On Sparse Gain Flattening in Pump-Constrained Submarine Links

Abstract

Having in mind the capacity optimization of power-constrained submarine links, by following the work in (Cho <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2020) we first compare the achievable information rate (AIR) of gain-flattened and un-flattened short links (called here blocks) of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}\leq 12$</tex-math></inline-formula> spans with span loss 16.5 dB and with end-span single-stage co-pumped erbium-doped fiber amplifiers (EDFA) when the transmitted wavelength division multiplexed (WDM) channels all have the same transmitted power. All EDFAs have the same pump power and the same physical parameters. In the flattened case, each EDFA is followed by an ideal gain-flattening filter (GFF) that chops off the EDFA gain exceeding the span loss. No GFFs are used in the un-flattended case. We show that, for block length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}&gt;7$</tex-math></inline-formula> , at large-enough input power the AIR of the GFF block exceeds that of the no-GFF block, while for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}\leq 7$</tex-math></inline-formula> at large input power the AIR is about the same. We next build a long submarine link by concatenating many <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}$</tex-math></inline-formula> -span no-GFF blocks, and placing a GFF at the last EDFA of each block in order to flatten the block gain down to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}$</tex-math></inline-formula> -span loss, and calculate the AIR of the resulting sparse-GFF submarine link, accounting also for nonlinear interference. For a 287-span case-study link with span loss 9.5 dB, we show that the best power efficiency is achieved by blocks of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{b}=6$</tex-math></inline-formula> (i.e., one GFF every 6 spans) when the pump is around 11 mW. When the GFF excess loss is 0.3 dB the top-AIR gain over the standard all-GFF system is 9.5%, a value that decreases to 4% when the excess loss is zero. Considering that modern submarine-grade GFFs have almost zero excess loss, and that the most efficient pump power is likely too low to operate with, we conclude that sparse-GFF links offer little advantage in practice over the current design.