Computational Bounds to Light-Matter Interactions via Local Conservation Laws.

Area of Science:

• Computational physics
• Electromagnetism
• Materials science

Background:

• Understanding light-matter interactions is key to designing advanced optical devices.
• Existing methods for bounding these interactions have limitations, especially over arbitrary bandwidths.

Purpose of the Study:

• To develop a novel computational framework for identifying fundamental bounds to light-matter interactions.
• To establish a method for determining the minimum size of scatterers for specific optical computations.
• To resolve bounds on far-field scattering properties across arbitrary bandwidths.

Main Methods:

• Utilized polarization-current-based formulations of local conservation laws within Maxwell's equations.
• Proposed an iterative method for imposing maximally violated constraints to ensure rapid convergence.
• Applied the framework to determine bounds for optical discrete Fourier transform computation.

Main Results:

• The framework successfully identifies global bounds for light-matter interactions.
• Demonstrated the ability to find minimum scatterer sizes for encoding specific linear operators based on material properties.
• Resolved previously divergent bounds on far-field scattering properties over arbitrary bandwidths.

Conclusions:

• The developed computational framework provides a robust method for establishing fundamental limits in light-matter interactions.
• This approach has significant implications for the design of efficient optical computing elements and advanced photonic materials.
• The framework overcomes limitations of previous methods, offering broader applicability in electromagnetic and optical research.