Inverse scattering with a non self-adjoint variational formulation.

Area of Science:

• Electromagnetism and Optics
• Computational Physics
• Materials Science

Background:

• The weak scattering approximation is commonly used in optical media design but lacks accuracy for multiple field interactions.
• Accurate design requires solutions consistent with Maxwell's equations for efficient coupling of incident and scattered fields.
• Existing methods may not fully capture the complex interactions within optical media.

Purpose of the Study:

• To develop a method consistent with Maxwell's equations for designing optical media.
• To extend the finite element method (FEM) to simultaneously determine both fields and the optical medium.
• To enable the design of highly efficient diffractive and refractive elements.

Main Methods:

• A variational formulation of Maxwell's equations, an extension of the finite element method (FEM), is employed.
• The method iteratively updates estimates of both the electromagnetic field and the optical medium.
• Designs were demonstrated using an iteratively updated finite-difference-frequency-domain (FDFD) solution.

Main Results:

• The proposed method successfully designs diffractive and refractive elements that efficiently couple fields.
• The iterative approach allows for simultaneous optimization of the medium and the field interactions.
• Demonstrated designs showcase the effectiveness of the Maxwell's equation-consistent approach.

Conclusions:

• The developed method provides a robust framework for designing optical media with high efficiency.
• This approach is crucial for advancing metamaterial design by exploiting strongly interacting elements.
• Future work can leverage this method for complex photonic device optimization.