Trade-offs in absorption and scattering by nanophotonic structures

Area of Science:

• Electromagnetics
• Materials Science
• Optimization Theory

Background:

• Understanding electromagnetic wave interaction with lossy materials is crucial for designing advanced devices.
• Quantifying the fundamental limits of absorption and scattering is essential for material and device optimization.
• Existing models often simplify obstacle shapes and material properties, limiting applicability.

Purpose of the Study:

• To formulate and solve the multi-objective optimization problem for trade-offs between absorption and scattering cross sections.
• To determine the Pareto-optimal set defining the feasibility of simultaneously extremal absorption and scattering.
• To investigate the influence of pre-assigned loss and reactive material parameters on these trade-offs.

Main Methods:

• Formulation of the problem as a multi-objective optimization task.
• Application of Lagrangian-dual methods to solve the optimization problem.
• Numerical comparison of derived multi-objective bounds with realized structures.
• Examination of low-frequency limits for specific cases.

Main Results:

• Derivation of a Pareto-optimal set that illustrates the achievable trade-offs between absorption and scattering.
• Identification of the feasibility of simultaneously achieving extremal absorption and scattering based on the shape of the Pareto set.
• Analysis of how different material parameters influence the optimal trade-offs.
• Validation of theoretical bounds through numerical comparisons with practical structures.

Conclusions:

• The study provides fundamental multi-objective bounds for absorption and scattering of lossy obstacles.
• Lagrangian-dual methods offer a robust framework for solving these complex trade-off problems.
• The findings are applicable to the design of metamaterials, antennas, and stealth technologies.
• Low-frequency behavior offers specific insights for electrically small structures.