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Journal of information and communication convergence engineering 2024; 22(4): 273-279

Published online December 31, 2024

https://doi.org/10.56977/jicce.2024.22.4.273

© Korea Institute of Information and Communication Engineering

Mid-span Spectral Inversion System with Random Triangular Dispersion Maps

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

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

Correspondence to : Seong-Real Lee (E-mail: reallee@mmu.ac.kr)
Division of Navigational Information System, Mokpo National Maritime University, 91 Haeyangdaehak-ro, Mokpo 58628, Republic of Korea

Received: August 27, 2024; Revised: November 14, 2024; Accepted: November 14, 2024

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.

In dispersion-managed links with mid-span spectral inversion (MSSI) systems, the symmetry of the cumulative dispersion profile is important for compensating the distorted wavelength division multiplexing (WDM) signals. The triangular dispersion map has antipodal symmetry with respect to the midway optical phase conjugator (OPC). A triangular dispersion map is proposed in this paper that has a singularity in which the lengths of the optical fibers that contribute to forming the cumulative dispersion profile are determined randomly. We analyzed three types for randomly determining and deploying the length of optical fibers to form the triangular dispersion map. We confirmed that triangular dispersion maps combined with MSSI systems are more advantageous for distorted WDM channel compensation than traditional uniform dispersion maps are. In particular, the dispersion map created via the “random-inverse” scheme, which randomly arges the optical fiber lengths of each span before the midway OPC while reversing the arrangement of the optical fiber lengths in the sections after the midway OPC, results in the best compensation.

Keywords Chromatic dispersion, Midway optical phase conjugator, Nonlinear Kerr effect, Random dispersion map

Optical fiber communication systems have undergone groundbreaking developments through technologies that have accumulated over the past several decades. Among the various technologies that comprise optical communication networks such as subscriber and backhaul networks, the development and application of optical fiber amplifiers such as erbiumdoped fiber amplifiers (EDFAs) [1], coherent optical transmission technology [2] and wavelength-division multiplexing (WDM) technology [3] have made it possible to dramatically increase transmission distance and capacity.

Unlike traditional semiconductor optical amplifiers, optical fiber amplification technology does not require complex processes such as photoelectric conversion, electro-optical conversion and signal reshaping and can directly perform full optical amplification of the signal with good transparency. Therefore, the realization of long-haul optical link was possible by increasing the optical-fiber span interval. However, as the optical fiber amplifier is used, the light intensity increases, so intensity-dependent nonlinear distortion (called Kerr nonlinear distortion) occurs in the optical signal. By using coherent optical transmission instead of intensity modulation (IM)-based transmission, Kerr nonlinear distortion can be minimized.

Although coherent optical transmission can reduce the effects of Kerr nonlinear distortion, it makes transceiver configuration difficult and ultimately complicates system configuration. For this reason, an optical communication system based on IM is constructed by applying a method that can eliminate or minimize the chromatic dispersion effect and Kerr nonlinear effect of single-mode fiber (SMF). A representative method commonly used to compensate for signal distortion caused by the chromatic dispersion effect is dispersion management (DM) [4,5]. Conversely, optical phase conjugation is a method that can minimize distortion caused by the Kerr nonlinear effect [6,7,8]. Although compensation can be effectively obtained even if these two methods are applied separately to the transmission link, we showed through previous research that combining the two methods can increase the compensation effect even in multichannel transmissions, such as WDM [9,10,11].

In phase conjugation, where the signal distorted while being transmitted is phase inverted at a specific location and then transmitted in the remaining section, the mid-span spectral inversion (MSSI) refers to the case where phase inversion occurs in half of the entire transmission link. The DM is achieved by inserting a dispersion compensating fiber (DCF) with a dispersion coefficient of the opposite sign as the SMF to the desired length to remove or reduce the amount of dispersion accumulated in the SMF, the main medium of the transmission link. As a result, in a dispersion-managed link, the amount of dispersion accumulated varies depending on the transmission distance, and this accumulated dispersion profile for the total transmission length is called a dispersion map.

Previous studies have shown that when the DM is applied to an MSSI system, the compensation effect can be greatly improved when the shape of the dispersion map is antipodal symmetric about the middle of the entire transmission link [9,10,11]. Triangular, square, and sine wave shapes are included in the dispersion map profile with an antipodalsymmetric structure. Differences in the shape of these dispersion maps can be created by varying the distribution of the sign and magnitude of the residual dispersion per span (RDPS) assigned to each optical fiber span. The simplest way to create these dispersion maps is to fix the lengths of the SMF and DCF that make up each fiber span in correspondence with the magnitude of the allocated RDPS.

However, it is also possible to randomly select the length of the SMF or DCF by making the RDPS of each optical fiber span, which contributes to determining the specific shape of the antipodal-symmetric dispersion map. If the length of one type of optical fiber is randomly selected, the lengths of the other types of optical fibers must be selected to achieve a predetermined RDPS magnitude.

In this paper, we propose a dispersion-managed link in which each optical fiber span has a constant magnitude of RDPS, but the lengths of the SMF and DCF that make up each optical fiber span are randomly selected. The basic scheme of the dispersion map designed in this paper is triangular in shape.

