Multi-layered bowtie nano-antennasMonir Morshed, Abdul Khaleque, and Haroldo T. Hattori

Citation: Journal of Applied Physics 121, 133106 (2017); doi: 10.1063/1.4979862View online: https://doi.org/10.1063/1.4979862View Table of Contents: http://aip.scitation.org/toc/jap/121/13Published by the American Institute of Physics

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Multi-layered bowtie nano-antennas

Monir Morshed,a) Abdul Khaleque, and Haroldo T. HattoriSchool of Engineering and Information Technology, University of New South Wales at Canberra, Canberra,Australian Capital Territory 2610, Australia

(Received 8 December 2016; accepted 26 March 2017; published online 6 April 2017)

This paper analyzes a multi-layered bowtie nano-antenna, consisting of alternate layers of silica

(SiO2) and gold (Au). We show that the multi-layered structure can produce six times higher elec-

tric field enhancement than a purely gold bowtie antenna. The antennas may find applications in

sensing (e.g., Surface Enhanced Raman Scattering) and imaging. Published by AIP Publishing.[http://dx.doi.org/10.1063/1.4979862]

I. INTRODUCTION

The emergence of plasmonic nano-antennas has attracted

significant interest because of their ability to convert freely

propagating optical radiation into localized optical waves and

vice versa.1 Localization and confinement of optical radiation

in the antenna gap are achieved by the coupling of localized

surface plasmon resonances (LSPRs), resulting in high elec-

tric field enhancement.1–5 Due to their electric field enhance-

ment capacity, they have been used as sensors or probes in

Surface Enhanced Raman Scattering (SERS), enabling the

detection of low concentrations of cancer cells,6 single algae

cell detection,7 and single-molecule detection.8 In addition,

they have been used in high-sensitive photodetection,9 near-

field optical trapping,10 nanoscale light sources,11,12 and solar

energy harvesting.13,14

In recent years, different nano-antennas have been devel-

oped such as dipole,15 bowtie,16 Yagi-Uda,17 spiral,18 phased-

array,19 staircase,20 and log-periodic antennas.18 Amongst the

different designs, bowtie nano-antennas (BNAs) provide

strong electric field confinement and enhancement because of

the near-field coupling across the gap.2,21 In addition, they are

suitable for broad-band operation18 and single molecule detec-

tion because of their design flexibility.22

Currently, many strategies are used to improve and engi-

neer the electric field enhancement and optical properties of a

bowtie nano-antenna. For example, Zhou and co-workers pro-

posed an aluminium (Al) based BNA with a fused silica sub-

strate for ultraviolet (UV) wavelengths, which could enhance

the electric field at the nano-antenna gap due to the localized

surface plasmon resonance.23 Ding et al.24 proposed and opti-

mized a silver (Ag) bowtie nano-antenna by varying bow

angles and achieved a high electric field. Wang et al.25

designed a plasmonic gold (Au) bowtie nano-ring array to pro-

duce a high electric field enhancement factor by optimizing

the antenna size and the period of the bowtie nano-ring array.

In addition, Sederberg and Elezzabi26 applied a triangular

contour on a bowtie antenna for the near to mid-infrared

region: they were able to improve the electric field enhance-

ment factor by 28% when compared to Wang’s geometry.

Moreover, Li et al.27 used nano-holes inside the triangular

arms of the antenna: they numerically computed electric field

enhancement and sensitivity by using the finite difference

time domain (FDTD) method. An Au-BNA based on a SiO2

pillar was introduced and analyzed experimentally and numer-

ically as a function of the BNA gap spacing, array periodicity,

and pillar height to enhance the electric field in the gap.28

However, the large optical spot size and less flexibility of

SERS probes are the main limitations of these antennas, and

therefore, it is still necessary to find a new geometry for bow-

tie nano-antennas that can overcome the above limitations as

well as improve the electric field enhancement factor.

