Plasmonic Lens with Multiple-Turn Spiral Nano-Structures

Abstract

In this paper, we investigate the focusing properties of a plasmonic lens with multiple-turn spiral nano-structures, and analyze
its field enhancement effect based on the phase matching theory and finite-difference time-domain simulation. The simulation
result demonstrates that a left-hand spiral plasmonic lens can concentrate an incident right-hand circular polarization light
into a focal spot with a high focal depth. The intensity of the focal spot could be controlled by altering the number of turns,
the radius and the width of the spiral slot. And the focal spot is smaller and has a higher intensity compared to the incident
linearly polarized light. This design can also eliminate the requirement of centering the incident beam to the plasmonic lens,
making it possible to be used in plasmonic lens array, optical data storage, detection, and other applications.

KeywordsPlasmonic lens–Archimedes’ spiral slot–Superfocusing–FDTD

Full text

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Plasmonic Lens with Multiple-Turn Spiral Nano-Structures
Junjie Miao & Yongsheng Wang & Chuanfei Guo &
Ye Tian & Shengming Guo & Qian Liu & Zhiping Zhou
Received: 17 August 2010 /Accepted: 27 December 2010 /Published online: 18 January 2011
# Springer Science+Business Media, LLC 2011
Abstract In this paper, we investigate the focusing
properties of a plasmonic lens with multiple-turn spiral
nano-structures, and analyze its field enhancement effect
based on the phase matching theory and finite-difference
time-domain simulation. The simulation result demon-
strates that a left-hand spiral plasmonic lens can concen-
trate an incident right-hand circular polarization light into
a focal spot with a high focal depth. The intensity of the
focal spot could be controlled by altering the number of
turns, the radius and the width of the spiral slot. And the
focal spot is smaller and has a higher intensity compared
to the incident linearly polarized light. This design can
also eliminate the requirement of centering the incident
beam to the plasmonic lens, making it possible to be used
in plasmonic lens array, optical data storage, detection,
and other applications.
Keywords Plasmonic lens.Archimedes’ spiral slot.
Superfocusing.FDTD
Introduction
Surface plasmon polaritons (SPPs) are surface electro-
magnetic waves bound to a metal/dielectric interface
with subwavelength scale features and field enhance-
ment effects [1], making them very attractive for a
variety of applications such as sensor [2, 3], microscopy
[4, 5], light focusing [6], and plasmonic devices [7–9].
Surface plasmon waves can be focused into a highly
confined spot with a size beyond the diffraction limit,
because of the short effective wavelength. Taking
advantage of this property, Zhang et al. proposed a
plasmonic lens with metallic nano-structures, which can
confine the electromagnetic energy to a small region and
focus the energy at a desired location. A single annular
structure plasmonic lens (SAPL) with a subwavelength
slit milled into a metal layer is in common use [10].
When the incident linearly polarized light reaches the slit,
the wave couples into SPPs which propagate through the
slit and then form a focal spot at the metal/dielectric
boundary. However, SPPs can only be excited by
transverse magnetic polarized light and their phase
difference on the two ragged edges of a spiral slit is π
[11]. This results in a low coupling efficiency and a
separation of the focal spot into two parts around the
focal center, limiting application of the SAPL.
Recently, the much smaller and finer focal spots have
been achieved by using radially polarized incident light
instead of linearly polarized incident light [12–17]. The
reason for the improvement is that surface plasmons are
excited from all directions and then homogeneous focus
through constructive interference. And due to the angular
selection of the SPPs, the plasmonic focus generated in
J. Miao:Y. Wang:C. Guo:Y. Tian:S. Guo:Q. Liu (*)
National Center for Nanoscience and Technology,
No. 11, Beiyitiao,
Beijing 100190, China
e-mail: liuq@nanoctr.cn
J. Miao:Z. Zhou
State Key Laboratory on Advanced Optical Communication
Systems and Networks, Peking University,
Beijing 100871, China
J. Miao:Y. Wang:C. Guo:Y. Tian
Graduate School of the Chinese Academy of Sciences,
Beijing 100190, China
Plasmonics (2011) 6:235–239
DOI 10.1007/s11468-010-9193-0