Fig. 1 shows the dispersion-managed link with the MSSI system for transmitting a 960 Gb/s WDM signal. The entire link consisted of 64 fiber spans. In the MSSI system, in addition to the symmetrical dispersion map, the arrangement of the two types of optical fibers that comprise the optical fiber span is also important. As shown in Fig. 1, the arrangement order of the SMF and DCF in each fiber span constituting the dispersion-managed link is different in the front and rear sections of the midway optical phase conjugator (OPC). This arrangement ensures perfect symmetry.

Fig. 1. The 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 bandpass filter, PD: photodetector.

The detailed parameters and values of the SMF are as follows: the attenuation coefficient (αSMF) is 0.2 dB/km, the dispersion coefficient (DSMF) is 17 ps/nm/km, and the nonlinear coefficient (γSMF) is 1.41 W−1 km−1. The DCF has an attenuation coefficient (αDCF) of 0.6 dB/km, a dispersion coefficient (DDCF) of −100 ps/nm/km, and a nonlinear coefficient (γDCF) of 5.06 W−1 km−1. However, the lengths of the two types of fibers (lSMF and lDCF) are varied to form the dispersion map shown in Fig. 2.

Fig. 2. The dispersion maps of the dispersion-managed link are plotted in Fig. 1.

As shown in Fig. 2, the shape of the dispersion map for the dispersion-managed link in Fig. 1 is triangular. The dispersion map in Fig. 2 can be created by using RDPS of the same magnitude with alternating signs for each of the eight fiber spans. The RDPS refers to the amount of residual dispersion accumulated for each optical fiber span. If defined as a formula, it is the same as (lSMF × DSMF) + (lDCF × DDCF). When the RDPS sign is eight consecutive positive paths and then eight consecutive negative paths, the slope of the dispersion profile increases uniformly and then decreases to the same slope. Alternatively, if the order of the signs is reversed, we can obtain a profile of the opposite shape.

The dispersion map marked with ‘TA’ in Fig. 2 is a structure that consistently increases/decreases and decreases/increases the cumulative dispersion slope for every 16 optical fibers spanning the section in front of the midway OPC. The cumulative dispersion slope in the section behind the midway OPC is symmetrical to the midpoint (i.e., decreases/increases and increases/decreases). By contrast, the dispersion map marked ‘TA−1’ can be obtained by reversing the sign of the RDPS assigned when forming the ‘TA.’

In a previous study, the RDPS of a certain magnitude assigned to each optical fiber span required to form a triangular-dispersion map was obtained by changing the length of the DCF while keeping the SMF length constant at 80 km for every span. This method simplifies the design of dispersion-managed links but has the disadvantage of having to restrict the variety of optical fiber lengths.

The purpose of this study is to expand the opportunity to overcome these limitations to some extent. The idea of this paper is relatively simple. In forming the dispersion map shown in Fig. 2, the SMF length of each optical fiber span is randomly determined as one of several. However, to maintain the RDPS magnitude allocated to the span, the length of the DCF must be determined in conjunction with the selected SMF length. For example, if the RDPS is 100 ps/nm and the SMF length is selected to be 50 km in any span, the DCF length should be 7.5 km, and if the SMF length is selected to be 90 km in another link, the DCF length should be 14.3 km.

Sixteen kinds of SMF lengths are considered in this study, ranging from 40 km to 115 km at 5 km intervals. The SMF length for each optical fiber span is randomly selected from one of these 16 lengths, and the arbitrary SMF length is selected twice in the front and rear sections of the midway OPC.

Because it is an MSSI system with the OPC in the middle of the link to which the dispersion map in Fig. 2 is applied, it is expected that the correlation between the random arrangement of the SMF length before and after the midway OPC can affect WDM channel distortion compensation. For this reason, we investigate the following three patterns of the alignment relationship of the SMF length before and after the midway OPC. First, when the randomly selected SMF length and its ordering are independent of each other before and after midway OPC, we express this as ‘all-random.’ Second, the SMF length of each optical fiber spanning the front section of the midway OPC is selected randomly, but the SMF length in each span in the rear section is arranged in the opposite order in the front section; this case is called ‘random-inverse.’ Third, the SMF length of each optical fiber span in the front section is selected randomly, but the SMF length of each span in the rear section follows the same order as that in the front, which is called ‘random-follow’.

As shown in Fig. 2, if the triangular-shaped dispersion profile is perfect, the amount of dispersion accumulated over the entire transmission link, which is defined as the net residual dispersion (NRD), is zero. However, according to Killey, in a pseudolinear system, the best NRD should have a value near 0 ps/nm rather than 0 ps/nm to increase the compensation effect [12]. Setting the NRD to a value near 0 ps/nm means that some fiber span must play a role in adjusting the NRD. In this study, the DCF of the first fiber span plays that role, as indicated by ‘pre-DC’ in Fig. 1. ‘DC’ stands for the dispersion calibrator. In summary, the DCF of the first span of the dispersion-managed link shown in Fig. 1 contributes to setting the RDPS in that span but is also simultaneously used to adjust the NRD through its variable length.

