Differentiable ABCD matrix solver for Gaussian beamlet decomposition

Area of Science:

• Optics and Photonics
• Computational Physics
• Optical Engineering

Background:

• Gaussian beamlet decomposition models coherent light propagation in complex optical systems.
• Accurate ABCD matrix evaluation is crucial but challenging using traditional finite-difference ray tracing, which suffers from numerical errors and sensitivity to step size.

Purpose of the Study:

• To present a novel differentiable ABCD matrix solver for direct and accurate computation.
• To overcome the limitations of conventional finite-difference ray tracing methods.

Main Methods:

• Formulating ray propagation as a differentiable computational graph.
• Utilizing automatic differentiation to compute the ABCD matrix directly.
• Validating the method in high-NA microscopic imaging and beam-shaping systems.

Main Results:

• The differentiable solver achieves high accuracy and numerical stability compared to traditional methods.
• Demonstrated effectiveness in both imaging and non-imaging optical systems.
• The framework supports gradient-based backpropagation for inverse design.

Conclusions:

• The differentiable ABCD matrix solver provides a more accurate and stable approach for modeling light propagation.
• This method facilitates seamless integration with optimization frameworks for inverse wave-optics design.
• Enables advanced applications in optical system design and analysis.