Research Article | Open Access | Download PDF
Volume 13 | Issue 6 | Year 2026 | Article Id. IJECE-V13I6P113 | DOI : https://doi.org/10.14445/23488549/IJECE-V13I6P113Prediction of Long-Haul Dark Pulse Propagation Using a Hybrid Physics-Guided Data-Driven Model
Chinu Priyadarshani, Krishna Chandra Patra, Prabeen Kumar Sahu
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 14 Mar 2026 | 13 Apr 2026 | 12 May 2026 | 27 Jun 2026 |
Citation :
Chinu Priyadarshani, Krishna Chandra Patra, Prabeen Kumar Sahu, "Prediction of Long-Haul Dark Pulse Propagation Using a Hybrid Physics-Guided Data-Driven Model," International Journal of Electronics and Communication Engineering, vol. 13, no. 6, pp. 154-169, 2026. Crossref, https://doi.org/10.14445/23488549/IJECE-V13I6P113
Abstract
In the optical fiber system, Long-Haul Dark Pulse Propagation (LHDPP) plays a vital role. The complex wavelength-dependent nonlinear interactions and the absence of dynamic oscillation modeling in existing approaches made it challenging to predict the propagation characteristics accurately. This work aims to develop a unified physics-guided and data-driven framework for modeling, characteristics prediction, and performance evaluation of dark pulse propagation in a Long-Haul Fiber Optic System. The proposed model integrates the coupled nonlinear Schrödinger equation with the Split-Step Fourier Method (SSFM) to simulate Long- Haul Dark Pulse Propagation under realistic conditions. A nonlinear polarization-maintained optical loop mirror-based multi-wavelength generation scheme, along with an early–late feed-forward equalized gate synchronization mechanism, is employed to enhance system fidelity. To capture dynamic wavelength interactions, a novel Tukey sliding window-based dynamic dual wavelength oscillation modeling approach is introduced using spectral conversion and cross-correlation analysis. Furthermore, a Deep Long Dirichlet E-Swish Short-Term Memory (DLDESTM) model is developed as a computationally efficient surrogate to learn the spatiotemporal dynamics of nonlinear propagation. The proposed framework achieves a prediction accuracy of 98.36%, demonstrates close agreement with experimental results at 1550 nm, and reduces computational complexity by approximately 46 times compared to conventional SSFM simulations. These results confirm improved prediction accuracy, enhanced signal quality, and reduced computational burden. The proposed approach provides a robust and scalable solution for accurate LHDPP characterization, enabling efficient design for next-generation optical communication systems.
Keywords
Coupled NLSE, Dark Pulse Propagation, Long-Haul Fiber Optic Communication, Physics-Guided Deep Learning, Split-Step Fourier Method.
References
- Asma Taskeen et al., “Bifurcation, Chaotic, Sensitivity Analysis, and Optical Soliton Profiles for the Spin Hirota-Maxwell-Bloch Equation in an Erbium-Doped Fiber,” Advances in Mathematical Physics, vol. 2025, no. 1, pp. 1-20, 2025.
[CrossRef] [Google Scholar] [Publisher Link] - Hermann A. Haus, and William S. Wong, “Solitons in Optical Communications,” Reviews of Modern Physics, vol. 68, 1996.
[CrossRef] [Google Scholar] [Publisher Link] - Jun Guo et al., “Anti-Dark Solitons in a Single-Mode Fiber Laser,” Physics Letters A, vol. 395, 2021.
[CrossRef] [Google Scholar] [Publisher Link] - Attila Fülöp et al., “High-Order Coherent Communications using Mode-Locked Dark-Pulse Kerr Combs from Microresonators,” Nature Communications, vol. 9, pp. 1-8, 2018.
[CrossRef] [Google Scholar] [Publisher Link] - Mohammed S. Alshaykh et al., “Kerr Combs for Stimulated Brillouin Scattering Mitigation in Long-Haul Analog Optical Links,” Journal of Lightwave Technology, vol. 37, no. 23, pp. 5773-5779, 2019.
