We demonstrated 1-Tb/s-class transmissions of field-deployed large-core low-loss fiber links, which is compliant with ITU-T G.654.E, using our newly developed real-time transponder consisting of a state-of-the-art 16-nm complementary metal-oxide-semiconductor (CMOS) based digital signal processing application-specific integrated circuit (DSP-ASIC) and an indium phosphide (InP) based high-bandwidth coherent driver modulator (HB-CDM). In this field experiment, we have achieved record transmission distances of 1122km for net data-rate 1-Tb/s transmission with dual polarization-division multiplexed (PDM) 32 quadrature amplitude modulation (QAM) signals, and of 336.6 km for net data-rate 1.2-Tb/s transmission with dual PDM-64QAM signals. This is the first demonstration of applying hybrid erbium-doped fiber amplifier (EDFA) and backward-distributed Raman amplifier were applied to terrestrial G.654.E fiber links. We also confirmed the stability of signal performance over field fiber transmission in wavelength division multiplexed (WDM) condition. The Q-factor fluctuations respectively were only less than or equal to 0.052dB and 0.07dB for PDM-32QAM and PDM-64QAM signals within continuous measurements for 60 minutes.