On the other hand, composite structures are attracting

growing interest in nano-photonics because they can confine

more light by increasing the effective refractive index at the

interface between two media and reduce the ohmic loss.29,30

In addition, when the separation between two interfaces is

comparable to or less than the penetration depth of the inter-

face modes, interactions between surface plasmon polaritons

(SPPs) give rise to coupled modes, whereby the electric field

strength can be amplified due to coupling of symmetric

mode profiles.31–34 Dey et al.33 introduced a composite

structure for single nano-rod at the wavelength of 5.98 lm

that enhanced the electric field intensity. A similar approach

was applied to design silica filled slot waveguides based on

hyperbolic metamaterials,29,35 multi-layered waveguides,36

and multi-layered dipole nano-antennas.37 In this paper, we

propose a multi-layered bowtie nano-antenna with a combi-

nation of gold (Au) and silica (SiO2), which produces a

615% higher electric field enhancement factor than a pure

gold bowtie antenna.

II. GENERAL DESCRIPTION OF THE STRUCTURES

Figures 1(a) and 1(b) show the three dimensional (3D)

view and the 2D side view (x-y plane) of the proposed multi-

layered bowtie structure, respectively. Key geometric parame-

ters of the bowtie antenna include the length of each triangle

l, width of the triangle w, apex angle a, gap width between

two triangles g, and total height H. The device is optimized

for the wavelength of 1053 nm. In addition, the thicknesses of

the gold and silica layers are referred by hg and hs,

respectively.

The orange color in Fig. 1 indicates a metallic gold

region, while the green color indicates a quartz substrate

a)Author to whom correspondence should be addressed. Electronic mail:

Monir.Morshed@student.adfa.edu.au

0021-8979/2017/121(13)/133106/9/$30.00 Published by AIP Publishing.121, 133106-1

JOURNAL OF APPLIED PHYSICS 121, 133106 (2017)

(SiO2). The whole structure is surrounded by air, and the

incident wave is assumed to be a quasi-plane wave propagat-

ing along the þy direction. Commercial 3D FDTD software

is used38 with a perfectly matched layer (PML)39 boundary

condition for the numerical analysis of the nano-antennas.

According to Lesina et al.,40 the FDTD method provides

faster convergence and better accuracy for the bowtie anten-

nas when compared with other methods (e.g., finite-element

method). In addition, in different research articles,20,41 they

had used mesh sizes of 10 nm and 20 nm for the theoretical

analysis and found similar results to experiments. In our

case, we are using non-uniform grid sizes, being refined at

the boundaries between the metallic and dielectric regions,

with Dx¼ 10 nm and Dy¼Dz¼ 20 nm, while close to the

metallic regions, Dx¼Dy¼Dz¼ 3 nm. The time step is cho-

sen as 5.7� 10�18 s. The refractive index of SiO2 is set to a

value of 1.45, and the refractive index of gold (Au) is given

by the following dispersive model:38

e xFullwaveð Þ ¼ 1þX6

k¼1

Dek

�akx2Fullwave � bk ixFullwaveð Þ þ ck

;

(1)

where xFullwave is defined by xFullwave ¼ x0=cvac, with x0

being the angular frequency of incoming light and cvac being

the speed of the light in vacuum, and ak, bk, ck, and Dek are

the built in coefficients of Fullwave software as listed in

Table I.

In the simulation, the incident wave is considered to be

a Gaussian wave with a large spot size diameter of 20 lm.

Since the electric field in the gap of the nano-antenna is

enhanced, the relative electric field enhancement factor can

be calculated and formulated as

Frel ¼jEgap;peakjjEinc;peakj

; (2)

where jEgap; peakj is the magnitude of the electric field calcu-

lated in the subwavelength gap of the nano-antenna, and

jEinc; peakj is the magnitude of the electric field of incoming

light.

The magnitude of the electric field may be higher at the

center of the nano-antenna gap but might not be uniform

along the vertical direction (þy direction). Therefore, it is

also better to calculate the average electric field enhance-

ment factor Favg which can be defined as37

Favg ¼

ÐH0

Frel x ¼ 0; y; z ¼ 0ð Þdy

H: (3)

The filling factor, FF, is defined by37

FF ¼HAu totalð Þ

HAu totalð Þ þ HSiO2 totalð Þ� �

!; (4)

where HAu(total) and HSiO2(total) are the total thickness of the

gold and silica layer, respectively.