The specific type of midway OPC required to build the MSSI system uses highly nonlinear dispersion shifted fiber (HNL-DSF) OPC, as in previous studies. The characteristics of HNL-DSF are as follows: an attenuation coefficient of 0.61 dB/km, a nonlinear coefficient of 20.4 W−1 km−1, a zero dispersion wavelength of 1,550.0 nm, a dispersion slope of 0.032 ps/nm2/km, and a length of 0.75 km.

The transmission and reception techniques of the 24 WDM channels shown on the right and left sides of Fig. 1 are intensity modulation/direct detection (IM/DD). In this study, the IM/DD modeling scheme and characteristic values used for 24 WDM channels are the same as those in reference [11]. The wavelength of the optical signal assigned to each of the 24 transmitters in Fig. 1 ranges from 1550.0 nm to 1568.4 nm at 0.8 nm intervals. When the 24 channels arrive at the midway OPC after being multiplexed, they are pumped by an optical signal of 1549.75 nm wavelength and converted into the conjugate signal after going through the four-wave mixing process. The wavelengths of the conjugate signals of the 24 channels range from 1549.5 nm to 1531.1 nm (−0.8 nm interval).

All signals before and after conjugate conversion must be interpreted via the nonlinear Schrödinger equation [13]. Numerical analysis of the transmission of optical signals governed by this equation is performed via the slit-step Fourier (SSF) technique [13]. We performed the simulation by coding the SSF technique with MATLAB, in which the aforementioned 24 WDM channels of 40 Gb/s were transmitted through the dispersion-managed link to which the dispersion map in Fig. 2 is applied. The performance evaluation in this study is based on an eye diagram. We used the eye opening penalty (EOP) and timing jitter (TJ) to assess the compensated optical signals in this work. The EOP is quantified (in dB) as EOP = 10 log10 (eye opening after transmission/eye opening before transmission). TJ is obtained by measuring the time deviation of half the peak power of each pulse. The performance criterion values of the received signal are 1 dB for EOP and 2.5 ps for TJ in this study.

First, we evaluate the degree of compensation depending on the NRD in each dispersion map. In the EOP evaluation of the received signal, the best compensation is achieved when the NRD of all dispersion maps is set to 10 ps/nm, as in previous studies, but in the TJ evaluation, the best compensation is achieved when the NRD is set to 0 ps/nm.

Figs. 3 and 4 show the results obtained when the NRD of the dispersion-managed links is set to 10 ps/nm and illustrate the EOP characteristics obtained from each of the proposed random triangular dispersion maps. Conversely, Figs. 5 and 6 show the TJ characteristics obtained when the NRD is set to 0 ps/nm in the same dispersion-managed links.

Fig. 3. Difference in the effective launch power of the proposed dispersion maps based on an EOP of 1 dB when the NRD = 10 ps/nm.

Fig. 4. Difference in the power margins of the proposed dispersion maps for an EOP of 1 dB when the NRD = 10 ps/nm.

Fig. 5. Difference in the effective launch power of the proposed dis-persion maps based on a timing jitter of 2.5 ps in the case of NRD = 0 ps/nm.

Fig. 6. Difference in the power margins of the proposed dispersion maps based on a timing jitter of 2.5 ps in the case of NRD = 0 ps/nm.

In every case, the RDPS of each fiber span is set to ±100 ps/nm. However, as previously explained, the dispersion map examined in this paper is based on the method in which the length of the SMF constituting each optical fiber span is determined randomly first, and then the DCF length is determined on the basis of it. The way to determine how well the three types of dispersion maps proposed in this paper compensate for distorted WDM channels is a relative comparison through the performance difference between the proposed dispersion maps and the uniform dispersion map. The uniform dispersion maps are formed by setting the DCF length to either 12.6 km or 14.6 km to achieve an RDPS of ±100 ps/nm for each fiber span under an SMF length of 80 km.

The difference in effective power shown in Fig. 3 and Fig. 5 is the maximum launch power that can obtain an EOP of 1 dB and a TJ of 2.5 ps for the worst channel, respectively, in the link to which the proposed dispersion map is applied minus the maximum launch power in the uniform dispersion map. The power margin is the range (width) from the minimum launch power to the maximum launch power that can achieve an EOP of 1 dB or a TJ of 2.5 ps for the worst channel. The difference in the power margins shown in Fig. 4 and Fig. 6 is the power margin obtained in the proposed dispersion map minus the power margin obtained in the uniform dispersion map.

As the performance comparison from Fig. 3 to Fig. 6 is based on the difference from the uniform dispersion map, if the result is greater than 0, the proposed random-based dispersion map has an improved compensation effect compared with the uniform dispersion map. The ‘descending order’ written on the x-axis in Figs. 3 to 6 means arranging 50 random cases in order of best performance.

First, analyzing the EOP characteristics of the worst channel, as shown in Fig. 3 and Fig. 4, among the three random distributions, when the ‘random-inverse’ arrangement is applied, excellent compensation can be obtained without being affected by the shape of the distribution profile (i.e., TA and TA−1).

Figs. 3 and 4 confirm that among the six dispersion maps classified according to the dispersion map profile shape and the RDPS distribution pattern before and after OPC, the scheme with the poorest compensation effect in evaluating EOP performance is ‘TA random-follow.’ However, even when the dispersion map of this scheme is applied, better compensation is achieved than when the uniform dispersion map is used for more than 25 patterns out of 50 random patterns. Figs. 5 and 6 show that even if the reception performance is changed to TJ, similar results are obtained as in the EOP analysis.

