Minkowski-Space Modeling of Hyperbolic Lenses

Area of Science:

• Optics and Photonics
• Materials Science
• Theoretical Physics

Background:

• Hyperbolic materials offer extreme wave confinement due to anisotropy.
• Misalignment between phase and energy flow complicates hyperbolic device design.

Purpose of the Study:

• To develop a simplified theoretical framework for hyperbolic wave propagation.
• To enable rational design of hyperbolic optical devices and analyze their performance limits.

Main Methods:

• Developed a Minkowski-space approach by embedding anisotropy into an effective Lorentzian metric.
• Analytically derived transfer functions and resolution limits for hyperbolic interfaces and lenses.
• Validated the theory using full-wave modeling of a polaritonic lens.

Main Results:

• The complexity in hyperbolic wave propagation is shown to be geometric.
• Established a rational design framework for hyperbolic optical components.
• Achieved ultralarge numerical apertures and deep subdiffraction focusing analytically.

Conclusions:

• The Minkowski-space approach provides a powerful tool for designing hyperbolic devices.
• This framework facilitates the realization of advanced optical functionalities like subdiffraction focusing.
• Validated for mid-infrared polaritonic lenses.