was improved in the dispersion map configured by the S−1-profile structure compared to the S-profile. Furthermore, it was confirmed that the S−1 (04:20) profile is the most desirable scheme for improving the compensation performance and flexibility of the optical link setup.

S−1 (04:20) is a structure in which the distribution shape of the cumulative dispersion is reversed after the 5th fiber span from the start of the entire link and in the 5th fiber span before the end of the link. That is, it is a structure in which the distribution change of the cumulative dispersion is the fastest among all proposed profiles. Consequently, we confirmed that when an antipodal-symmetric dispersion map is applied to a dispersion-managed link with midway OPC, it is more effective to compensate for the deteriorated WDM channel by constructing a dispersion map to widen the optical pulse width such that it is less affected by the nonlinear Kerr effect in the initial stage of transmission.

References

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Biographies

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Jae-Pil Chun

received the B.S. and M.S. degrees in Electronic Engineering from Dankook University, Korea in 1985 and 1989, respectively, in addition to the Ph.D. degree in Telecommunication and Information Engineering from Korea Aerospace University, Korea in 2000. He is currently a professor in Department of Electronic Engineering, Gachon University. His research interests include wireless communication systems, wireless sensor network, and optical WDM systems.


Seong-Real Le

received the B.S., M.S., and Ph.D. degrees in telecommunication and information engineering from Korea Aerospace University, Korea in 1990, 1992, and 2002, respectively. He is currently a professor of Division of Navigational Information System at Mokpo National Maritime University. His research interests include optical WDM systems, optical soliton systems, and optical nonlinear effects.


Article

Regular paper

Journal of information and communication convergence engineering 2023; 21(2): 103-109

Published online June 30, 2023 https://doi.org/10.56977/jicce.2023.21.2.103

Copyright © Korea Institute of Information and Communication Engineering.

Dispersion-managed Optical Link Configured Antipodalsymmetric Dispersion Maps with Respect to Midway Optical Phase Conjugator

Jae-Pil Chung 1 and Seong-Real Lee2* , Member, KIICE

1Department of Electronic Engineering, Gachon University, Seongnam 13120, Korea
2Division of Navigational Information System, Mokpo National Maritime University, Mokpo 58628, Korea

Correspondence to:Seong-Real Lee (E-mail: reallee@mmu.ac.kr)
Division of Navigational Information System, Mokpo National Maritime University, Mokpo 58628, Republic of Korea

Received: March 10, 2023; Revised: May 2, 2023; Accepted: May 2, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigated the antipodal-symmetric dispersion maps of a dispersion-managed link with a midway optical phase conjugator to compensate for the distorted 960 Gb/s wavelength division multiplexed (WDM) signal caused by these effects. The proposed antipodal-symmetric dispersion map has various shapes depending on the detailed design scheme. We confirmed that the dispersion-managed link designed with the dispersion map of the antipodal-symmetric structure is more advantageous than the conventional uniform dispersion map for compensating WDM channels. It was also confirmed that among the antipodal-symmetric structures, the dispersion map configured with the S-1-profile, in which S is inverted up and down, was more effective for distortion compensation than the dispersion map configured with the S-profile. In particular, we confirmed that the S-1-profile can broaden the optical pulse width intensively at a short transmission distance, more effectively compensating for the distorted WDM channel. Because this structure makes the intensity of the optical pulse relatively weak, it can decrease the nonlinear Kerr effect.

Keywords: Antipodal-symmetric dispersion map, Chromatic dispersion, Midway optical phase conjugator, Nonlinear Kerr effect, Split-step Fourier method

I. INTRODUCTION

The hyper-connected era initiated by the Internet and accelerated with the technology of the 4th industrial revolution can break time and spatial restrictions based on a high-speed optical communication network [1]. For a hyper-connected society to develop daily, the optical network infrastructure must meet new requirements of ultra-low latency, high integration, and low power [2]. In addition, the flexibility of optical networks must be guaranteed to realize a hyperconnected society. Following this trend, optical network technology has been developed to reliably transmit ultrawide-bandwidth signals through wavelength division multiplexing (WDM) technology and reconfigurable optical add/drop multiplexing (ROADM) links.

