Flat lens without optical axis: Theory of imaging.

Area of Science:

• Optics and Photonics
• Materials Science

Background:

• Flat lenses offer potential for advanced optical systems.
• Conventional lenses often rely on curved surfaces and optical axes.
• Understanding novel imaging mechanisms is crucial for optical miniaturization.

Purpose of the Study:

• To establish a general theory for imaging using flat lenses without a defined optical axis.
• To identify the material properties required for such imaging.
• To explore practical realizations and limitations of flat lens imaging.

Main Methods:

• Derivation of a general theory for flat lens imaging.
• Analysis of materials with elliptic dispersion relations and negative group refraction.
• Investigation of anisotropic and inhomogeneous media, including photonic crystals.

Main Results:

• Identified elliptic dispersion relations with negative group refraction as essential for flat lens imaging.
• Introduced two intrinsic material parameters, sigma and kappa.
• Demonstrated that imaging is possible with both negative and positive wave vector refraction.
• Revealed a general law of refraction for anisotropic media.
• Presented numerical examples for sub-wavelength imaging.

Conclusions:

• The derived theory provides a framework for designing flat lenses.
• Anisotropic and inhomogeneous media, especially photonic crystals, are promising for realizing flat lens imaging.
• The study highlights requirements for achieving sub-wavelength imaging with flat lenses.