[Google Scholar] [Publisher Link] - Jason D. McKinney, Vincent J. Urick, and John Briguglio, “Optical Comb Sources for High Dynamic-Range Single-Span Long-Haul Analog Optical Links,” IEEE Transactions on Microwave Theory and Techniques, vol. 59, no. 12, pp. 3249-3257, 2011.
[CrossRef] [Google Scholar] [Publisher Link] - Yuri S. Kivshar, and Barry Luther-Davies, “Dark Optical Solitons: Physics and Applications,” Physics Reports, vol. 298, no. 2-3, pp. 81-197, 1998.
[CrossRef] [Google Scholar] [Publisher Link] - Yaoyao Qi et al., “Generation of Bright–Dark Pulse Pairs in the Er-Doped Mode-Locked Fiber Laser based on Doped Fiber Saturable Absorber,” Photonics, vol. 11, no. 6, pp. 1-10, 2024.
[CrossRef] [Google Scholar] [Publisher Link] - Yapeng Xie et al., “Machine Learning Applications for Short-Reach Optical Communication,” Photonics, vol. 9, no. 1, pp. 1-38, 2022.
[CrossRef] [Google Scholar] [Publisher Link] - Yvan Pointurier, “Machine Learning Techniques for Quality of Transmission Estimation in Optical Networks,” Journal of Optical Communications and Networking, vol. 13, no. 4, pp. 60-71, 2021.
[CrossRef] [Google Scholar] [Publisher Link] - Haci Mehmet Baskonus, Tukur Abdulkadir Sulaiman, and Hasan Bulut, “Bright, Dark Optical and Other Solitons to the Generalized Higher-Order NLSE in Optical Fibers,” Optical and Quantum Electronics, vol. 50, 2018.
[CrossRef] [Google Scholar] [Publisher Link] - Houria Trik et al., “Dark Solitons in an Extended Nonlinear Schrödinger Equation with Higher-Order Odd and Even Terms,” Optik, vol. 164, pp. 661-670, 2018.
[CrossRef] [Google Scholar] [Publisher Link] - Saroja V. Siddamal, R.M. Banakar, and B.C. Jinaga, “Split-Step Method in the Analysis and Modeling of Optical Fiber Communication System,” Advances in Computing, Communication and Control, pp. 254-261, 2011.
[CrossRef] [Google Scholar] [Publisher Link] - Hang Yang et al., “Fast and Accurate Waveform Modeling of Long-Haul Multichannel Optical Fiber Transmission using a Hybrid Model-Data Driven Scheme,” Journal of Lightwave Technology, vol. 40, no. 14, pp. 4571-4580, 2022.
[CrossRef] [Google Scholar] [Publisher Link] - Ezra Ip et al., “DAS Over 1,007-km Hybrid Link With 10-Tb/s DP-16QAM Co-Propagation Using Frequency-Diverse Chirped Pulses,” Journal of Lightwave Technology, vol. 41, no. 4, pp. 1077-1086, 2023.
[CrossRef] [Google Scholar] [Publisher Link] - Stavros Deligiannidis et al., “Multichannel Nonlinear Equalization in Coherent WDM Systems based on Bi-Directional Recurrent Neural Networks,” Journal of Lightwave Technology, vol. 42, no. 2, pp. 541-549, 2024.
[CrossRef] [Google Scholar] [Publisher Link] - Kyo Inoue, and Koji Igarashi, “Nonlinear Wave Equation for Wavelength/Polarization Multiplexed Signals in Fiber Transmission,” Optics Continuum, vol. 2, no. 69, pp. 1331-1339, 2023.
[CrossRef] [Google Scholar] [Publisher Link] - Aly R. Seadawy, and Nadia Cheemaa, “Propagation of Nonlinear Complex Waves for the Coupled Nonlinear Schrödinger Equations,” Physica A: Statistical Mechanics and its Applications, vol. 529, 2019.