It is necessary to compensate for the temporal spread of light pulses due to the chromatic dispersion inherent in standard single-mode fiber (SSMF) to realize ultralow latency in optical transmission networks [3]. A representative technique is dispersion management, in which the dispersion is eliminated or reduced by additionally configuring a dispersion-compensating fiber (DCF) with the opposite dispersion characteristic to the SSMF in each fiber span [4].

It is also necessary to mitigate or eliminate the spectral distortion of light pulses owing to the nonlinear Kerr effect of SSMF for transmitting ultrawide-band signals in optical transmission systems. Various techniques have been proposed and demonstrated to compensate for the nonlinear Kerr effect, such as digital back propagation [5,6], phase-conjugated twin waves [7], phase-sensitive amplification [8], optical soliton transmission [9], and optical phase conjugation [10-13]. Optical phase conjugation is a technology that can restore distorted signals similarly to the original signals by phase-conjugating the distorted optical signals through an optical phase conjugator (OPC) located at the midpoint of the entire transmission link and transmitting the phase-conjugated signals through the remaining section [14].

However, dispersion management is limited because it cannot completely compensate for the distortion caused by the nonlinear Kerr effect by itself. Meanwhile, optical phase conjugation is limited because it does not make the link configuration flexible, as the OPC must be in the middle or near the entire transmission link [15]. Furthermore, in the case of a WDM system, dispersion management has a problem that the wavelength of each channel is different, and as a result, it is difficult to compensate for the dispersion amount, which is accumulated differently depending on the wavelength of each channel [16]. Fortunately, if these two technologies are properly combined, the limitations of each can be overcome to a certain extent [17-21].

Optical phase conjugation performed intensively at the midpoint of the entire link is called midspan spectral inversion (MSSI). Our previous study demonstrated that the degree of compensation of a distorted WDM channel depends on the dispersion map when MSSI is applied to the dispersion-managed link [21]. The dispersion map is defined as the overall profile of the accumulated dispersion over the transmission distance. The shape of the distribution map is determined according to the specific method of applying the residual dispersion to each fiber. It was confirmed that the antipodal-symmetry structure is more advantageous for mitigating the distorted 960 Gb/s (= 40 Gb/s × 24 channels) WDM signals than the bilateral-symmetry structure in the MSSI system, in which the symmetry represents the dispersion distribution profile for the midpoint OPC [21].

In this paper, we propose and investigate various dispersion maps of antipodal-symmetry structures capable of compensating for the distorted WDM signal suffered through multifiber spans consisting of SSMF and DCF in an MSSI system, associated with our previous study [21]. More specifically, we analyzed the effect of the antipodal-symmetric distribution map of various structures, which were created by varying the magnitude and application pattern of the residual dispersion per span (RDPS) applied to each fiber span, on the compensation of the distorted 960 Gb/s WDM signals.

II. MODELING OF DISPERSION-MANAGED LINK WITH MSSI

Fig. 1 shows 960 Gb/s WDM transmitters, receivers, the dispersion-managed link, and the midway OPC. The entire link consists of 50 fiber spans; thus, the former half section (FHS) and latter half section (LHS) with respect to midway OPC have the same 25 fiber spans. In dispersion management, the chromatic dispersion effect on the propagated WDM signals is controlled by inserting the DCF into SSMF for each fiber section. Furthermore, the deployment of each fiber should be opposite to each other about the midway OPC to increase the symmetry of the dispersion distribution, as shown in Fig. 1.

Figure 1. Configuration of an optical link for transmitting 24-channel wavelength-division multiplexing (WDM). DFB-LD: distributed feedback laser diode, PRBS: pseudo random bit sequence, MOD: modulator, SMF: single-mode fiber, DCF: dispersion compensating fiber, EDFA: erbium doped fiber amplifier, OPC: optical phase conjugator, DC: dispersion calibrator, HNL-DSF: highly-nonlinear dispersion shifted fiber, OBPF: optical band pass filter, PD: photo detector.