III. RESULTS AND DISCUSSION

A. Comparative discussion of multi-layered andsingle-layered bowtie structures

The relative and the average electric field enhancement

factors for the optimum design of the proposed structure and

a comparison with a single-layered bowtie antenna at the

wavelength of 1053 nm are shown in Figs. 2(a) and 2(b),

respectively. From the figures, it is clear that the proposed

antenna has 615% and 387% higher peak and average elec-

tric field enhancement factors, respectively, than a standard

gold bowtie antenna, as a result of the constructive interfer-

ence among the different electric modes in the gap along the

vertical direction. Note that the single-layered antenna is

optimized by considering a thickness of 500 nm.

In addition, the electric field profiles of the proposed

geometry are shown in Fig. 3. Although, in the lateral direc-

tion, the electric field in both single-layered (Fig. 3(a)) and

multi-layered structures (Fig. 3(b)) looks similar, there is a

significantly stronger vertical confinement in a multi-layered

FIG. 1. (a) 3D diagram of the multi-

layered bowtie nano-antenna and (b)

2D side view in the x-y plane.

TABLE I. Dispersion coefficients of gold from the Fullwave material

library.38

De A b c

1589.516 1 0.268419 0

50.19525 1 1.220548 4.417455

20.91469 1 1.747258 17.66982

148.4943 1 4.406129 226.0978

1256.973 1 12.63 475.1378

9169 0 11.21284 4550.765

133106-2 Morshed, Khaleque, and Hattori J. Appl. Phys. 121, 133106 (2017)

structure when compared with a single-layered structure, as

it is clearly observed in Fig. 3(c). An initial explanation for a

higher electric field enhancement in the multi-layered

antenna is that it has a higher refractive index, creating more

abrupt transitions between the antenna/air and antenna/sub-

strate interfaces—leading to a stronger confinement of

energy in the central region of the antenna. However, the

stronger concentration of light in the central region might be

FIG. 2. Comparative performance of

optimized (a) multi-layered (H¼ 500 nm,

FF¼ 50%, a¼ 90�, l¼ 211 nm,

w¼ 422 nm, and g¼ 50 nm) and (b)

single-layered (H¼ 500 nm, a¼ 90�,l¼ 128 nm, w¼ 256 nm, and g¼ 50 nm)

bowtie structures at the wavelength of

1053 nm.

FIG. 3. Electric field profile (x-z plane) of (a) single-layered and (b) multi-layered bowtie nanoantennas for optimum parameters; (c) electric field distribution

along the y plane at x¼ 0 and z¼ 0.

133106-3 Morshed, Khaleque, and Hattori J. Appl. Phys. 121, 133106 (2017)

due to the multiple scattering and interference of light in the

vertical direction,31–34 leading to a much stronger concentra-

tion of the electric field energy in the central region (x¼ 0,

y¼ 250 nm, and z¼ 0) and, consequently, a higher electric

field enhancement factor. Moreover, the multi-layered struc-

ture provides additional flexibility to concentrate the energy

of the electric field in the vertical direction.

B. Optimization of the geometric parameters of theproposed structure

The optimized electric field enhancement factor at the

resonant wavelength can be determined by tuning the geo-

metrical parameters of the bowtie multi-layered shape

because the optical properties such as the optical wave-

length, electric field intensity, and confinement of the electric

field depend on the geometrical parameters.23,25–28 In this

work, the resonant condition of the proposed antenna at the

wavelength of 1053 nm is obtained by using the FDTD

method. The optimization of the parameters at this wave-

length has been carried out by following the procedure dis-

cussed by Zhou et al.23 We have simulated different sets of

antennas by varying the length l, width w, and height of gold

hg, height of the silica layer hs, and total height of layers Hwith fixed gap width g and apex angle a.

