超薄变宽金属狭缝阵列实现超振荡远场聚焦微透镜

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本文研究了一种创新的超振荡远场聚焦透镜，其核心是基于超薄且宽度可变的子波长金属狭缝阵列的设计与实现。这项实验性的成果发表在一项研究论文中，主要关注于突破传统的光学限制，探索光的衍射规律下的新突破。论文的标题"基于超薄变宽金属狭缝阵列的超振荡远场聚焦透镜"明确指出了研究对象，即通过利用连续幅度调制技术，设计出能够在632.8纳米波长下具有优异性能的微透镜。该透镜的尺寸为228×200微米²，具有数值孔径高达0.976，焦距为40.1个波长，这对于提升光学系统的分辨率和聚焦能力具有重要意义。实验结果显示，这款超薄透镜实现了约26.5±1微米的焦距，聚焦线的半宽度全宽（FWHM）仅为0.379个波长。这显著小于传统的衍射极限0.512个波长，以及超级振荡的标准临界值0.389个波长，表明了透镜在远场聚焦方面的卓越性能。论文还强调了侧向散射的显著减少，侧峰强度仅占中央峰的10.6%，这使得透镜具有更广阔的视场和更清晰的成像质量。这种抑制侧峰的能力对于光通信、成像系统和微纳光学器件等领域具有极大的应用潜力，比如提高光信号的传输效率和减少噪声干扰。研究者们引入了“超振荡”这一概念，这是一种利用光的干涉效应，通过优化结构参数，使光束在超过衍射极限的尺度上保持相干性的现象。这项技术突破了传统光学的理论框架，为未来设计更小、更高效的光学元件开辟了新的途径。这篇论文不仅阐述了基于超薄变宽金属狭缝阵列的超振荡远场聚焦透镜的理论基础，还提供了关键的实验数据来证明其性能优越性，对未来的微纳光学技术和衍射控制有着重要的理论和实践价值。



Abstract— A super-oscillation far-field focusing micro-lens

based on continuous amplitude modulation is experimentally

demonstrated with 40-nm thick width-varied sub-wavelength

metallic slit array. The 228×200 µm

micro-lens is designed and

fabricated with numerical aperture 0.976 and focal length 40.1 λ

for wavelength λ=632.8 nm. Experimental results show that the

focal length is about 26.5±1µm and the focal line full width at half

maximum is 0.379 λ, which is smaller than the corresponding

diffraction limit 0.512 λ and the super-oscillation criterion 0.389 λ.

A great suppression of sidelobes was observed in the measured

focal plane area and the largest sidelobe intensity was found only

10.6% of the central lobe intensity, leading to a wide field of view.

Index Terms—subwavelength focusing, diffractive lenses,

subwavelength structure, lenses, optical modulation.

I. INTRODUCTION

ue to the diffraction of light, the focal spot size of

conventional optical lens is restricted by the diffraction

limit 0.5λ/NA, where λ is the wavelength and NA is the lens

numerical aperture [1]. Recently, super-oscillation has

generated wide interest in the design and fabrication of optical

devices beyond diffraction limit for sub-wavelength light

focusing and super-resolution imaging [2-4]. The design of lens

transmission function is the key to realize super-oscillation

focusing. Phase modulation has been adopted in micro-lenses,

where spatial phase variation is realized by controlling the

effective refractive index through sub-wavelength structures.

Metallic pillars [5], waveguides [6,7], and slits [8-10] have

Manuscript received xxx. This work was supported by China National Key

Basic Research and Development Program under Grant No. 2013CBA01700,

2012CB933004, and 2013CB932804, the China National Natural Science

Foundation under Grant No. 61177093 and 21273053, the Fundamental

Research Funds for the Central Universities under Project No.

106112013CDJZR120019, and the visiting scholarship No. 0902011812401_1

from the Key Laboratory of Optoelectronic Technology and Systems

(Chongqing University).

Gang Chen, Yuyan Li, Zhongquan Wen, Li Chen, Yinghu He, Sheng Liu are

with Key Laboratory of Optoelectronic Technology and Systems (Chongqing

University), Ministry of Education, Key Disciplines Lab of Novel Micro-nano

Devices and System Technology, Chongqing University, Shapingba,

Chongqing 400044, China. Xianyou Wang and Luru Dai are with National

Center for Nanoscience and Technology, No.11 Zhong Guan CunBei Yi Tiao,

Beijing 100190, China. Feng Lin is with School of Physics, State Key

Laboratory for Mesoscopic Physics, Peking University, Beijing 100871, China

(corresponding author: Gang Chen, Phone: +86-23-65111022; e-mail:

GCHEN1@ cqu.edu.cn).

However, permission to use this material for any other purposes must be

obtained from the IEEE by sending a request to pubs-permissions@ieee.org.

been reported for phase control by varying their geometrical

size, and phase delay is proportional to the thickness of these

structures. However, large phase delay is a great challenge in

phase-based micro-lens for sub-wavelength focusing,

especially for short wavelength, due to the difficulty in

fabricating sub-wavelength structure with high depth-to-width

ratio. Although V-shape optical antenna can achieve phase

delay up to 2π, its poor amplitude transmittance is limited to

only several percent [11]. Binary amplitude (BA) slit is the

most commonly used structure for sub-wavelength focusing

micro-lens [12-14], because of its simplicity in fabrication.

Unfortunately, the focal spot is always accompanied by huge

sidelobes, and the size of the field of view is only several tens of

wavelengths. As demonstrated in our previous theoretical work,

increase in the design freedom of phase and amplitude can

greatly improve the focusing performance of micro-lenses [15].

This can be understood in following way. For an optimized

focusing optical field, its amplitude and phase distribution is

continuous except for several single points. According to the

angular spectrum theory, the amplitude and phase distribution

should also be continuous on the lens output surface. Therefore,

any deviation from the continuous distribution of the lens

transmission function will leads to degradation of the optimized

focusing performance. Continuous amplitude (CA) modulation

is convenient to realize with sub-wavelength structure. In this

paper, a lens based on CA modulation was designed and

fabricated, and its sub-wavelength focusing performance was

experimentally investigated.

II. D

ESIGN OF SUPER-OSCILLATION FOCUSING LENS

Fig. 1. The structure of a super-oscillation lens based on slit array.

Figure1 illustrates a lens based on periodical slits, where

only the right half of the lens is plotted because of symmetry.

The gray areas are aluminum and the blue area is glass substrate.

The orange lines are guides to eyes and they separate

neighboring slit units. The slit units are parallel to each other

with a fixed period of T, which is smaller than the working

wavelength λ. In the figure, x

, w

, and d are the central position,

Super-oscillation Far-Field Focusing Lens based

on Ultra-thin Width-varied Metallic Slit Array

Gang Chen, Yuyan Li, Xianyou Wang, Zhongquan Wen, Feng Lin, Luru Dai, Li Chen, Yinghu He,

Sheng Liu

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.

The final version of record is available at http://dx.doi.org/10.1109/LPT.2015.2496148

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