  In this paper, we propose a geometric shaping (GS) strategy to design 8, 16,
32 and 64-ary modulation formats for the optical fibre channel impaired by both
additive white Gaussian (AWGN) and phase noise. The constellations were
optimised to maximise generalised mutual information (GMI) using a mismatched
channel model. The presented formats demonstrate an enhanced signal-to-noise
ratio (SNR) tolerance in high phase noise regimes when compared with their
quadrature amplitude modulation (QAM) or AWGN-optimised counterparts. By
putting the optimisation results in the context of the 400ZR implementation
agreement, we show that GS alone can either relax the laser linewidth (LW) or
carrier phase estimation (CPE) requirements of 400 Gbit/s transmission links
and beyond. Following the GMI validation, the performance of the presented
formats was examined in terms of post forward error correction (FEC)
bit-error-rate (BER) for a soft decision (SD) extended Hamming code (128, 120),
implemented as per the 400ZR implementation agreement. We demonstrate gains of
up to 1.2 dB when compared to the 64-ary AWGN shaped formats.
