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
2
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).
Copyright (c) 2015 IEEE. Personal use of this material is permitted.
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
i
, w
i
, 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
D
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
Copyright (c) 2015 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.