An interference-based method for the detection of strongly lensed gravitational waves

The strongly lensed gravitational wave (SLGW) is a promising transient phenomenon. However, the long-wave nature of gravitational waves poses a considerable challenge in the identification of its host galaxy. Here, to tackle this challenge, we propose a method triggered by the wave optics effect of microlensing. The microlensing interference introduces frequency-dependent fluctuations in the waveform. Our method consists of three steps. First, we reconstruct the waveforms by using template-independent and template-dependent methods. The mismatch of two reconstructions serves as an indicator of SLGWs. This step can identify approximately 10% SLGWs. Second, we pair the multiple images of the SLGWs by using sky localization overlapping. Because we have preidentified at least one image through microlensing, the false-alarm probability for pairing SLGWs is significantly reduced. Third, we search the host galaxy by requiring the consistency of time delays between galaxy–galaxy lensing and SLGW. By combing the stage-IV galaxy survey and the third-generation gravitational wave detectors, we expect to find, on average, one quadruple-image system per 3 years. This method can substantially facilitate the pursuit of time-delay cosmography, discovery of compact objects and multimessenger astronomy. The microlensing of strongly lensed gravitational waves by compact objects leads to interference patterns in the waveform, the detection of which facilitates the identification and localization of the gravitational wave source.