Ray Theory of Waves

Accurate and efficient prediction of three-dimensional (3D) fields in wave interactions with large, complex-shaped objects is essential for applications in electromagnetic computation, computer graphics, optical metrology, and freeform optics. However, existing methods face significant challenges: numerical techniques are computationally intensive and impractical for large objects, while ray tracing neglects wave properties and remains inefficient, relying solely on ray bundles. In this Letter, we present the Ray Theory of Waves (RTW), which introduces wavefront curvature (WFC) as an intrinsic property of a ray to describe wave divergence and convergence. Using differential geometry, we derive the wavefront equation, rigorously relating WFC of incident, reflected, and refracted waves, enabling accurate calculation of field amplitude and phase along a ray. To address diffraction effects at singularities and compute the total field, we propose an anti-conventional strategy. The flexibility, precision and performance of RTW are demonstrated through the calculation of 3D scattering pattern of an ellipsoidal drop. Importantly, the method clarifies several longstanding queries about Airy theory since the 19th century. RTW constitutes a theoretical breakthrough, opening new avenues for practical applications.