A noteworthy result in Figs. 5 and 6 is that the improvement in the TJ of the WDM channel through the proposed random-based triangle dispersion map is obtained in TA−1 rather than in TA for all three random patterns. It appears that the proposed TA−1-scheme random-based dispersion maps are not particularly effective for TJ compensation but rather are due to the relatively poor TJ compensation effect of the TA−1-scheme uniform dispersion map.

All of the effective launch power and power margins seen thus far were obtained when the NRD was set to its optimal value, i.e., 0 ps/nm or 10 ps/nm. However, as in previous studies, an EOP of 1 dB or a TJ of 2.5 ps can be obtained at other NRDs near this value in the links to which the dispersion map analyzed in this study is applied. If the NRD, which results in a 1 dB EOP (or TJ of 2.5 ps), is obtained for each launch power and plotted, it becomes a closed curve, as in the our other studies. In this paper, we refer to the area of this closed curve as the product of the effective incident power and NRD (simply abbreviated as the ‘product’), as in previous studies. The larger the product is, the greater the utilization of NRD and launch power in that dispersion-managed link. In other words, the larger the product is, the more flexible the link becomes.

Figs. 7 and 8 show the differences between the products obtained from the proposed dispersion map and the uniform dispersion map for EOP and TJ, respectively. When analyzed from the EOP perspective, we can confirm in Fig. 7 that the link flexibility improves in the order of random-inverse, all-random, and random-follow, similar to the results obtained previously. However, Fig. 8 shows that the random triangular dispersion map proposed in this paper is overall more effective in improving TJ than EOP and can thereby increase link flexibility. In particular, the effect is greater when the dispersion map profile type is TA−1 than when it is TA, as in the results from the effective power and power margin analysis of the received WDM channels.

Fig. 7. Difference in the product based on an EOP of 1 dB.

Fig. 8. Difference in the product based on a TJ of 2.5 ps.

Thus far, we have analyzed the effect of the MSSI system in the dispersion-managed link composed of a random triangular dispersion map on the distortion compensation of the 960 Gb/s WDM signal. The triangular dispersion map examined in this paper had an antipodal-symmetric structure for midway OPC and was of two types, TA and TA−1, depending on the cumulative dispersion profile. The triangular dispersion map was created by randomly selecting the SMF length of each optical fiber span and was analyzed by considering three random distribution methods before and after midway OPC. The TJ was also included as a performance factor of the received signal in addition to the EOP.

The numerical analysis confirmed that the random triangular dispersion map proposed in this paper, when combined with midway OPC, is more effective in WDM channel compensation than the traditional uniform dispersion map. In particular, when the SMF length and DCF length of each optical fiber span were determined via the 'random-inverse' distribution pattern, more improved results were obtained than compensation through the uniform dispersion map for all 50 random cases considered. The 'random-inverse' distribution pattern means that the deployment of the SMF and DCF lengths in every optical fiber spans behind the midway OPC follows the opposite of the random arrangement allocated in the optical fiber spans before the midway OPC, but the order is reversed. If the arrangement order of the optical fiber lengths constituting each span is determined in this way for the midway OPC, the overall shape of the dispersion map is the same, but a substantial mirroring effect appears for the midway OPC, consequently, there is a greater increase in antipodal symmetry than in the other two cases. On the basis of this validity, we judged that the compensation effect was greater in the ‘random-inverse’ pattern than in the other cases.

Furthermore, through simulation and analysis, we confirmed that the TA−1-shaped dispersion map is more advantageous than the TA-shaped dispersion map in compensating for the temporal fluctuation (timing error) of the received WDM pulse. Consequently, the triangular dispersion map compensates for the deteriorated WDM channel by creating an antipodal-symmetric dispersion profile for the midway OPC, but the method of randomly determining the lengths of the optical fibers in forming the triangular dispersion map is better than the traditional method, such as the uniform distribution.

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Jae-Pil Chung

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


Seong-Real Lee

He 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 2024; 22(4): 273-279

Published online December 31, 2024 https://doi.org/10.56977/jicce.2024.22.4.273

Copyright © Korea Institute of Information and Communication Engineering.

Mid-span Spectral Inversion System with Random Triangular Dispersion Maps

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

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

Correspondence to:Seong-Real Lee (E-mail: reallee@mmu.ac.kr)
Division of Navigational Information System, Mokpo National Maritime University, 91 Haeyangdaehak-ro, Mokpo 58628, Republic of Korea

Received: August 27, 2024; Revised: November 14, 2024; Accepted: November 14, 2024

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

In dispersion-managed links with mid-span spectral inversion (MSSI) systems, the symmetry of the cumulative dispersion profile is important for compensating the distorted wavelength division multiplexing (WDM) signals. The triangular dispersion map has antipodal symmetry with respect to the midway optical phase conjugator (OPC). A triangular dispersion map is proposed in this paper that has a singularity in which the lengths of the optical fibers that contribute to forming the cumulative dispersion profile are determined randomly. We analyzed three types for randomly determining and deploying the length of optical fibers to form the triangular dispersion map. We confirmed that triangular dispersion maps combined with MSSI systems are more advantageous for distorted WDM channel compensation than traditional uniform dispersion maps are. In particular, the dispersion map created via the “random-inverse” scheme, which randomly arges the optical fiber lengths of each span before the midway OPC while reversing the arrangement of the optical fiber lengths in the sections after the midway OPC, results in the best compensation.

