On the Optimum Energy-per-bit Launch Power in Coherent Hollow-core Fibre Transmission Systems

Technical Summary: On the Optimum Energy-per-bit Launch Power in Coherent Hollow-core Fibre Transmission Systems

Problem Statement
Hollow-core fibres (HCFs) have emerged as a promising alternative to conventional silica single-mode fibres (SMFs) due to their potential for reduced latency, significantly lower nonlinearity, and attenuation below 0.1 dB/km. These characteristics enable longer span lengths (exceeding 200 km) and higher launch powers (potentially exceeding 40 dBm), which could reduce the number of required amplifiers and improve energy efficiency. However, while ultra-wideband (UWB) transmission is a key goal for scaling throughput, the power conversion efficiency (PCE) of amplifiers for non-C-band wavelengths (O, E, S-bands) is currently lower than that of C-band Erbium-doped fibre amplifiers (EDFAs).

A critical assumption in conventional SMF systems is that for few-span links, the power consumption of optical amplifiers is negligible compared to that of coherent transceivers. This paper investigates whether this assumption holds for HCF systems. Given that HCFs support much higher launch powers than SMFs, the authors posit that amplifier power consumption may become comparable to, or even exceed, transceiver power consumption at high launch powers. This discrepancy suggests that the launch power required to achieve maximum throughput ($T_{max}^{tot}$) may differ significantly from the launch power required to achieve minimum energy-per-bit ($E_b^{min}$), a distinction that is less pronounced in SMF systems.

Methodology
The authors developed a closed-form Gaussian Noise (GN) model to estimate the per-channel Signal-to-Noise Ratio (SNR) and total energy-per-bit ($E_b$) for HCF transmission systems. The model was extended to support UWB systems by incorporating wavelength-dependent HCF attenuation and dispersion profiles, based on simulated first-window Double-Clad Anti-Resonant Nodeless Fibre (DNANF) designs.

Key modeling parameters and assumptions include:

• Fibre Profile: Simulated profiles with ~0.075 dB/km attenuation at 1550 nm and ~0.12 dB/km at 1310 nm, with low dispersion across the OESCL bands.
• System Configuration: Simulations covered 1000 km links (composed of 5 × 200 km spans) across C-band and UWB (O, E, S, C, L) configurations.
• Noise and Impairments: The SNR calculation included accumulated Amplified Spontaneous Emission (ASE), nonlinear interference (NLI), inter-modal interference (IMI), and transceiver noise. Inter-channel stimulated Raman scattering (ISRS) was neglected.
• Power Consumption: Total link power was calculated as the sum of amplifier power ($P_{amp}^e$) and transceiver power ($P_{trx}^e$). Amplifier power was derived using the number of spans, input/output powers, and wavelength-specific PCE values (ranging from 0.7% for O-band to 6.0% for C-band). Transceiver power was modeled as a constant 24 W per module.
• Throughput: Calculated using Shannon capacity based on the SNR and a fixed baud rate of 140 GBd.

Key Contributions and Results
The study demonstrates that unlike SMF systems, where transceiver power dominates and the optimum launch power for energy efficiency aligns closely with maximum throughput, HCF systems exhibit two distinct operating points due to the interplay between high launch powers and amplifier efficiency.

1. Divergence of Operating Points: In HCF, as launch power increases toward the maximum throughput point, the amplifier power consumption grows rapidly and becomes comparable to transceiver power. Because HCF throughput is limited by transceiver SNR rather than Kerr nonlinearity (which limits SMF), increasing launch power beyond a certain point yields negligible throughput gains while significantly increasing power consumption. Consequently, the launch power for minimum energy-per-bit ($E_b^{min}$) is significantly lower than that for maximum throughput ($T_{max}^{tot}$).
2. Quantitative Gains:
   • C-band (1000 km): Operating at $E_b^{min}$ (approx. 22 dBm total launch power) instead of $T_{max}^{tot}$ (approx. 37 dBm total launch power) results in a 41.5% reduction in total power consumption with only a 2.2% penalty in throughput.
   • U-band Systems (OESCL): The trade-off is even more favorable in multi-band systems. Operating at $E_b^{min}$ yields a 71.9% reduction in total power consumption for an 8.5% throughput penalty.
3. Scaling Behavior: The analysis shows that for HCF, $E_b^{min}$ consistently occurs around 7 dBm per channel (22 dBm total for C-band), whereas $T_{max}^{tot}$ occurs around 22 dBm per channel (37 dBm total).

Significance
The paper concludes that the assumption of negligible amplifier power consumption in few-span systems is invalid for HCFs when operating at high launch powers. By identifying and operating at the specific launch power that minimizes energy-per-bit, HCF transmission systems can achieve substantial energy savings (up to ~72%) with minimal impact on data throughput. This finding suggests that for energy-efficient HCF deployment, particularly in UWB scenarios, system design should prioritize the $E_b^{min}$ operating point over the $T_{max}^{tot}$ point. This approach not only reduces total power consumption but also alleviates the need for high-power amplifiers in scenarios where throughput is limited by transceiver SNR rather than fibre nonlinearity.