[CrossRef] [Google Scholar] [Publisher Link] - Mamta Kapoor, “Dark Soliton Solutions of Cubic-Quartic Nonlinear Schrödinger Equation via Sumudu HPM,” Results in Optics, vol. 21, pp. 1-15, 2025.
[CrossRef] [Google Scholar] [Publisher Link] - Paramjit Kaur, Divya Dhawan, and Neena Gupta, “Mitigation of Nonlinearities in Long-Haul DWDM Soliton-Based Communication System,” Journal of Optical Communications, vol. 45, no. S1, pp. 1031-1038, 2023.
[CrossRef] [Google Scholar] [Publisher Link] - Kovendhan Vijayan et al., “Phase-Sensitively Amplified Wavelength-Division Multiplexed Optical Transmission Systems,” Optics Express, vol. 29, no. 21, pp. 33086-33096, 2021.
[CrossRef] [Google Scholar] [Publisher Link] - Muhammad Amin S. Murad et al., “The Fractional Soliton Solutions and Dynamical Investigation for Planar Hamiltonian System of Fokas Model in Optical Fiber,” Alexandria Engineering Journal, vol. 121, pp. 27-37, 2025.
[CrossRef] [Google Scholar] [Publisher Link] - Kang-Jia Wang et al., “The Perturbed Chen–Lee–Liu Equation: Diverse Optical Soliton Solutions and Other Wave Solutions,” Advances in Mathematical Physics, vol. 2024, no. 1, pp. 1-13, 2024.
[CrossRef] [Google Scholar] [Publisher Link] - Asbah Masih, and Gurjit Kaur, “Machine Learning-Based Regression Models for Predicting Signal Quality of Dense Wavelength Division Multiplexing Optical Communication Network,” International Journal of Communication Systems, vol. 36, no. 13, 2023.
[CrossRef] [Google Scholar] [Publisher Link] - Guanju Peng et al., “Coherent All-Optical Reservoir Computing for Nonlinear Equalization in Long-Haul Optical Fiber Communication Systems,” Optics and Laser Technology, vol. 174, 2024.
[CrossRef] [Google Scholar] [Publisher Link] - Wafy M. Hasan et al., “Exploring Highly Dispersive Optical Solitons and Modulation Instability in Nonlinear Schrödinger Equations,” Scientific Reports, vol. 15, pp. 1-20, 2025.
[CrossRef] [Google Scholar] [Publisher Link] - Mohammed F. Shehab et al., “Analytic Solutions for Stochastic Fourth-Order (2+1)-Dimensional NLSE with Higher-Order Terms,” Optical and Quantum Electronics, vol. 56, 2024.
[CrossRef] [Google Scholar] [Publisher Link] - Annamalai Muniyappan et al., “Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers using Extended Rational Sinh–Cosh and Sine–Cosine Methods,” Symmetry, vol. 16, no. 5, pp. 1-20, 2024.
[CrossRef] [Google Scholar] [Publisher Link] - A. Muniyappan et al., “Chirped Dark Soliton Propagation in Optical Fiber under a Self Phase Modulation and a Self-Steepening Effect for Higher Order Nonlinear Schrödinger Equation,” Optical and Quantum Electronics, vol. 56, 2024.
[CrossRef] [Google Scholar] [Publisher Link] - Song Yang et al., “Recent Advances and Challenges on Dark Solitons in Fiber Lasers,” Optics and Laser Technology, vol. 152, 2022.
[CrossRef] [Google Scholar] [Publisher Link] - Eugene Aban Chenui, and Alain Moïse Dikandé, “Soliton-Mode Proliferation Induced by Cross-Phase Modulation of Harmonic Waves by a Dark-Soliton Crystal in Optical Media,” Microwave and Optical Technology Letters, vol. 63, no. 10, pp. 2681-2688, 2021.