The filling factor, FF, is optimized for the total thick-

ness H¼ 300 nm by keeping the other parameters such as the

gap width (g) and apex angle (a) constant at 50 nm and 90�,respectively. To optimize the filling factor for the fixed

parameters at the wavelength of 1053 nm, we have changed

the length of the antenna, which is shown in Fig. 4(a). The

width of this antenna is also changed because of the relation

w¼ 2l for a triangular shape since the apex angle is fixed at

90�. Figure 4(a) shows that the highest electric field enhance-

ment factor occurs for a 50% filling factor (hg¼ 50 nm and

hs¼ 75 nm) at the length of 206 nm, with a value of 21.92. In

the case of the 50% filling factor, the amount of gold and sil-

ica is approximately the same, leading to a reduction in the

overall loss of the nano-antenna37—however, we have noted

that in metals with higher losses (e.g., titanium), the fraction

of silica needs to be increased to overcome the higher losses

of the metal. In addition, the strength of the electric field

increases by the collective electron oscillation characteristic

of a strongly coupled plasma.34 Fig. 4(b) shows that the

resonance first blue shifts and then red shifts as the filling

factor increases. The resonance blue shifts while increasing

the filling factor from 40% because the thickness of the gold

layer is increased, which decreases the effective refractive

index. According to Ding et al.,42 the reduction in the effec-

tive refractive index of SPPs blue shifts the resonance. In

addition, the peak wavelength can be determined by34

k0 � 2Ð l=2

�l=2nef f xð Þdxþ d, where d is the offset introduced

by the gap width and the reflection of the two extremities.

Since the length and the gap are fixed in Fig. 4(b), the effect

of d is minor. Now, it is clear that the reduction of the effec-

tive index blue shifts the resonance wavelength. However,

this equation is no longer valid when FF exceeds 50%. It can

be observed in Fig. 4(b) that the resonance wavelength red

shifts when the thickness of gold is changed from a 50% fill-

ing factor. In this case, large filling factors increase the thick-

ness of the gold layer, which isolates the SPPs at the

interfaces resulting in the decoupling of the plasmonic

modes. Therefore, the electric field is reduced, but back and

forth propagation of SPPs in each of the interfaces and addi-

tive interferences gives rise to standing waves whose wave-

length scales with the length of the triangles, thus redshifting

the resonance as the filling factor increases.24

The total thickness of the antenna (H) is changed as

shown in Figs. 5(a)–5(c): it is noted that the optimum length

of the antenna changes as H changes as expected since the

total height affects the interference of the electromagnetic

fields that are scattered by the different gold/silica interfaces

and also affects the coupling of the plasmonic modes propa-

gating at different gold/silica interfaces.32,34 However, the

optimum filling factor remains FF¼ 50% for different

heights as can be observed in Figs. 5(a)–5(c). A maximum

electric field enhancement Frel¼ 32.3 is reached for

H¼ 500 nm, as can be observed in Fig. 5(b). The introduc-

tion of the silica layers has reduced the overall losses of the

antennas,37 but at the same time, it is necessary to have

enough metal to produce the surface plasmon polaritons at

different boundaries of gold/silica layers. It seems that a

50% filling factor produces a good compromise between

reducing the antenna ohmic losses and, at the same time, cre-

ating surface plasmon waves. Another factor that needs to be

taken into account is that FF¼ 50% leads to an electric field

which has a maximum at the center of the antenna, while

FIG. 4. (a) Optimization of the filling

factor (FF) for the height H¼ 300 nm

while other parameters are constant

(a¼ 90� and g¼ 50 nm), (b) Frel as a

function of wavelength for different

filling factors (FF), while other param-

eters are constant (H¼ 300 nm,

a¼ 90�, l¼ 206 nm, w¼ 412 nm, and

g¼ 50 nm).

133106-4 Morshed, Khaleque, and Hattori J. Appl. Phys. 121, 133106 (2017)

other filling factors produce more asymmetric electric field

profiles.