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this way is an evanescent non-spreading Bessel beam
[12]. However, it is impossible to build the SAPL array
in this case, because the center of radially polarized light
must be exactly aligned to the center of the SAPL.
Therefore, further study should be carried out to realize
the practical application of plasmonic lenses by improv-
ing the structure of the lens and adopting more suitable
incident light.
Interactions between chiral metallic structures and
circularly polarized light have been reported recent years
[18–22]. A plasmonic vortex induced by Archimedes’ spiral
grooves was investigated, where the spiral grooves
serve as gratings to excite the surface plasmon [19]. It
has been also demonstrated that a spiral plasmonic lens
can be used as a miniature circular polarization analyzer,
because it can focus the left- and right-hand circular
polarizations into spatially separated plasmonic fields
[20, 21]. In addition, complex polarization response and
symmetry-breaking features have been studied in the
spiral structures [22].
Scheme and Structure Layout
In this work, we study a simpler, more practical design
of a plasmonic lens with a multiple-turn spiral slot
structure. In our design of the spiral plasmonic lens
(SPL), a thin metallic film-based spiral structure is used
to manipulate the required phase modulation for super-
focusing. The focusing properties for clockwise and anti-
clockwise circular polarizations, as well as the relations
among the focus intensity, the size, the width, and the
turns of the spiral slot, are studied systematically in the
SPL.
We consider the left-hand multiple-turn Archimedes’
spiral slot structure as a plasmonic lens for subwavelength
focusing, as shown in Fig. 1a. The structure consists of
multiple turns penetrated through a silver thin film with a
thickness of 300 nm, the slit width w is chosen to be
250 nm, the structure can be described as
rnf ð Þ ¼ rn0þf
2plsp;
for 0 ? f ? 2p;n ¼ 1;2;3 ? ??;
ð1Þ
where rn0is a constant of the nth turn, rn(φ) is the distance
from the point (rn, φ) on the inner side of nth spiral slot to
the center of the structure in the polar coordinate, and the
pitch of spiral slot is equal to the wavelength of the
surface plasmon. A right-hand circularly (RHC) polar-
ized plane wave is incident along the negative
z-direction as shown in Fig. 1b. The incident wave is
generated by using the superposition of two linearly
polarized plane waves (transverse magnetic and trans-
verse electric) with a phase difference of π/2, which can
be expressed as E
ed at the spiral slot will propagate along the exit facet and
interfere with each other constructively.
!¼ e!xþ i e!y. Surface plasmons excit-
Method and Parameters
The electromagnetic field intensity for the SPL is analyzed
by the three-dimensional finite-difference time-domain
(FDTD) approach with an absorption boundary condition.
The dispersive data are based on the experimental data
given by Palik [23]. In this design, free space wavelength
λ0=660 nm is adopted, and the relative permittivity of the
silver material used in the FDTD is εm=–17.7+1.18j. The
effective refractive index of the surface plasmon at the
interface between the Ag layer and air is nsp=1.03,
corresponding to the surface plasmon wavelength λSP=
641 nm. The surface plasmons excited at all azimuthal
directions propagate along the air-silver interface toward
Fig. 1 a Schematic diagram
of the left-hand multiple-turn
Archimedes’ spiral slot. b The
left-hand SPL under the illumi-
nation of right-hand circular
polarization plane wave along
the negtive z-direction. c
Schematic diagram of the
relative phase of the SP waves
excited by the SPL under the
right-handed circular polariza-
tion. The red, yellow, green, and
blue arrows correspond to the
out-of-plane electric field Ez
with relative phases of 3π/2, π,
π/2, and 0, respectively
236Plasmonics (2011) 6:235–239

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the center of the plasmonic lens with a propagation loss of
exp[−Im(ksp)·r], where
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
"
ksp¼2p
l
"
0
mþ "d
0
m"d
s
:
ð2Þ
Here, εdand "
and the real part of the relative permittivity of the silver
film, respectively. The propagation length of the surface
plasmon in this case is Lp=25.7 μm. Of course we can use
other noble metals such as gold or aluminum instead of
silver so long as they can excite surface plasmons and the
surface plasmons have a large propagation length. If we
choose other material of metals or use an incident light with
different wavelength, we should pay special attention that
the pitch of spiral slot must be equal to the corresponding
wavelength of the surface plasmon in order to match phase.
The relative phase of the surface plasmon waves in
the exit plane of the SPL under the RHC polarization is
illustrated in the Fig. 1c. In the exit plane of the silver thin
film, the surface plasmon waves will keep the same phase
0
mare the relative permittivity of medium (air)
Fig. 2 a Simulated |E|2distribution in the x–y plane at the
longitudinal distance z=350 nm from the out-of-plane for a left-hand
SPL under RHC illumination. b |E|2distribution in x–z plane. c Cross
section of |E|2at the focal plane, 350 nm away from the exit surface
(in the z-direction). d Spot size versus z
Fig. 3 Simulated |E|2at the central point versus a the slit width
(oneturn,theoutmostr0=4 μm) and the turns of the spiral nano-structures
(slit width w=250 nm, maximal r0=4 μm), b r0(one turn, slit width
w=250 nm). The distance between the central point and the exit surface is
350 nm
Fig. 4 Array of left-hand SPL (the white parts) with four different r0
(2λSP, 3λSP, 4λSP, 5λSP) under the incident RHC polarization light,
simulated |E|2distribution in the x–y plane at the longitudinal distance
z=350 nm from the out-of-plane, for the case of one spiral turn and a
spiral slot width of 100 nm
Fig. 5 Simulated |E|2distribu-
tion in the x–y plane at the
longitudinal distance z=350 nm
from the out-of-plane for a
left-hand SPL under LHC
illumination
Plasmonics (2011) 6:235–239237