Keywords: Chromatic dispersion, Midway optical phase conjugator, Nonlinear Kerr effect, Random dispersion map

I. INTRODUCTION

Optical fiber communication systems have undergone groundbreaking developments through technologies that have accumulated over the past several decades. Among the various technologies that comprise optical communication networks such as subscriber and backhaul networks, the development and application of optical fiber amplifiers such as erbiumdoped fiber amplifiers (EDFAs) [1], coherent optical transmission technology [2] and wavelength-division multiplexing (WDM) technology [3] have made it possible to dramatically increase transmission distance and capacity.

Unlike traditional semiconductor optical amplifiers, optical fiber amplification technology does not require complex processes such as photoelectric conversion, electro-optical conversion and signal reshaping and can directly perform full optical amplification of the signal with good transparency. Therefore, the realization of long-haul optical link was possible by increasing the optical-fiber span interval. However, as the optical fiber amplifier is used, the light intensity increases, so intensity-dependent nonlinear distortion (called Kerr nonlinear distortion) occurs in the optical signal. By using coherent optical transmission instead of intensity modulation (IM)-based transmission, Kerr nonlinear distortion can be minimized.

Although coherent optical transmission can reduce the effects of Kerr nonlinear distortion, it makes transceiver configuration difficult and ultimately complicates system configuration. For this reason, an optical communication system based on IM is constructed by applying a method that can eliminate or minimize the chromatic dispersion effect and Kerr nonlinear effect of single-mode fiber (SMF). A representative method commonly used to compensate for signal distortion caused by the chromatic dispersion effect is dispersion management (DM) [4,5]. Conversely, optical phase conjugation is a method that can minimize distortion caused by the Kerr nonlinear effect [6,7,8]. Although compensation can be effectively obtained even if these two methods are applied separately to the transmission link, we showed through previous research that combining the two methods can increase the compensation effect even in multichannel transmissions, such as WDM [9,10,11].

In phase conjugation, where the signal distorted while being transmitted is phase inverted at a specific location and then transmitted in the remaining section, the mid-span spectral inversion (MSSI) refers to the case where phase inversion occurs in half of the entire transmission link. The DM is achieved by inserting a dispersion compensating fiber (DCF) with a dispersion coefficient of the opposite sign as the SMF to the desired length to remove or reduce the amount of dispersion accumulated in the SMF, the main medium of the transmission link. As a result, in a dispersion-managed link, the amount of dispersion accumulated varies depending on the transmission distance, and this accumulated dispersion profile for the total transmission length is called a dispersion map.

Previous studies have shown that when the DM is applied to an MSSI system, the compensation effect can be greatly improved when the shape of the dispersion map is antipodal symmetric about the middle of the entire transmission link [9,10,11]. Triangular, square, and sine wave shapes are included in the dispersion map profile with an antipodalsymmetric structure. Differences in the shape of these dispersion maps can be created by varying the distribution of the sign and magnitude of the residual dispersion per span (RDPS) assigned to each optical fiber span. The simplest way to create these dispersion maps is to fix the lengths of the SMF and DCF that make up each fiber span in correspondence with the magnitude of the allocated RDPS.

However, it is also possible to randomly select the length of the SMF or DCF by making the RDPS of each optical fiber span, which contributes to determining the specific shape of the antipodal-symmetric dispersion map. If the length of one type of optical fiber is randomly selected, the lengths of the other types of optical fibers must be selected to achieve a predetermined RDPS magnitude.

In this paper, we propose a dispersion-managed link in which each optical fiber span has a constant magnitude of RDPS, but the lengths of the SMF and DCF that make up each optical fiber span are randomly selected. The basic scheme of the dispersion map designed in this paper is triangular in shape.

II. MODELING OF DISPERSION-MANAGED LINK, MSSI SYSTEM, AND WDM SYSTEM

Fig. 1 shows the dispersion-managed link with the MSSI system for transmitting a 960 Gb/s WDM signal. The entire link consisted of 64 fiber spans. In the MSSI system, in addition to the symmetrical dispersion map, the arrangement of the two types of optical fibers that comprise the optical fiber span is also important. As shown in Fig. 1, the arrangement order of the SMF and DCF in each fiber span constituting the dispersion-managed link is different in the front and rear sections of the midway optical phase conjugator (OPC). This arrangement ensures perfect symmetry.

Figure 1. The 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 bandpass filter, PD: photodetector.

The detailed parameters and values of the SMF are as follows: the attenuation coefficient (αSMF) is 0.2 dB/km, the dispersion coefficient (DSMF) is 17 ps/nm/km, and the nonlinear coefficient (γSMF) is 1.41 W−1 km−1. The DCF has an attenuation coefficient (αDCF) of 0.6 dB/km, a dispersion coefficient (DDCF) of −100 ps/nm/km, and a nonlinear coefficient (γDCF) of 5.06 W−1 km−1. However, the lengths of the two types of fibers (lSMF and lDCF) are varied to form the dispersion map shown in Fig. 2.