In Fig. 6, we examine the effect of changing the total

height H for the multi-layered nano-antenna, and for an opti-

mized antenna, FF¼ 50%, a¼ 90�, l¼ 211 nm, w¼ 422 nm,

and g¼ 50 nm. It can be observed that the electric field

enhancement factor reaches a maximum for H¼ 500 nm but

does not change significantly in the region between

H¼ 400 nm and 600 nm. In a multi-layered antenna, there is

multiple scattering of the incident electric field along the

boundaries of different layers, and for a height H¼ 500 nm,

the interference between the multiple scattered fields reaches

a maximum at the center of the antenna. In addition, differ-

ent plasmonic modes at the silica-gold interfaces may poten-

tially couple and interfere with each other,32,34 creating a

very complex scenario. In the case of a single-layered

antenna, the boundaries are limited to air/gold and gold/sub-

strate interfaces with a gap between the metallic regions,

somewhat simplifying the analysis since the plasmonic

modes do not strongly interfere with each other in the verti-

cal direction. However, there is still interference between the

multiple scattered fields along the vertical direction, leading

to a maximum at the mid-height as can be observed in Fig.

3(c), but the electric field energy is more uniformly distrib-

uted along the volume of the gap.

So far, the apex angle and the number of layers have

been kept constant to optimize the length, filling factor, and

total height of the antenna. Now, the effects of the apex

angle on the electric field enhancement factor are further

examined. Figure 7 shows the impact of the apex angle (a)

on the electric field in the sub-wavelength gap as a function

of the wavelength, while other parameters such as length (l),gap (g), and total height H are kept constant, but the width

(w) is changed because of the relationship w ¼ 2l sin a=2ð Þfor a bowtie shape. From Fig. 7, it can be inferred that as the

apex angle increases, the resonance wavelength is red shifted

because the back and forth propagation and interference of

surface plasmon polaritons (SPPs) at the interfaces of trian-

gles give rise to a standing wave in which its resonance

wavelength scales with the length of the triangle edges and

FIG. 5. Effect of the length (l) on Frel

at the wavelength of 1053 nm with dif-

ferent filling factors (FF), while other

parameters are constant (a¼ 90� and

g¼ 50 nm) for (a) H¼ 400 nm, (b)

H¼ 500 nm, and (c) H¼ 600 nm.

FIG. 6. Effect of the total height (H) on Frel at the wavelength of 1053 nm

by keeping other parameters constant as FF¼ 50%, a¼ 90�, l¼ 211 nm,

w¼ 422 nm, and g¼ 50 nm.

133106-5 Morshed, Khaleque, and Hattori J. Appl. Phys. 121, 133106 (2017)

thus redshifts as the apex angles increase.24 In addition, the

electric field enhancement factor increases with the increas-

ing apex angles, which is the maximum for the angle of 90�

at the wavelength of 1053 nm. However, the enhancement is

reduced due to the destructive interferences and increasing

losses in the wider part of the structure16 when the apex

angle exceeds 90�.A variation of the electric field with respect to the num-

ber of layers for different total heights (H) in the gap is

shown in Fig. 8, while all other parameters such as length (l),width (w), gap (g), filling factor (FF), and apex angle (a) are

kept constant as 211 nm, 422 nm, 50 nm, 50%, and 90�,respectively. It can be observed from Fig. 8 that the proposed

antenna has the highest electric field enhancement for a five

layer antenna. However, the electric field enhancement fac-

tor is reduced when the number of layers is increased since

at this stage the metal losses start to dominate the response

of the structure and the decoupling of the resonant electric

fields.31–34

The magnitude of Frel for all the above figures was taken

at the mid-point of the gap (x¼ 0, y¼ 250 nm, and z¼ 0), but

the electric field distribution inside the antenna might not be

uniform. We have placed several monitors along the þx and

þy direction to calculate the electric field along these direc-

tions. To distinguish the electric field distribution for the dif-

ferent position in the y-plane, we placed 8 electric field

monitors with a constant distance from top to bottom in the

plane at x¼ 0 and z¼ 0 for optimum parameters: H¼ 500 nm,

FF¼ 50%, a¼ 90�, l¼ 211 nm, w¼ 422 nm, and g¼ 50 nm.

The relative electric field distribution along the þy direction

is shown in Fig. 9. The electric field enhancement factor at the

mid-point (x¼ 0, y¼ 250 nm, and z¼ 0) of the middle metal-

lic layer is 32.30, which reduces for the other metallic layer

away from the middle layer and is comparatively lower in the

silica substrate.

