Probing Binary Lens Caustics with Gravitational Waves: A Uniform Approximation Approach

We present a new framework for modeling gravitational wave diffraction near fold caustics using the Uniform Approximation (UA), focusing on binary mass lenses - axially asymmetric systems with complex caustic structures. Full-wave methods based on the Kirchhoff integral become impractical in this regime due to highly oscillatory integrands. The UA provides a robust and accurate description of the wave field near folds, resolving the breakdown of Geometrical Optics at caustics and improving upon Transitional Asymptotics - based on Airy function approximations - which lack global validity. Central to our approach is the concept of the caustic width, $d_c$, a characteristic length scale defining the region where diffraction significantly alters wave propagation. We find that $d_c$ scales universally with the gravitational wavelength as ~ $ \lambda^{2/3}$ and inversely with the redshifted lens mass as ~ $ M_{Lz}^{-2/3}$. The wave amplification near the fold grows as ~ $ d_c^{-1/4}$, substantially enhancing the signal and potentially playing a key role in the detection of gravitational waves lensed near caustics. Notably, for lens masses below the galactic scale, the caustic width for gravitational waves is not negligible compared to the Einstein radius - as it is in electromagnetic lensing - making the UA essential for accurately capturing wave effects.