Figure 2. The dispersion maps of the dispersion-managed link are plotted in Fig. 1.

As shown in Fig. 2, the shape of the dispersion map for the dispersion-managed link in Fig. 1 is triangular. The dispersion map in Fig. 2 can be created by using RDPS of the same magnitude with alternating signs for each of the eight fiber spans. The RDPS refers to the amount of residual dispersion accumulated for each optical fiber span. If defined as a formula, it is the same as (lSMF × DSMF) + (lDCF × DDCF). When the RDPS sign is eight consecutive positive paths and then eight consecutive negative paths, the slope of the dispersion profile increases uniformly and then decreases to the same slope. Alternatively, if the order of the signs is reversed, we can obtain a profile of the opposite shape.

The dispersion map marked with ‘TA’ in Fig. 2 is a structure that consistently increases/decreases and decreases/increases the cumulative dispersion slope for every 16 optical fibers spanning the section in front of the midway OPC. The cumulative dispersion slope in the section behind the midway OPC is symmetrical to the midpoint (i.e., decreases/increases and increases/decreases). By contrast, the dispersion map marked ‘TA−1’ can be obtained by reversing the sign of the RDPS assigned when forming the ‘TA.’

In a previous study, the RDPS of a certain magnitude assigned to each optical fiber span required to form a triangular-dispersion map was obtained by changing the length of the DCF while keeping the SMF length constant at 80 km for every span. This method simplifies the design of dispersion-managed links but has the disadvantage of having to restrict the variety of optical fiber lengths.

The purpose of this study is to expand the opportunity to overcome these limitations to some extent. The idea of this paper is relatively simple. In forming the dispersion map shown in Fig. 2, the SMF length of each optical fiber span is randomly determined as one of several. However, to maintain the RDPS magnitude allocated to the span, the length of the DCF must be determined in conjunction with the selected SMF length. For example, if the RDPS is 100 ps/nm and the SMF length is selected to be 50 km in any span, the DCF length should be 7.5 km, and if the SMF length is selected to be 90 km in another link, the DCF length should be 14.3 km.

Sixteen kinds of SMF lengths are considered in this study, ranging from 40 km to 115 km at 5 km intervals. The SMF length for each optical fiber span is randomly selected from one of these 16 lengths, and the arbitrary SMF length is selected twice in the front and rear sections of the midway OPC.

Because it is an MSSI system with the OPC in the middle of the link to which the dispersion map in Fig. 2 is applied, it is expected that the correlation between the random arrangement of the SMF length before and after the midway OPC can affect WDM channel distortion compensation. For this reason, we investigate the following three patterns of the alignment relationship of the SMF length before and after the midway OPC. First, when the randomly selected SMF length and its ordering are independent of each other before and after midway OPC, we express this as ‘all-random.’ Second, the SMF length of each optical fiber spanning the front section of the midway OPC is selected randomly, but the SMF length in each span in the rear section is arranged in the opposite order in the front section; this case is called ‘random-inverse.’ Third, the SMF length of each optical fiber span in the front section is selected randomly, but the SMF length of each span in the rear section follows the same order as that in the front, which is called ‘random-follow’.

As shown in Fig. 2, if the triangular-shaped dispersion profile is perfect, the amount of dispersion accumulated over the entire transmission link, which is defined as the net residual dispersion (NRD), is zero. However, according to Killey, in a pseudolinear system, the best NRD should have a value near 0 ps/nm rather than 0 ps/nm to increase the compensation effect [12]. Setting the NRD to a value near 0 ps/nm means that some fiber span must play a role in adjusting the NRD. In this study, the DCF of the first fiber span plays that role, as indicated by ‘pre-DC’ in Fig. 1. ‘DC’ stands for the dispersion calibrator. In summary, the DCF of the first span of the dispersion-managed link shown in Fig. 1 contributes to setting the RDPS in that span but is also simultaneously used to adjust the NRD through its variable length.

The specific type of midway OPC required to build the MSSI system uses highly nonlinear dispersion shifted fiber (HNL-DSF) OPC, as in previous studies. The characteristics of HNL-DSF are as follows: an attenuation coefficient of 0.61 dB/km, a nonlinear coefficient of 20.4 W−1 km−1, a zero dispersion wavelength of 1,550.0 nm, a dispersion slope of 0.032 ps/nm2/km, and a length of 0.75 km.

The transmission and reception techniques of the 24 WDM channels shown on the right and left sides of Fig. 1 are intensity modulation/direct detection (IM/DD). In this study, the IM/DD modeling scheme and characteristic values used for 24 WDM channels are the same as those in reference [11]. The wavelength of the optical signal assigned to each of the 24 transmitters in Fig. 1 ranges from 1550.0 nm to 1568.4 nm at 0.8 nm intervals. When the 24 channels arrive at the midway OPC after being multiplexed, they are pumped by an optical signal of 1549.75 nm wavelength and converted into the conjugate signal after going through the four-wave mixing process. The wavelengths of the conjugate signals of the 24 channels range from 1549.5 nm to 1531.1 nm (−0.8 nm interval).

