A passive optical network having an optical-signal monitor configured to monitor carrier-wavelength drifts during optical bursts transmitted between the optical line terminal and optical network units thereof. In an example embodiment, the optical-signal monitor uses heterodyne beating between two differently delayed portions of an optical burst to generate an estimate of the carrier-wavelength drift during that optical burst. The passive optical network may also include an electronic controller configured to use the estimates generated by the optical-signal monitor to make configuration changes at the optical network units and/or implement other control measures directed at reducing to an acceptable level the amounts of carrier-wavelength drift during the optical bursts and/or mitigating some adverse effects thereof.