Rigorous analytical modeling of high-aperture focusing through a spherical interface

Area of Science:

• Optics and Photonics
• Electromagnetism

Background:

• High-aperture focusing through spherical interfaces is crucial for optical data storage, photolithography, and microscopy.
• Existing models for evaluating focal fields have limitations and create ambiguities in scientific literature.

Purpose of the Study:

• To develop and validate accurate models for analyzing focal fields in high-aperture focusing systems.
• To resolve existing discrepancies in the literature regarding the behavior of these optical systems.
• To provide a framework for analyzing more general focusing systems.

Main Methods:

• Development of an approximate model using geometrical optics and Fourier optics.
• Formulation of a rigorous model based on multipole theory, employing spherical harmonic expansions of electromagnetic fields.

Main Results:

• The approximate model clarifies ambiguities found in previous research on focal field evaluation.
• The rigorous model offers broader applicability to diverse and complex focusing systems.
• The study establishes a foundation for precise analysis of light focusing through spherical interfaces.

Conclusions:

• The proposed models provide enhanced accuracy and clarity for understanding high-aperture focusing phenomena.
• These advancements are expected to benefit the design and optimization of optical instruments in microscopy and data storage.
• The multipole-based rigorous model represents a significant step towards analyzing more general optical focusing scenarios.