The features of SSMF and DCF depend on the transmission wavelength. The transmission features of both fibers were chosen as the values at 1,550 nm. The detailed parameters and values of SSMF are as follows: the attenuation coefficient (αSMF) is 0.2 dB/km, dispersion coefficient (DSMF) is 17 ps/nm/km, and nonlinear coefficient (γSMF) is 1.41 W−1 km−1. The DCF has an attenuation coefficient (αDCF) of 0.6 dB/km, dispersion coefficient (DDCF) of -100 ps/nm/km, and nonlinear coefficient (γDCF) of 5.06 W−1 km−1. We assume that the length of SSMF (lSMF) in all fiber spans is 80 km, but the length of DCF (lDCF) varies depending on the RDPS according to the expression (lSMF · DSMF – RDPS)/│DDCF│, except for the first and last fiber spans. Moreover, RDPS is defined as the accumulated dispersion for a fiber span; thus, this is determined by the equation lSMF · DSMF – lDCF · DDCF.

We consider the two antipodal-symmetric dispersion map types illustrated in Fig. 2: S-profile and inverse S (S−1)-profile. This dispersion map can be obtained by artificially controlling the accumulated dispersion of each fiber span. As will be discussed later, the first and last fiber spans play roles other than forming a dispersion map profile. That is, 48 fiber spans are involved in the dispersion map profile.

Figure 2. Dispersion maps of dispersion-managed link plotted in Fig. 1.

The S-profile dispersion map can be created by linearly decreasing and increasing the cumulative dispersion as the fiber span number increases in the front and rear parts of the FHS, respectively, while the increase and decrease in the linearly cumulative dispersion in the LHS are reversed compared to those in the FHS. Comparing Figs. 2(a) and 2(b), it can be seen that the S−1-profile can be obtained by applying the cumulative distribution method used in profile S, in reverse.

As shown in Figs. 2(a) and 2(b), various S-profiles and S−1-profiles can be obtained according to the number of fiber spans, for which the cumulative dispersion continuously increases or continuously decreases in each half section. We considered five specific profiles such as 04:20, 08:16, 12:12, 16:08, and 20:04 for S-profile and S−1-profile, which are based on the FHS.

Successive increases and decreases in the cumulative dispersion are determined by selecting and arranging the magnitudes and signs of the RDPSs. As shown in Fig. 2, the maximum and minimum cumulative dispersion amounts are designed to be the same for all dispersion map profiles. This scheme can only be achieved when the magnitude of each RDPS is set differently, as shown in Table 1.

Table 1 . RDPS distribution in FHS for S-profile dispersion maps for the case of │Dcum│.

Profile typeFront part of FHSRear part of FHS
Span numberRDPS valueSpan numberRDPS value
S(04:20)#2 ~ #5-600 ps/nm#6 ~ #25120 ps/nm
S(08:16)#2 ~ #9-300 ps/nm#10 ~ #25150 ps/nm
S(12:12)#2 ~ #13-200 ps/nm#14 ~ #25200 ps/nm
S(16:08)#2 ~ #17-150 ps/nm#18 ~ #25300 ps/nm
S(20:04)#2 ~ #21-120 ps/nm#22 ~ #25600 ps/nm


Table 1 summarizes the detailed RDPS in each span constituting the FHS for only five types of S-profiles and for the maximum and minimum cumulative dispersion amounts of 2,400 ps/nm and -2,400 ps/nm, respectively. The absolute values of the maximum and minimum cumulative dispersion amounts are denoted as │Dcum│. The RDPS distribution on the LHS can be obtained by reversing the sign of the RDPS, as listed in Table 1. The RDPS distribution for the five types of S-1-profile can be obtained by exchanging the RDPS distributed for the S-profiles. We also investigated the case of │Dcum│= 4,800 ps/nm. This can be achieved by doubling all the RDPS magnitudes mentioned thus far.

