Airy theory revisited with the method combining vectorial complex ray model and physical optics

Abstract

Airy published his theory in the 1830s to remedy the problem of infinite intensity in the rainbow angles of a spherical droplet predicted by geometrical optics. This theory has been studied by mathematicians and physicists since then from different points of view. In what concerns the scattering diagram around the rainbow angles, Airy theory has been improved by researchers in order to predict correctly the intensity of the supernumerary bows. However, it is known that the positions and the intensities of the supernumerary bows predicted by Airy theory differ from those of rigorous Debye theory with increasing order p and the scattering angles from the rainbow angle. In the present Letter, we will show that this discrepancy is caused by the approximations in Airy theory and can be revised by combining the vectorial complex ray model and physical optics (PO). The former permits us to calculate rigorously the amplitudes and phases of all rays and predicts precisely the scattering pattern except for the main bows. The combination with PO predicts very precisely all the supernumerary bows for both perpendicular and parallel polarization. This method can be applied directly to the light scattering of non-spherical particles with smooth surfaces.