CHIN.PHYS.LETT. Vol. 26, No. 1 (2009) 014211-1
Near-Field Optical Transfer Function for Far-Field Super-Resolution Imaging
∗
ZHANG Zhi-You(Ül)
1
, DU Jing-Lei(Ú¯X)
1∗∗
, GUO Yong-Kang(H[x)
1
, NIU Xiao-Yun(Ú¡)
1
,
LI Min(o¯)
1
, LUO Xian-Gang(Ûkf)
2
, DU Chun-Lei(ÚSX)
2
1
Department of Physics, Sichuan University, Chengdu 610064
2
State Key Laboratory of Optical Technologies for Microfabrication, Institute of Optics and Electronics, Chinese
Academy of Sciences, Chengdu 610209
(Received 14 April 2008)
The far-field superlens based on surface plasmon polaritons (SPP) has shown great application potential, but it
is difficult and time-consuming to reconstruct the far-field image. We derive a near-field optical transfer function
(NOTF) of silver slab and analyse its validity so that the accurate information of nano-scale object in the near-
field can be computed rapidly. The NOTF is helpful not only for analysing the super resolution imaging process
in far-field, but also for providing a track to describe the transmission of optical information from near-field to
far-field by using the optical transfer functions theory only.
PACS: 42. 30. −d, 42. 79. −e, 73. 20. mf
So far, many approaches of imaging beyond
the diffraction limit with superlens have been
reported.
[1−7]
Unfortunately, it was pointed out that
these superlenses could only produce sub-diffraction-
limited images in near field.
[8]
Recently, an optical
microscope capable of projecting the images with su-
per resolution to the far field is great noticed,
[9−12]
although it is difficult and time-consuming to recon-
struct the near-field image. In fact, the imaging pro-
cess of far-field superlens (FSL) can be divided into
two steps: super resolution imaging with silver film,
and the transmission of information from near-field to
far-field modulated by the coupling device.
[11]
Then,
the far-field image can be easily reconstructed by op-
tics or computer technology. In this Letter, we re-
gard the near-field imaging of silver lamella as a lin-
ear spatially invariant system, and present the con-
cept of a generalized near-field optical transfer func-
tion (NOTF) and its formula. We try to demonstrate
that it is feasible to describe the imaging pro cess by
the NOTF formula. The simulations show that the
computing time of the near-field imaging or object
information reconstruction in the far-field will be re-
duced greatly by NOTF.
Figure 1(a) shows the scheme of far-field superlens
system. Figure 1(b) is the near field silver sup erlens in
the FSL system. Here the thickness of silver with per-
mittivity ε
2
is d, and there are two kinds of dielectrics
on both sides of the slab with dielectric constants ε
1
and ε
3
, respectively. It should be noted that magnetic
permeability µ = 1 everywhere in such a system. Fig-
ure 1(c) shows the imaging process of silver superlens
at λ
0
= 441 nm with the relative permittivity of silver
ε
2
= −3.372 + i0.253 by FDTD method. In the FSL
system, the evanescent waves can be enhanced by the
silver superlens. Namely, the super resolution infor-
mation of object in the low refraction index medium
can be coupled into propagating waves in high re-
fraction index medium by the SPP effect, and then
the propagating waves can be transferred to far-field
by coupling elements such as prism grating, subwave-
length metal grating and so on, when the matching
condition is satisfied.
[9,11]
We assume a p-polarized
monochromatic point object source in the medium 1
at a distance z
1
. The near-field image plane is inside
medium 3 at a distance z
2
from the edge of the silver
slab. The object at z = −z
1
can be characterized by
its emanating field distribution whose magnetic vector
H
o
(r) can be expressed as a Fourier integral over all
the wave-vectors,
H
o
(r) =
Z
e
H
o
(k) exp[i(k · r)]dk, (1)
where
e
H
o
(k) is the Fourier transfer of source object.
The evanescent and propagating waves components
are all contained in this formula. Supposing that
the incident waves are in the x − zplane, the dis-
persion equation in different media can be written as
k
2
ix
+ k
2
iz
= ε
i
ω
2
/c
2
(i = 1, 2, 3 denote the three me-
dia). For the propagating components (k
2
ix
≤ ε
i
ω
2
),
we have k
iz
= (ε
i
ω
2
− k
2
ix
)
1/2
and for the evanes-
cent waves components (k
2
ix
≥ ε
i
ω
2
) we have k
iz
=
i(k
2
ix
−ε
i
ω
2
)
1/2
. To each of the components, the trans-
mission coefficient for the Fourier spectrum across the
slab can be written as
T = 4ε
2
ε
3
k
1z
k
2z
exp(ik
2z
d)
£
(ε
2
k
z1
+ ε
1
k
2z
)
· (ε
3
k
2z
+ ε
2
k
3z
) + (ε
2
k
1z
− ε
1
k
2z
)
· (ε
3
k
2z
− ε
2
k
3z
) exp(2ik
2z
d)
¤
−1
. (2)
∗
Supported by the National Natural Science Foundation of China under Grant Nos 60878031 and 60676024, the National Basic
Research Programme of China under Grant No 2006CB302902, and the Specialized Research Fund for Doctoral Programme of
Higher Education of China under Grant No 20060610006.
∗∗
To whom correspondence should be addressed. Email: DuJL@scu.edu.cn
c
° 2009
Chinese Physical Society and IOP Publishing Ltd