III. NUMERICAL ANALYSIS AND PERFORMANCE ASSESSMENT

All signals before and after conjugate conversion must be interpreted via the nonlinear Schrödinger equation [13]. Numerical analysis of the transmission of optical signals governed by this equation is performed via the slit-step Fourier (SSF) technique [13]. We performed the simulation by coding the SSF technique with MATLAB, in which the aforementioned 24 WDM channels of 40 Gb/s were transmitted through the dispersion-managed link to which the dispersion map in Fig. 2 is applied. The performance evaluation in this study is based on an eye diagram. We used the eye opening penalty (EOP) and timing jitter (TJ) to assess the compensated optical signals in this work. The EOP is quantified (in dB) as EOP = 10 log10 (eye opening after transmission/eye opening before transmission). TJ is obtained by measuring the time deviation of half the peak power of each pulse. The performance criterion values of the received signal are 1 dB for EOP and 2.5 ps for TJ in this study.

IV. SIMULATION RESULTS AND DISCUSSIONS

First, we evaluate the degree of compensation depending on the NRD in each dispersion map. In the EOP evaluation of the received signal, the best compensation is achieved when the NRD of all dispersion maps is set to 10 ps/nm, as in previous studies, but in the TJ evaluation, the best compensation is achieved when the NRD is set to 0 ps/nm.

Figs. 3 and 4 show the results obtained when the NRD of the dispersion-managed links is set to 10 ps/nm and illustrate the EOP characteristics obtained from each of the proposed random triangular dispersion maps. Conversely, Figs. 5 and 6 show the TJ characteristics obtained when the NRD is set to 0 ps/nm in the same dispersion-managed links.

Figure 3. Difference in the effective launch power of the proposed dispersion maps based on an EOP of 1 dB when the NRD = 10 ps/nm.

Figure 4. Difference in the power margins of the proposed dispersion maps for an EOP of 1 dB when the NRD = 10 ps/nm.

Figure 5. Difference in the effective launch power of the proposed dis-persion maps based on a timing jitter of 2.5 ps in the case of NRD = 0 ps/nm.

Figure 6. Difference in the power margins of the proposed dispersion maps based on a timing jitter of 2.5 ps in the case of NRD = 0 ps/nm.

In every case, the RDPS of each fiber span is set to ±100 ps/nm. However, as previously explained, the dispersion map examined in this paper is based on the method in which the length of the SMF constituting each optical fiber span is determined randomly first, and then the DCF length is determined on the basis of it. The way to determine how well the three types of dispersion maps proposed in this paper compensate for distorted WDM channels is a relative comparison through the performance difference between the proposed dispersion maps and the uniform dispersion map. The uniform dispersion maps are formed by setting the DCF length to either 12.6 km or 14.6 km to achieve an RDPS of ±100 ps/nm for each fiber span under an SMF length of 80 km.

The difference in effective power shown in Fig. 3 and Fig. 5 is the maximum launch power that can obtain an EOP of 1 dB and a TJ of 2.5 ps for the worst channel, respectively, in the link to which the proposed dispersion map is applied minus the maximum launch power in the uniform dispersion map. The power margin is the range (width) from the minimum launch power to the maximum launch power that can achieve an EOP of 1 dB or a TJ of 2.5 ps for the worst channel. The difference in the power margins shown in Fig. 4 and Fig. 6 is the power margin obtained in the proposed dispersion map minus the power margin obtained in the uniform dispersion map.

As the performance comparison from Fig. 3 to Fig. 6 is based on the difference from the uniform dispersion map, if the result is greater than 0, the proposed random-based dispersion map has an improved compensation effect compared with the uniform dispersion map. The ‘descending order’ written on the x-axis in Figs. 3 to 6 means arranging 50 random cases in order of best performance.

First, analyzing the EOP characteristics of the worst channel, as shown in Fig. 3 and Fig. 4, among the three random distributions, when the ‘random-inverse’ arrangement is applied, excellent compensation can be obtained without being affected by the shape of the distribution profile (i.e., TA and TA−1).

Figs. 3 and 4 confirm that among the six dispersion maps classified according to the dispersion map profile shape and the RDPS distribution pattern before and after OPC, the scheme with the poorest compensation effect in evaluating EOP performance is ‘TA random-follow.’ However, even when the dispersion map of this scheme is applied, better compensation is achieved than when the uniform dispersion map is used for more than 25 patterns out of 50 random patterns. Figs. 5 and 6 show that even if the reception performance is changed to TJ, similar results are obtained as in the EOP analysis.

A noteworthy result in Figs. 5 and 6 is that the improvement in the TJ of the WDM channel through the proposed random-based triangle dispersion map is obtained in TA−1 rather than in TA for all three random patterns. It appears that the proposed TA−1-scheme random-based dispersion maps are not particularly effective for TJ compensation but rather are due to the relatively poor TJ compensation effect of the TA−1-scheme uniform dispersion map.