In a pseudo-linear system, the net residual dispersion (NRD) is another factor that influences dispersion compensation [22]. The NRD is defined as the exact dispersion accumulated over all fiber links. According to [22], the optimal NRD should be near but not equal to 0 ps/nm. Referring to this fact, the arbitrary fiber span should play a role in adjusting the NRD to achieve the best compensation, because all the proposed dispersion map schemes have an NRD of 0 ps/nm in each half section. In this study, this role is played by the first fiber span (expressed as ‘pre-DC’ in Fig. 1) in FHS and the last fiber span (expressed as ‘post-DC’) in LHS, where DC is the dispersion calibrator. In other words, they ultimately decide the total dispersion accumulated over 24 fiber spans of FHS and LHS by adjusting the length of the corresponding DCF.

III. MODELING OF WDM SYSTEM AND MIDWAY OPC

We assume intensity modulation (IM) as the transmission method for each WDM transmitter and use the direct detection (DD) method for the reception process of the WDM channels. In this study, the configurations of the WDM transmitter and receiver and parameter values for their modeling were the same as those used in [21].

We assume that the conjugated wave of each channel is generated through a four-wave mixing (FWM) process between the incident signal wave and pump light of 1549.75 nm in highly nonlinear-dispersion shifted fiber (HNL-DSF). In the HNL-DSF, the attenuation coefficient is 0.61 dB/km, nonlinear coefficient is 20.4 W−1 km−1 , zero dispersion wavelength is 1,550.0 nm, dispersion slope is 0.032 ps/nm2/ km, and length is 0.75 km. For signal wavelengths of 1550.0 to 1568.4 nm (0.8 nm intervals), the wavelengths of the conjugated wave generated through FWM correspond to 1549.5 to 1531.1 nm (−0.8 nm intervals). The 3-dB bandwidth of the conversion efficiency in the midway OPC is 48 nm (1526 nm ~1574 nm). Therefore, both the signal and conjugate wavelengths of the 24 WDM channels belong to this 3dB bandwidth.

IV. NUMERICAL ANALYSIS AND PERFORMANCE ASSESSMENT

To analyze the performance of the distorted WDM signal, the nonlinear Schrödinger equation (NLSE) should be applied to the optical link in Fig. 1. The NLSE describes the propagation mechanism of the optical signal through a dielectric medium, where losses, dispersion, and nonlinear Kerr effects dominate.

The performance evaluation of the optical fiber system is generally based on the eye diagram of the received signals. The eye opening penalty (EOP) and bit error rate (BER) were measured using the eye diagram. In this study, we used the EOP to assess compensated optical signals.

The EOP, as the measure of system performance used in this study, is obtained through the “eye opening” of the eye diagram. EOP was quantified (in dB) as EOP = 10 log10 (eye opening after transmission/eye opening before transmission). As the decision threshold is set at the center of the open portion of the eye, any reduction in eye opening indicates an increase in BER. In other words, the EOP is related to the BER. We take 1 dB as the performance criterion for the EOP of the worst channel, which corresponds to a BER of 10−12.

V. SIMULATION RESULTS AND DISCUSSION

Fig. 3 shows the NRD resulting in a 1-dB EOP as a function of the launch power of the WDM channel when the RDPS of all fiber spans in the dispersion-managed link in Fig. 1 is uniformly distributed at 0 ps/nm. The result of the uniform distribution in Fig. 3 is the subject of comparison to evaluate the performance of the antipodal-symmetric dispersion maps. This is because a uniform distribution is the most common dispersion-managed link configuration.

Figure 3. Launch power versus allowable NRD in the uniform distribution of RDPSs.

Fig. 3 shows that the effective ranges of the launch power and NRD that can achieve 1-dB EOP results in a closed curve. In other words, effective compensation can be achieved by selecting NRD and launch power within the closed curve shown in Fig. 3. Through the launch power versus the allowable NRD curve shown in Fig. 3, the maximum and minimum effective launch powers and optimal NRD can be obtained simultaneously. That is, the optimal NRD in the link that adjusts the NRD by pre-DC in the uniform distribution is 10 ps/nm, and in this case, the minimum and maximum launch power are obtained as −7.71 dBm and 4.47 dBm, respectively. Meanwhile, the optimal NRD in the link controlled by post-DC is −10 ps/nm, and the minimum and maximum launch power are obtained as −7.2 dBm and 4.83 dBm, respectively.

