Power efficiency of long-haul optical fiber transmission has emerged as a critical challenge to cost-effectively increasing submarine cable capacity. Building on previous experimental work and informed by physical system modeling and optimization, we report on extensive amplified transmission experiments characterizing the metric of fiber capacity per unit pump power over a range of amplifier powers and link distances relevant to power-limited spatial-division-multiplexed submarine systems. We compare experimental results with modeling incorporating optical amplifier physics as well as generalized droop, demonstrating excellent agreement over the range of powers and distances tested. We predict the performance gains achievable by further optimizing the system design and implementation within tolerances ideally achieved in deployed submarine systems, and estimate fiber pair counts and total cable capacities achievable for the link distances investigated. Our results suggest the utility of amplifier pump powers as low as 20 mW and output powers as low as 6.5 dBm in reaching Pb/s cable capacities.

Modeling and Experimental Measurement of Power Efficiency for Power-Limited SDM Submarine Transmission Systems

We review the fundamentals of the recently proposed Generalized Droop model and highlight its use in power efficiency optimization of long-haul low-SNR space-division multiplexed submarine links.

The Generalized Droop Model for Submarine Fiber-Optic Systems

The capacity in space division multiplexing (SDM) systems with coupled channels is fundamentally limited by mode-dependent loss (MDL) and mode-dependent gain (MDG) generated in components and amplifiers. In these systems, MDL/MDG must be accurately estimated for performance analysis and troubleshooting. Most recent demonstrations of SDM with coupled channels perform MDL/MDG estimation by digital signal processing (DSP) techniques based on the coefficients of multiple-input multiple-output (MIMO) adaptive equalizers. 
Although these methods provide a valid indication of the order of magnitude of the accumulated MDL/MDG over the link, MIMO equalizers are usually updated according to the minimum mean square error (MMSE) criterion, which is known to depend on the channel signal-to-noise ratio (SNR). Therefore, MDL/MDG estimation techniques based on the adaptive filter coefficients are also impaired by noise. In this paper, we model analytically the influence of the SNR on DSP-based MDL/MDG estimation, and show that the technique is prone to errors. Based on the transfer function of MIMO MMSE equalizers, and assuming a known SNR, we calculate a correction factor that improves the estimation process in moderate levels of MDL/MDG and SNR. The correction factor is validated by simulation of a 6-mode long-haul transmission link, and experimentally using a 3-mode transmission link. The results confirm the limitations of the standard estimation method in scenarios of high additive noise and MDL/MDG, and indicate the correction factor as a possible solution in practical SDM scenarios.

Mode-dependent Loss and Gain Estimation in SDM Transmission Based on MMSE Equalizers

We discuss SDM as a method for significant capacity increase in undersea transmission while managing optical power efficiently. We show the existence of power efficiency optimum and review experimental demonstrations.

SDM for power-efficient undersea transmission

In power-limited trans-oceanic submarine systems, the electrical-to-optical (E/O) power conversion efficiency determines the amount of optical signal power generated by repeaters, which governs the cable capacity. In contrast to conventional submarine systems, recent single mode fiber spatial division multiplexing (SDM) systems operate at a lower channel power and support a larger number of optical fibers. Moreover, pump sharing technology is used in SDM systems to enhance cable capacity and system reliability, where a group of pump lasers are combined to feed a group of fiber pairs. The repeater E/O power conversion efficiency is directly related with cable capacity, as well as capacity per power and cost per capacity analysis. Therefore, it is important to understand the characteristics of repeater E/O efficiency. We developed a model to analyze the repeater E/O efficiency in submarine SDM systems. Experimental measurement data of pump lasers and numerical simulation results of Erbium doped fiber amplifiers (EDFAs) were used as input information to the model to analyze repeater E/O efficiency in various system designs. Based on the E/O efficiency model results, we investigated cable capacity using the Gaussian noise (GN) model. Moreover, cable capacity per power was calculated and compared based on three different power metrics: (i) electrical supply power, (ii) pump optical power and (iii) EDFA output power. With the aid of the repeater E/O efficiency model, one can analyze the efficiency of submarine systems using the direct metric of cable capacity per electrical supply power.

