Wave-optical effects in the microlensing of continuous gravitational waves by star clusters

Rapidly rotating neutron stars are promising sources for existing and upcoming gravitational-wave interferometers. While relatively dim, these systems are expected to emit continuously, allowing for signal to be accumulated through persistent monitoring over year-long timescales. If, at some point during the observational window, the source comes to lie behind a dense collection of stars, transient gravitational lensing may occur. Such events, though rare, would modulate the waveform, induce phase drifts, and ultimately affect parameter inferences concerning the nuclear equation of state and/or magnetic field structure of the neutron star. Importantly, the radiation wavelength will typically exceed the Schwarzschild radius of the individual perturbers in this scenario, implying that (micro-)lensing occurs in the diffractive regime where geometric optics does not apply. In this paper, we make use of numerical tools that borrow from Picard-Lefschetz theory to efficiently evaluate the relevant Fresnel-Kirchhoff integrals for $n \gtrsim 10^{2}$ microlenses. Modulated strain profiles are constructed both in general and for particular neutron star trajectories relative to some simulated macrolenses.