Fig. 4 compares the two cases with the largest differences in launch power characteristics versus the allowable NRD among the proposed antipodal-symmetric dispersion maps. The results in Fig. 4 indicate that even in antipodal-symmetric configurations, the compensation characteristics can be different, and the link design conditions for the best compensation must be different depending on the specific antipodal-symmetric configuration.

Figure 4. Launch power versus allowable NRD in several antipodal-symmetric dispersion maps.

For a clear analysis and comparison of the 12 cases specified by S-profiles and S−1-profiles, the DC method, and optimal NRD value, we now use the power margin, product of allowable NRD, and effective launch power, which are obtained secondarily from the launch power versus allowable NRD curve shown in Figs. 3 and 4.

A notable result from the analysis thus far is that the best NRDs determined by the pre- and post-DC are 10 ps/nm and -10 ps/nm, respectively, regardless of the dispersion map shape. Thus, we performed a compensation analysis on antipodal-symmetric dispersion maps with the NRD set to 10 ps/ nm pre-DC and -10 ps/nm post-DC. In Figs. 3 and 4, the difference between the maximum and minimum values of the effective launch power can be considered as the power margin applied to the corresponding link. Fig. 5 shows the power margin when five specific antipodal-symmetric dispersion maps are applied to the dispersion-managed link in Fig. 1.

Figure 5. Power margins of the antipodal-symmetric dispersion maps.

From Fig. 5, it can be determined that the antipodal-symmetry dispersion maps that increase the power margin of the uniform distribution are S−1 (04:20), S−1 (08:16), S (16:08), and S (20:04). In other words, when the point where the cumulative dispersion reversal occurs is closer to the transmitter and receiver (i.e., (04:20) or (08:16)), the S−1-profiles are advantageous for compensation, whereas if the reversal point is closer to the OPC (i.e., (16:08) or (20:04)), effective compensation will be obtained by applying the S-profile rather than the S−1-profiles.

For the power margin of the system, it is also confirmed that when the antipodal-symmetric dispersion map of the S−1 (04:20) profile is applied, excellent compensation can be achieved, regardless of the DC method, optimal NRD value, and value of │Dcum│. A notable fact is that the maximum power margin is obtained when │Dcum│ of the dispersion-managed link is set to 4,800 ps/nm and the NRD is set to 10 ps/nm by pre-DC by applying the S−1(04:20) profile.

The larger the area of the closed curve shown in Figs. 3 and 4, the wider the diversity of the launch power and NRD selection for good compensation. In other words, the flexibility of the link design increases as the area of the closed curve widens. Therefore, to evaluate the design flexibility of the proposed antipodal-symmetric dispersion maps, the area of the closed curve obtained from each dispersion map was analyzed. The area of the closed curve formed by the effective NRD and launch power is equivalent to the product of the effective NRD and (launch) power.

Figs. 6(a) and 6(b) show the product of the effective NRD and power (hereinafter, referred to as “the product”) for a dispersion-managed link designed with a │Dcum│ of 2,400 and 4,800 ps/nm, respectively. The square- and round-ended bars are the products in the NRD controlled by pre-DC and post-DC, respectively. It can be confirmed that the dispersion calibration method, which is a method for determining the NRD, does not significantly affect the product. This product provides flexibility in the design of dispersion maps.

Figure 6. Product of NRD and power.

As with the previous results, it is known that the flexibility of the dispersion map configured with the S−1-profiles is generally better than that with S-profiles; this feature is particularly noticeable in dispersion-managed links with large │Dcum│. In terms of design flexibility, it can also be confirmed that the dispersion map configured with S−1 (04:20) is the most advantageous for compensating distorted WDM channels compared to other dispersion maps.

VI. CONCLUSIONS

Up to now, we have examined the compensation characteristics of 40 Gb/s × 24 channel WDM signals deteriorated by the combined effect of the nonlinear Kerr effect and chromatic dispersion by applying various types of antipodal-symmetric dispersion maps to midway OPC-applied dispersion-managed links. Computer simulations confirmed that the compensation in all the proposed antipodal-symmetric dispersion maps was superior to that in the conventional dispersion map configured with uniformly distributed RDPSs.

