Characteristic features of gravitational wave lensing as probe of lens mass model

To recognize gravitational wave lensing events and being able to differentiate between similar lens models will be of crucial importance once one will be observing several lensing events of gravitational waves per year. In this work, the lensing of gravitational waves is studied in the context of LISA sources and wave-optics regime. While different papers before the studied microlensing effects enhanced by simultaneous strong lensing, the focus is on frequency (time) dependent phase effects produced by one lens that will be visible with only one lensed signal. It is shows how, in the interference regime (i.e., when interference patterns are present in the lensed image), one is able to i) distinguish a lensed waveform from an unlensed one, and ii) differentiate between different lens models. In pure wave-optics, on the other hand, the feasibility of the study depends on the signal-to-noise ratio of the signal and/or the amplitude of the lensing effect. To achieve these goals, the phase of the amplification factor of the different lens models and its effect on the unlensed waveform is studied, and the signal-to-noise calculation to provide some quantitative examples is exploited.