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once they propagate to the edge of the internal circle
(black dotted line), although the phases are different when
they were excited at the spiral slot initially. Such patterns
of the phase are same as that of SAPL illuminated by the
radially polarized incident light. More importantly, due to
the isotropy of the circular polarization, the SPL avoids
the difficulty of having to align the center of the incident
radially polarized beam to be coincident with the center of
the SAPL, thereby providing a more practical plasmonic
lens array.
Numerical Analysis and Discussion
Figure 2a shows the intensity distribution of |E|2in the x–y
plane at the longitudinal distance z=350 nm from the out
plane of the silver thin film. From this figure, we can see
that the left-hand SPL focuses a RHC polarization into a
spot with a central peak. The electric field at the point of
(R, ϕ) on the outer plane of the silver thin film is
proportional to zero-order Bessel function J0(krR), as
shown in Fig. 2a. The cross section of the field intensity
pattern is shown in the Fig. 2c. The full width at half
maximum (FWHM) of the focal spot is about 240 nm
(∼0.33λ0), lower than the diffraction limit. And the non-
spreading effect of zero-order evanescent Bessel beam
favors a beam focus in high quality. From Fig. 2b and d,
we can also see that the FWHM of the focal beam nearly
keeps a constant along the z axis, indicating the focus spot
with a high focus depth.
Furthermore, we investigate the influence of the struc-
ture parameters of the spiral slot to the performance of the
left-hand spiral plasmonic lens under RHC illumination,
such as the size, the number of turns, and the width of the
spiral slot, as shown in the Fig. 3. It is obvious that the
relative electric field intensity can be controlled by adjusting
the turns of the spiral slot. We can see from Fig. 3a that the
intensity becomes stronger and stronger with the increase of
the turns of the spiral slot from one to five. And the intensity
will begin to reach a plateau when the number of turns is
five. Moreover, the increasing rate will decrease quickly with
the further increase of the turns because of the limitation of
the propagation length of the SPPs.
Since more energy can be coupled to the focal spot with
the increase of r0, the intensity of the focal spot increases
by expanding the turning radius, r0, as show in Fig. 3b. The
slit width of the spiral structure is also a key parameter to
manipulate the focusing intensity. The results of simula-
tions for the electric field intensity for varying the slit width
from 0.1 to 0.3 μm by a step of 0.05 μm relative to that
with a slit width of 250 nm at the center point (z=350 nm)
are shown in Fig. 3a. Here, we use only one turn (r0=4 μm)
of the spiral structures to simplify the analysis. The
intensity at the focal point shows an increase with the slit
width. This is mainly because that the slit width could
strongly affect the transmissivity of the incident light. It
should be noted that the size of the focal spot is mainly
related to the wavelength of the incident light, therefore it
can be kept nearly constant when we adjust the turns, the
width, and r0of the spiral slot.
As discussed above, the intensity of the focal spot can be
flexibly controlled by varying the turns, r0 and the slit
width of the spiral slot while the FWHM remains nearly
constant for a given wavelength of the incident light.
Hence, an array of the SPL with different parameters could
be applied as an attenuator of light intensity or/and a nano-
scale beam splitter, as shown in Fig. 4.
As a contrast, we also investigate the effect of the left-
hand circular (LHC) polarization incident light illuminating
the left-hand SPL. Unlike the RHC polarization focusing
into a central peak spot, the LHC polarization focus into a
ring with a dark center spot as shown in Fig. 5. This
property will be quite useful in detecting polarization
characters of light for a nano-scale area.
Summary
In conclusion, the left-hand SPL with multiple-turn Archi-
medes’ spiral slot under the illumination of a RHC
polarization can focus the light into a small bright spot at
the center of the lens with a high focal depth, and can also
focus the LHC polarization light into a dark spot at the
center. Unlike SAPL with a radial polarization, the SPL
does not require alignment of the radiation to the center of
the structure. Therefore, our method supplies a much more
effective and convenient way for the practical use of
plasmonic lenses in optical probing and plasmonic lens
arrays. More interestingly, we found that the electric field
intensity at the center of the exit surface could be
modulated by altering the turns, the size and the width of
the spiral slot, while nearly keeping the FWHM in a
constant, which have many potential applications for
intensity actuating, focusing beams, nano-scale beam
splitters, and other applications.
Acknowledgments
work by NSFC (10974037), NBRPC (2010CB934102) and Program
of International S&T Cooperation (2010DFA51970).
We gratefully acknowledge the support to this
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