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Repeater Power Conversion Efficiency in Submarine Optical Communication Systems

Motivated by the recent interest in single-mode semiconductor optical amplifiers and multimode erbium-doped fiber amplifiers, we present a unified, comprehensive treatment of the effect of polarization- and mode-dependent gain (PDG and MDG) on the capacity of ultra-long-haul transmission systems. We study the problem using simulations of a multisection model, including the effects of PDG or MDG and polarization mode dispersion (PMD) or modal dispersion. We also analytically derive exact expressions for the capacity distribution of PDG-impaired single-mode systems. In agreement with previous work, we find that PDG and MDG cause fluctuations in capacity, which reduces average capacity and may cause outage. We show that the multimode systems studied, with at least $D = 14$ spatial/polarization modes, have sufficient modal diversity and frequency diversity to strongly suppress capacity fluctuations and reduce outage probability so that the outage capacity approaches the average capacity. We show that single-mode systems, by contrast, inherently provide low modal and frequency diversity, making them more prone to outage. To alleviate this problem, frequency diversity can be increased by artificially inserting PMD. Finally, we quantify the PDG/MDG requirements of optical amplifiers to ensure that the average capacity is close (within a 1-2 dB effective SNR loss) to the theoretical optimum. We show that these PDG/MDG requirements are stringent, especially considering the minimum-mean-square error linear equalizers implemented in typical multiple-input multiple-output receivers.

Impact of Polarization- and Mode-Dependent Gain on the Capacity of Ultra-Long-Haul Systems

We examine fiber capacity per unit amplifier pump power relevant to power-constrained spatial-division-multiplexing submarine systems via extensive amplified transmission experiments and modeling. Our results suggest the utility of amplifier pump powers as low as 20 mW and output powers as low as 6.5 dBm.

Experimental Characterization of Power Efficiency for Power-Limited SDM Submarine Transmission Systems

We show by analysis and simulation of a multisection model that polarization- or mode-dependent gain from single-mode semiconductor optical amplifiers or multimode erbium-doped fiber amplifiers causes the channel capacity with minimum-mean-square error detection to become substantially lower than that of optimal maximum likelihood detection. However, the capacity loss can be mitigated with techniques such as successive interference cancellation (SIC) that retain reasonable complexity. We reaffirm that frequency diversity enables the outage capacity to approach the average capacity and evaluate the performance of frequency-domain SIC equalizers for single-carrier transmission on frequency-selective optical fiber channels operating at 64 Gbaud up to 15,000 km.

Impact and Mitigation of Polarization- or Mode-Dependent Gain in Ultra-Long-Haul Systems

Scaling up cable capacity in a power- and cost-efficient manner is a goal of spatial-division multiplexing (SDM) in long-haul optical communication systems. Integration is a key to scaling SDM beyond the parallel single-mode fiber paradigm. Multicore or multimode fiber systems promise higher integration, but native multicore or multimode amplifiers pose challenges in efficient coupling of pump light into the amplifier, and in control of mode-dependent gain (MDG). We propose an integrated multimode amplifier design for signals in six spatial modes (12 spatial and polarization modes) that relies on excitation of only four pump spatial modes at 980 nm. Simulations of an exemplary amplifier predict a relatively flat gain above 10 dB, noise figure below 5 dB, and MDG standard deviation below 0.1 dB over the C-band (1530–1565 nm), with a power-conversion efficiency close to 30%. Key design features include a graded-index multimode fiber amplifier with optimized ring erbium doping profile, length and pump mode powers; and a cascade of wavelength- and mode-selective couplers that efficiently couples four pump diodes to four pump modes, while passing signal modes with minimal loss. Our design approach, which uses fewer pump diodes per signal mode than parallel single-mode systems, may provide an option for efficient, economical scaling of SDM long-haul systems. 

Hrishikesh Srinivas

Papers

Impact of Polarization- and Mode-Dependent Gain on the Capacity of Ultra-Long-Haul Systems

Modeling and Experimental Measurement of Power Efficiency for Power-Limited SDM Submarine Transmission Systems

Experimental Characterization of Power Efficiency for Power-Limited SDM Submarine Transmission Systems

Impact and Mitigation of Polarization- or Mode-Dependent Gain in Ultra-Long-Haul Systems

Efficient Integrated Multimode Amplifiers for Scalable Long-Haul SDM Transmission