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Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging

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High-resolution Fourier lens utilizing transformation materials.

Yunyun Lai, Wenxiu Dong, Jin Hu

|August 12, 2025

Summary

This study introduces a novel Fourier transform lens using transformation optics. The new design significantly enhances focus separation and resolution for optical Fourier transforms.

Area of Science:

Optics
Transformation Optics
Metamaterials

Background:

Conventional optical Fourier transform lenses often rely on paraxial approximations, limiting their resolution and performance.
Achieving high-resolution Fourier transforms with large bandwidths is crucial for various optical applications.
Luneburg lenses offer unique properties but typically require specific configurations.

Purpose of the Study:

To propose a novel Fourier transform lens with enhanced resolution and focus separation.
To design a lens that overcomes the limitations of paraxial approximations in optical Fourier transforms.
To adapt Luneburg lens principles into a planar configuration using transformation optics.

Main Methods:

Employing transformation optics to achieve conformal space mapping.

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Step-by-step adjustment of in-plane principal stretches for approximate space mapping.

Deforming the output surface of a Luneburg lens into a planar configuration.

Numerical simulations to evaluate lens performance.

Main Results:

The proposed lens maintains relaxed dependence on paraxial approximations for optical Fourier transform.
Numerical simulations demonstrate improved focus separation by up to 60% compared to conventional lenses.
The lens achieves enhanced Fourier transform resolution under specified conditions.

Conclusions:

The developed transformation optics lens offers superior focus separation and Fourier transform resolution.
This design provides a pathway to high-performance, planar optical Fourier transform systems.
The method validates the effectiveness of transformation optics in enhancing optical lens capabilities.