Rescaled Schwarz-Christoffel Transformations for Isotropic, Polygon, and Multiphysics Metamaterials

Area of Science:

• Metamaterials science
• Multiphysics engineering
• Applied mathematics

Background:

• Conformal transformation is key for isotropic metamaterials.
• Conventional methods struggle with concurrent thermal and electromagnetic field control due to differing field dissipation.
• Precise multiphysics control, especially for thermal and electromagnetic fields, remains a challenge.

Purpose of the Study:

• To propose a common design paradigm for multiphysics-applicable interface matching.
• To overcome limitations in conventional conformal transformations for concurrent thermal and electromagnetic field regulation.
• To establish a general platform for perfect interface matching using isotropic media.

Main Methods:

• Utilizing rescaled Schwarz-Christoffel transformation (RSCT).
• Leveraging the Schwarz-Christoffel transformation for energy flow direction.
• Integrating rescaling techniques for energy flow density redistribution.
• Simultaneously controlling energy flow and energy flow density in isotropic media.

Main Results:

• RSCT provides a general platform for perfect interface matching in multiphysics.
• Successfully designed and experimentally validated three energy-flow regulators: expanders, guiders, and cloaks.
• Demonstrated the capability of RSCT to form devices of arbitrary polygonal shapes.

Conclusions:

• RSCT offers a novel approach for precise multiphysics control, particularly for thermal and electromagnetic fields.
• The method enables coordinated signal and heat management in integrated circuits.
• RSCT holds significant promise for advanced metamaterial applications requiring concurrent field regulation.