Light scattering by a large bubble with vectorial complex ray model and physical optics

In light scattering by a large spherical bubble, the scattered intensity near the critical angle predicted by geometrical optics shows significant discrepancies with Mie theory due to total reflection. Several authors have applied physical optics (PO) using an approximate phase function to improve the results, but the accuracy remains limited. In this paper, we propose a hybrid method VCRM+PO, which combines the vectorial complex ray model (VCRM) with PO. Since VCRM rigorously calculates the amplitude and phase on the virtual line in the framework of the ray model, this hybrid method significantly improves accuracy when compared to the rigorous Mie theory, and it works naturally for two polarization states. Geometrical optics (GO) accurately predicts the scattering pattern of a bubble in most directions, except near the critical angle. The VCRM+PO method corrects the scattering intensity in this critical region while reducing to GO elsewhere, ensuring, therefore, a smooth transition between the two approaches. We have also shown that Marston's approach can be recovered from VCRM+PO after three approximation steps. Furthermore, thanks to the flexibility of VCRM and PO, the proposed method can be extended to non-spherical bubbles.