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

Area of Science:

• Optics
• Light Scattering
• Mathematical Physics

Background:

• Geometrical optics predicted infinite intensity in rainbow angles.
• Airy theory (1830s) addressed this but has limitations in predicting supernumerary bows.
• Discrepancies exist between Airy theory and rigorous Debye theory for supernumerary bows.

Purpose of the Study:

• To identify the cause of discrepancies in supernumerary bow predictions.
• To improve the accuracy of supernumerary bow intensity prediction.
• To present a revised method applicable to various particle shapes.

Main Methods:

• Utilized a combination of the vectorial complex ray model and physical optics (PO).
• The vectorial complex ray model calculates amplitudes and phases of rays.
• Physical optics (PO) refines predictions for supernumerary bows.

Main Results:

• The study identified approximations in Airy theory as the cause of discrepancies.
• The combined model precisely predicts the scattering pattern, including supernumerary bows.
• Accurate predictions were achieved for both perpendicular and parallel polarization.

Conclusions:

• The revised method overcomes Airy theory's limitations in predicting supernumerary bows.
• This approach offers high accuracy for light scattering from spherical and non-spherical particles.
• The method provides a more precise understanding of rainbow phenomena.