Polarisation-insensitive operations of a parametric tunable dispersion compensator based on a polarisation diversity scheme using a polarisation-maintaining highly nonlinear fibre are demonstrated. The polarisation-dependent power penalty is less than 0.5 dB for 43 Gbit/s non-return-to-zero on-off-keying signals with polarisation scrambling.Introduction: In contrast to digital coherent transmission technologies, an optical tunable dispersion compensator [1] has features of bit rates and modulation format independences, which are particularly important for future dynamic optical networking. We have proposed a parametric tunable dispersion compensator (P-TDC) that consists of a dispersive medium having frequency-dependent group velocity dispersion (GVD) following a parametric tunable wavelength conversion based on four-wave mixing (FWM) process in a highly-nonlinear fibre (HNLF) [2]. The amount of GVD can be tuned through changing the wavelength of the signal passing the dispersive medium. The proposed compensation scheme has intrinsic advantages in the operation bandwidth and tuning speed. We have so far achieved wideband operations of more than 1 THz with a large dispersion tuning range [3] and record-fast microsecond responses of the dispersion tuning [4]. In the experimental demonstrations, we set the polarisation controller (PC) at the input of the HNLF to keep the efficiency of the wavelength conversion based on FWM. For practical uses of the P-TDC however, polarisation-sensitivity is a critical issue as the state of polarisation (SOP) changes rapidly in field fibres [5], and also the SOP of each carrier is different in wavelength-division multiplexing transmissions.In this Letter, we propose a polarisation-insensitive P-TDC employing a polarisation diversity scheme [6,7] with our developed polarisation-maintaining HNLF (PM-HNLF) having a low-dispersion slope [8], and report polarisation-insensitive optical dispersion compensation in 43 Gbit/s non-return-to-zero on-off-keying (NRZ-OOK) transmissions over 59.1 km singlemode fibre (SMF). We achieved a polarisation-dependent power penalty of less than 0.5 dB for polarisationscrambled transmission signals with a scrambling rate of 6.2 rad/s.