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, we study the lensing of gravitational waves in the context of LISA sources and wave-optics regime. While different papers before ours studied microlensing effects enhanced by simultaneous strong lensing, we focus on frequency (time) dependent phase effects produced by one lens that will be visible with only one lensed image. We will show how, in the interference regime (i.e. when interference patterns are present in the lensed image), we are 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 SNR of the signal and/or the magnitude of the lensing effect. To achieve these goals we study the phase of the amplification factor of the different lens models and its effect on the unlensed waveform, and we exploit the signal-to-noise calculation for a qualitative analysis.