Generalized propagation of light through optical systems. I. Mathematical basics

Area of Science:

• Optics and Electromagnetism
• Computational Physics

Background:

• Modeling electromagnetic field propagation is crucial for various optical and electronic applications.
• Existing methods may face challenges with complex geometries like tilted and curved surfaces.

Purpose of the Study:

• To develop and present a field tracing routine for accurate electromagnetic field propagation.
• To optimize coordinate customization and field sampling for tilted and curved surfaces.

Main Methods:

• Utilizes a ray tracing method for coordinate customization, addressing linear phase terms from tilted coordinates.
• Proposes methods to optimize field sampling, tackling astigmatic phase fronts and surface curvature.
• Employs two solution methods for propagating fields from curved surfaces through homogeneous space.

Main Results:

• The developed routine effectively handles field propagation through tilted and curved surfaces.
• The approach is fully vectorial and Maxwell exact, with approximations for Fresnel coefficients at curved surfaces.
• A numerical propagation example demonstrates the method's applicability.

Conclusions:

• The presented field tracing routine offers an efficient and accurate method for modeling electromagnetic field propagation.
• The optimization techniques enhance the robustness of the propagation calculations for complex surface geometries.