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Generalized propagation of light through optical systems. II. Numerical implications
Summary
This study introduces a MATLAB toolbox for simulating light wave propagation through lenses. The algorithm enables accurate, high numerical aperture field tracing for macroscopic optics, enhancing optical design capabilities.
Area of Science:
- Optics and Photonics
- Computational Electromagnetics
- Mathematical Modeling
Background:
- Accurate simulation of light propagation is crucial for designing macroscopic optical systems.
- Previous methods had limitations in handling complex lens geometries and arbitrary input beams.
- The Helmholtz equation provides a framework for wave propagation but requires approximations for curved surfaces.
Purpose of the Study:
- To present a novel algorithm and MATLAB toolbox for computing coherent visible light wave propagation through macroscopic lenses.
- To extend previous work by enabling computations for arbitrarily directed input beams and high numerical aperture (NA) field tracing.
- To provide a Maxwell-exact method for macroscopic structures with large curvature radii, including reflection and transmission.
Main Methods:
- Implementation of an algorithm in a MATLAB toolbox.
- Utilizing fast Fourier routines for efficient field tracing.
- Analytical treatment of curvature-dependent terms in the Helmholtz equation (first perturbation order) and inclusion in propagation distance for computational efficiency.
Main Results:
- The developed toolbox enables high numerical aperture field tracing for macroscopic lenses.
- The method is Maxwell exact for macroscopic structures and large curvature radii, accounting for reflection and transmission.
- Demonstrated strengths of the approach through various examples, highlighting differences from prior methods.
Conclusions:
- The presented algorithm and toolbox offer a powerful tool for simulating wave propagation in complex macroscopic optical systems.
- The method provides accurate results for high NA field tracing, essential for advanced optical design.
- Identified drawbacks and potential simplifications suggest avenues for future research and algorithm refinement.
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