All of the effective launch power and power margins seen thus far were obtained when the NRD was set to its optimal value, i.e., 0 ps/nm or 10 ps/nm. However, as in previous studies, an EOP of 1 dB or a TJ of 2.5 ps can be obtained at other NRDs near this value in the links to which the dispersion map analyzed in this study is applied. If the NRD, which results in a 1 dB EOP (or TJ of 2.5 ps), is obtained for each launch power and plotted, it becomes a closed curve, as in the our other studies. In this paper, we refer to the area of this closed curve as the product of the effective incident power and NRD (simply abbreviated as the ‘product’), as in previous studies. The larger the product is, the greater the utilization of NRD and launch power in that dispersion-managed link. In other words, the larger the product is, the more flexible the link becomes.

Figs. 7 and 8 show the differences between the products obtained from the proposed dispersion map and the uniform dispersion map for EOP and TJ, respectively. When analyzed from the EOP perspective, we can confirm in Fig. 7 that the link flexibility improves in the order of random-inverse, all-random, and random-follow, similar to the results obtained previously. However, Fig. 8 shows that the random triangular dispersion map proposed in this paper is overall more effective in improving TJ than EOP and can thereby increase link flexibility. In particular, the effect is greater when the dispersion map profile type is TA−1 than when it is TA, as in the results from the effective power and power margin analysis of the received WDM channels.

Figure 7. Difference in the product based on an EOP of 1 dB.

Figure 8. Difference in the product based on a TJ of 2.5 ps.

V. CONCLUSIONS

Thus far, we have analyzed the effect of the MSSI system in the dispersion-managed link composed of a random triangular dispersion map on the distortion compensation of the 960 Gb/s WDM signal. The triangular dispersion map examined in this paper had an antipodal-symmetric structure for midway OPC and was of two types, TA and TA−1, depending on the cumulative dispersion profile. The triangular dispersion map was created by randomly selecting the SMF length of each optical fiber span and was analyzed by considering three random distribution methods before and after midway OPC. The TJ was also included as a performance factor of the received signal in addition to the EOP.

The numerical analysis confirmed that the random triangular dispersion map proposed in this paper, when combined with midway OPC, is more effective in WDM channel compensation than the traditional uniform dispersion map. In particular, when the SMF length and DCF length of each optical fiber span were determined via the 'random-inverse' distribution pattern, more improved results were obtained than compensation through the uniform dispersion map for all 50 random cases considered. The 'random-inverse' distribution pattern means that the deployment of the SMF and DCF lengths in every optical fiber spans behind the midway OPC follows the opposite of the random arrangement allocated in the optical fiber spans before the midway OPC, but the order is reversed. If the arrangement order of the optical fiber lengths constituting each span is determined in this way for the midway OPC, the overall shape of the dispersion map is the same, but a substantial mirroring effect appears for the midway OPC, consequently, there is a greater increase in antipodal symmetry than in the other two cases. On the basis of this validity, we judged that the compensation effect was greater in the ‘random-inverse’ pattern than in the other cases.

Furthermore, through simulation and analysis, we confirmed that the TA−1-shaped dispersion map is more advantageous than the TA-shaped dispersion map in compensating for the temporal fluctuation (timing error) of the received WDM pulse. Consequently, the triangular dispersion map compensates for the deteriorated WDM channel by creating an antipodal-symmetric dispersion profile for the midway OPC, but the method of randomly determining the lengths of the optical fibers in forming the triangular dispersion map is better than the traditional method, such as the uniform distribution.

Fig 1.

Figure 1.The 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 bandpass filter, PD: photodetector.
Journal of Information and Communication Convergence Engineering 2024; 22: 273-279https://doi.org/10.56977/jicce.2024.22.4.273

Fig 2.

Figure 2.The dispersion maps of the dispersion-managed link are plotted in Fig. 1.
Journal of Information and Communication Convergence Engineering 2024; 22: 273-279https://doi.org/10.56977/jicce.2024.22.4.273

Fig 3.

Figure 3.Difference in the effective launch power of the proposed dispersion maps based on an EOP of 1 dB when the NRD = 10 ps/nm.
Journal of Information and Communication Convergence Engineering 2024; 22: 273-279https://doi.org/10.56977/jicce.2024.22.4.273

Fig 4.

Figure 4.Difference in the power margins of the proposed dispersion maps for an EOP of 1 dB when the NRD = 10 ps/nm.
Journal of Information and Communication Convergence Engineering 2024; 22: 273-279https://doi.org/10.56977/jicce.2024.22.4.273

Fig 5.

Figure 5.Difference in the effective launch power of the proposed dis-persion maps based on a timing jitter of 2.5 ps in the case of NRD = 0 ps/nm.
Journal of Information and Communication Convergence Engineering 2024; 22: 273-279https://doi.org/10.56977/jicce.2024.22.4.273

Fig 6.

Figure 6.Difference in the power margins of the proposed dispersion maps based on a timing jitter of 2.5 ps in the case of NRD = 0 ps/nm.
Journal of Information and Communication Convergence Engineering 2024; 22: 273-279https://doi.org/10.56977/jicce.2024.22.4.273

Fig 7.

Figure 7.Difference in the product based on an EOP of 1 dB.
Journal of Information and Communication Convergence Engineering 2024; 22: 273-279https://doi.org/10.56977/jicce.2024.22.4.273

Fig 8.

Figure 8.Difference in the product based on a TJ of 2.5 ps.
Journal of Information and Communication Convergence Engineering 2024; 22: 273-279https://doi.org/10.56977/jicce.2024.22.4.273

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