In this paper, in order to achieve low differential mode group delay (DMGD) over the C+L band, we propose the hole-assisted graded-index few mode fiber (FMF) design supporting four nondegenerated linear polarized (LP) modes for a mode division multiplexing system. In order to determine the fiber core parameters, an optimization has been made between the enlargement of the effective area $({{A_{eff}}})$ and the reduction of macrobending loss (MBL). The ${A_{eff}}$ about 107 $\mu {m^2}$ for LP01 mode at the wavelength of 1550 nm and the MBL lower than 0.005 dB/100 turns for LP02 mode at the curvature radius of 30 mm and at the wavelength of 1550 nm are achieved simultaneously. The numerical simulation results prove that the hole-assisted structure can greatly reduce the absolute value of DMGD of the FMF. Particularly, the maximum DMGD less than |35| ps/km within the spectrum range from 1530 to 1630 nm is achieved. A tolerance analysis against manufacturing errors has been discussed, and we further propose a self-managed low DMGD transmission line solution with the controllable air-hole size.
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