[CrossRef] [Google Scholar] [Publisher Link] - N. Nasreen et al., “Propagation of Optical Pulses in Fiber Optics Modeled by Coupled Space-Time Fractional Dynamical System,” Alexandria Engineering Journal, vol. 73, pp. 173-187, 2023.
[CrossRef] [Google Scholar] [Publisher Link] - Faissal Mansouri et al., “Chirped Localized Pulses in a Highly Nonlinear Optical Fiber with Quintic Non-Kerr Nonlinearities,” Results in Physics, vol. 43, 2022.
[CrossRef] [Google Scholar] [Publisher Link] - Xinyu Liu et al., “Bi-Directional Gated Recurrent Unit Neural Network-Based Nonlinear Equalizer for Coherent Optical Communications,” Optics Express, vol. 29, no. 4, pp. 5923-5938, 2021.
[CrossRef] [Google Scholar] [Publisher Link] - Weijie Sheng et al., “Complex-Valued Recurrent Neural Network Equalizer with Low Complexity for a 120-Gbps 50-km Optical PAM-4 IM/DD System,” Optics Express, vol. 32, no. 16, pp. 27624-27634, 2024.
[CrossRef] [Google Scholar] [Publisher Link] - Riyaz Saiyyed et al., “Comprehensive Analysis of Nonlinear Effects in Fiber Optic Communication Systems: Exploring SPM, XPM, SS, and FWM,” Journal of Optics, 2025.
[CrossRef] [Google Scholar] [Publisher Link] - Li Wang et al., “PMD Estimation and its Enabled Feedforward Adaptive Equalization based on Superimposed FrFT Training Sequences,” Optics Letters, vol. 46, no. 7, pp. 1526-1529, 2021.
[CrossRef] [Google Scholar] [Publisher Link] - Alper Demir, “Nonlinear Phase Noise in Optical-Fiber Communication Systems,” Journal of Lightwave Technology, vol. 25, no. 8, pp. 2002-2032, 2007.
[Google Scholar] [Publisher Link] - Luís C.B. Silva et al., “Long-Haul Propagation Analysis of Dark Pulses Employing an Optical Recirculating Fiber Loop Technique,” Optics Communications, vol. 495, 2021.
[CrossRef] [Google Scholar] [Publisher Link] - Gerd Keiser, Fiber Optic Communication Networks, Fiber Optic Communications, pp. 507-575, 2021.
[CrossRef] [Google Scholar] [Publisher Link] - Neveen G. A. Farag et al., “Extended Split-Step Fourier Transform Approach for Accurate Characterization of Soliton Propagation in a Lossy Optical Fiber,” Journal of Function Spaces, vol. 2022, no. 1, pp. 1-17, 2022.
[CrossRef] [Google Scholar] [Publisher Link] - Emad H.M. Zahran et al., “Dark-Soliton Behaviors Arising from a Coupled Nonlinear Schrödinger System,” Results in Physics, vol. 36, pp. 1-16, 2022.
[CrossRef] [Google Scholar] [Publisher Link] - Rui Jiang et al., “Data-Driven Method for Nonlinear Optical Fiber Channel Modeling based on Deep Neural Network,” IEEE Photonics Journal, vol. 14, no. 4, pp. 1-8, 2022.
[CrossRef] [Google Scholar] [Publisher Link] - Xiaotian Jiang et al., “Physics-Informed Neural Network for Nonlinear Dynamics in Fiber Optics,” Laser & Photonics Reviews, vol. 16, no. 9, 2022.
[CrossRef] [Google Scholar] [Publisher Link] - Wenting Wang et al., “Free-Space Terabit/s Coherent Optical Links via Platicon Frequency Microcombs,” eLight, vol. 5, pp. 1-16, 2025.
[CrossRef] [Google Scholar] [Publisher Link]