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Combining optical injection and polarization-rotated optical feedback in a semiconductor laser can induce self-referenced periodic output that is widely tunable by simply varying the dc-bias points of the master and slave lasers. We observed feedback-induced reduction of the pulsation peak linewidth by more than two orders of magnitude relative to the injection-only case. The nonlinear dynamics of the optically injected semiconductor laser can be used to minimize sensitivity to fluctuations in the operating points. Performance is negatively affected by interference between the external injection signal and residual feedback in the same polarization.