The antipodal-symmetric structure investigated in this study is largely divided into an S-profile and S−1-profile. The S-profile is a structure in which the overall shape of the cumulative dispersion across the entire transmission link is in the form of an S. If the dispersion map of the dispersion-managed link takes the form of the S-profile, in the FHS (i.e., front of the midway OPC), the cumulative dispersion is overall negative; thus, it compresses the optical pulse width, whereas in the LHS, the cumulative dispersion is overall positive; thus, it increasing the optical pulse width. The shape of the cumulative dispersion distribution of the S−1profile is opposite to that of the S-profile, and the fluctuation of the optical pulse width in this configuration is also opposite to that for the S-profile.

Various simulation results confirmed that the distorted WDM channel compensation was improved in the dispersion map configured by the S−1-profile structure compared to the S-profile. Furthermore, it was confirmed that the S−1 (04:20) profile is the most desirable scheme for improving the compensation performance and flexibility of the optical link setup.

S−1 (04:20) is a structure in which the distribution shape of the cumulative dispersion is reversed after the 5th fiber span from the start of the entire link and in the 5th fiber span before the end of the link. That is, it is a structure in which the distribution change of the cumulative dispersion is the fastest among all proposed profiles. Consequently, we confirmed that when an antipodal-symmetric dispersion map is applied to a dispersion-managed link with midway OPC, it is more effective to compensate for the deteriorated WDM channel by constructing a dispersion map to widen the optical pulse width such that it is less affected by the nonlinear Kerr effect in the initial stage of transmission.

Fig 1.

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Figure 1.Configuration of an optical link for transmitting 24-channel wavelength-division multiplexing (WDM). DFB-LD: distributed feedback laser diode, PRBS: pseudo random bit sequence, MOD: modulator, SMF: single-mode fiber, DCF: dispersion compensating fiber, EDFA: erbium doped fiber amplifier, OPC: optical phase conjugator, DC: dispersion calibrator, HNL-DSF: highly-nonlinear dispersion shifted fiber, OBPF: optical band pass filter, PD: photo detector.
Journal of Information and Communication Convergence Engineering 2023; 21: 103-109https://doi.org/10.56977/jicce.2023.21.2.103

Fig 2.

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Figure 2.Dispersion maps of dispersion-managed link plotted in Fig. 1.
Journal of Information and Communication Convergence Engineering 2023; 21: 103-109https://doi.org/10.56977/jicce.2023.21.2.103

Fig 3.

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Figure 3.Launch power versus allowable NRD in the uniform distribution of RDPSs.
Journal of Information and Communication Convergence Engineering 2023; 21: 103-109https://doi.org/10.56977/jicce.2023.21.2.103

Fig 4.

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Figure 4.Launch power versus allowable NRD in several antipodal-symmetric dispersion maps.
Journal of Information and Communication Convergence Engineering 2023; 21: 103-109https://doi.org/10.56977/jicce.2023.21.2.103

Fig 5.

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Figure 5.Power margins of the antipodal-symmetric dispersion maps.
Journal of Information and Communication Convergence Engineering 2023; 21: 103-109https://doi.org/10.56977/jicce.2023.21.2.103

Fig 6.

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Figure 6.Product of NRD and power.
Journal of Information and Communication Convergence Engineering 2023; 21: 103-109https://doi.org/10.56977/jicce.2023.21.2.103

Table 1 . RDPS distribution in FHS for S-profile dispersion maps for the case of │Dcum│.

Profile typeFront part of FHSRear part of FHS
Span numberRDPS valueSpan numberRDPS value
S(04:20)#2 ~ #5-600 ps/nm#6 ~ #25120 ps/nm
S(08:16)#2 ~ #9-300 ps/nm#10 ~ #25150 ps/nm
S(12:12)#2 ~ #13-200 ps/nm#14 ~ #25200 ps/nm
S(16:08)#2 ~ #17-150 ps/nm#18 ~ #25300 ps/nm
S(20:04)#2 ~ #21-120 ps/nm#22 ~ #25600 ps/nm

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