Comparison of different theories for focusing through a plane interface: comment

Area of Science:

• Optics and Photonics
• Electromagnetism and Wave Propagation

Background:

• Previous research by Wiersma et al. suggested minimal differences between Debye-Wolf diffraction theory and m-theory for axial focal fields.
• A potential inaccuracy in the apodization factor used in m-theory calculations was identified.

Purpose of the Study:

• To re-evaluate the axial focal fields predicted by m-theory by correcting the apodization factor.
• To compare the corrected m-theory predictions with the established Debye-Wolf diffraction theory.

Main Methods:

• Identification and correction of an inaccurate apodization factor within the m-theory integral.
• Recalculation of axial intensity distributions using the corrected m-theory.
• Comparative analysis of the corrected m-theory results against Debye-Wolf diffraction theory predictions.

Main Results:

• The corrected apodization factor significantly improves the agreement between m-theory and Debye-Wolf diffraction theory.
• Axial intensity distributions predicted by the revised m-theory show enhanced concordance with the Debye-Wolf theory.
• The previously reported "little difference" is refined, indicating better theoretical alignment.

Conclusions:

• The correction of the apodization factor is crucial for accurate m-theory predictions of light focusing.
• This work reconciles discrepancies between m-theory and Debye-Wolf diffraction theory, enhancing our understanding of focal fields.
• The findings contribute to the precise modeling of light propagation and focusing phenomena in optical systems.