The next generation of optical access communication networks that support 100 Gbps and beyond, require advances in modulation schemes, spectrum utilization, new transmission bands, and efficient devices, particularly laser diodes. In this paper, we investigated the viability of new-class of InAs/InP Quantum-dash laser diode (Qdash-LD) exhibiting multiple longitudinal light modes in the L-band to carry high-speed data rate for access network applications. We exploited external and self injection-locking techniques on Qdash-LD to generate large number of stable and tunable locked modes, and compared them. To stem the capability of each locked mode as a potential subcarrier, data transmission is carried out over two mediums; single mode fiber (SMF) and free space optics (FSO) to emulate real deployment scenarios of optical networks. The results showed that with external-injection locking (EIL), an error-free transmission of 100 Gbps dual polarization quadrature phase shift keying (DP-QPSK) signal is demonstrated over 10 km SMF and 4 m indoor FSO channels, with capability of reaching up to 128 Gbps, demonstrated under back-to-back (BTB) configuration. On the other hand, using self-injection locking (SIL) scheme, a successful data transmission of 64 Gbps and 128 Gbps DP-QPSK signal over 20 km SMF and 10 m indoor FSO links, respectively, is achieved.