Three-dimensional transformation optics for arbitrary coordinate systems: transforming conductive materials and...

Area of Science:

• Electromagnetism
• Optics
• Materials Science

Background:

• Transformation optics (TO) is a powerful tool for designing electromagnetic devices.
• Conventional TO often requires complex, inhomogeneous materials.
• Designing devices with arbitrary geometries and homogeneous materials remains a challenge.

Purpose of the Study:

• To present a 3D transformation optics method for designing devices with homogeneous materials.
• To apply the method to arbitrary coordinate systems and object cross-sections.
• To determine both conductive boundaries and internal material properties.

Main Methods:

• A 3D transformation optics formulation is developed.
• The method determines conductive boundaries and material properties simultaneously.
• The formulation is demonstrated for circular waveguide couplers and an external cloak.

Main Results:

• The method successfully designs devices with homogeneous materials, simplifying properties.
• A right-angle circular waveguide bend using a single homogeneous material is demonstrated.
• Transformation of conductive materials and boundaries is analyzed, showing conductivity can be preserved or approximated.

Conclusions:

• The presented method offers a versatile approach for designing electromagnetic devices with homogeneous materials.
• It simplifies material requirements and expands the applicability of transformation optics.
• The findings have implications for waveguide, radiation, and cloaking applications.