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Differential Form of Maxwell's Equations

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...

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Scattering And Absorption of Light in Planetary Regoliths

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Differentiable scattering matrix for optimization of photonic structures.

Ziwei Zhu, Changxi Zheng

|December 31, 2020

Summary

This study introduces a novel algorithm for calculating scattering matrix derivatives, crucial for optimizing photonic structures. The method bypasses difficult eigen-decomposition differentiation, enabling robust metasurface design and performance enhancement.

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Area of Science:

Photonics and Optical Engineering
Computational Electromagnetics
Materials Science

Background:

The scattering matrix is essential for characterizing optical properties like reflection and transmission in photonic structures.
Understanding how optical performance changes with design parameters (derivatives) is vital for photonic design.
Existing semi-analytical methods face numerical challenges when computing these derivatives due to eigen-decomposition.

Purpose of the Study:

To develop a new, accurate, and robust algorithm for computing scattering matrix derivatives.
To address the numerical difficulties associated with differentiating eigen-decomposition in semi-analytical methods.
To enable efficient optimization of photonic structures, particularly metasurfaces.

Main Methods:

A novel algorithm is presented to compute scattering matrix derivatives.
The method specifically targets semi-analytical techniques like rigorous coupled-wave analysis.
The algorithm sidesteps the direct differentiation of the eigen-decomposition problem, enhancing robustness.

Main Results:

The proposed algorithm accurately and robustly computes scattering matrix derivatives.
It overcomes significant numerical challenges inherent in differentiating eigen-decomposition.
The algorithm's efficacy is demonstrated through metasurface optimization.

Conclusions:

The new algorithm provides a robust solution for calculating scattering matrix derivatives.
This advancement facilitates the optimization of photonic devices and metasurfaces.
The method enhances the design process for structures with specific optical functionalities.