The magnitude of the electric field, along the x plane, is

measured at y¼ 250 nm and z¼ 0, which is shown in Fig.

10, and the electric field distribution is almost uniform along

the gap. However, it is higher at the edges of the nano-

antenna, for example, Frel with a gap width of 50 nm is 32.30

at the middle position of the gap (x¼ 0 nm, y¼ 250 nm,

z¼ 0 nm) while it reaches the value of 47.06 (x¼625 nm,y¼ 250 nm, and z¼ 0 nm) at the edges, i.e., at the interface

between metal and air in the gap.

From Fig. 9, it is clear that the electric field is not uni-

form along the vertical direction and it can significantly

change from top to bottom. For this reason, the average elec-

tric field enhancement factor is calculated for the optimum

parameters from Equation (3), which is shown in Fig. 11.

The maximum Favg at the wavelength of 1053 nm is 17.2.

Finally, Fig. 12 shows the effect of the gap width (g) on

the average electric field enhancement factor. Any variation

of the gap between the two arms of the antenna can change

the coupling and thereby the resonance wavelength.37 To

make a precise comparison and obtain the highest electric

field enhancement factor at the resonant wavelength of

1053 nm for each gap width, the length has been retuned and

optimized with the fixed total height H¼ 500 nm, filling ratio

FF¼ 50%, and apex angle a¼ 90�. The optimized length

sizes for the gap width of 10 nm, 20 nm, 40 nm, 60 nm,

80 nm, and 100 nm are 189 nm, 190 nm, 210 nm, 211 nm, and

212 nm, respectively, and the corresponding average electric

FIG. 7. Frel as a function of wavelength for different apex angles (a) of the

nano-antenna while other parameters (H¼ 500 nm, FF¼ 50%, l¼ 211 nm,

and g¼ 50 nm) are in the optimized condition.

FIG. 8. Effect of the number of layers on Frel at the wavelength of 1053 nm,

while other parameters (FF¼ 50%, a¼ 90�, l¼ 211 nm, w¼ 422 nm, and

g¼ 50 nm) are constant.

FIG. 9. Distribution of Frel along the þy direction in the gap of the nano-

antenna at x¼ 0 and z¼ 0 for the optimum parameters: H¼ 500 nm,

FF¼ 50%, a¼ 90�, l¼ 211 nm, w¼ 422 nm, and g¼ 50 nm.

133106-6 Morshed, Khaleque, and Hattori J. Appl. Phys. 121, 133106 (2017)

field enhancement factors are 60.45, 36.39, 18.43, 13.7, 8.4,

and 6.14, respectively. In this paper, we have optimized the

structure and compared with the pure gold single-layered

bowtie antenna for the gap width of 50 nm. As expected, the

average electric field enhancement changes exponentially

with the gap width.

C. Impedance analysis of the proposed structures

Impedance is an important property of antennas: in this

section, we calculate the impedance of multi-layered and

single-layered nano-antennas. Since nano-antennas do not

support TEM modes, the impedance of the devices for TE

modes can be calculated as43 Z ¼Ð1�1 Exdx=

Ð1�1 Hzdz,

where Ex and Hz are the in-plane electric field and magnetic

field components. The integral paths are chosen along the

central cuts of the antenna’s cross-section (paths along the

mid-height and the center of the antenna gap, as shown in

Fig. 1(a)).43 The impedance is calculated by using the Finite

Difference Time Domain (FDTD) method, which employs a

Fast Fourier Transform to calculate the wavelength depen-

dent real and imaginary parts of the electric and magnetic

fields along the integration paths.

Figures 13(a) and 13(b) show the real (solid curves) and

imaginary (dotted curves) parts of the impedance for the opti-

mized single and multi-layered antennas, respectively. It is

also clear from the figures that the impedance of the optimized

single and multi-layered antennas is 245.19þ j94.16 X and

1929.05þ j1811.33 X, respectively. Choi and Sarabandi44

have found an impedance of 2400 � j1200 X for their bow-tie

antenna, meaning that our results are comparable to those

reported in the literature. While calculating the impedance, we

noted that the values of the magnetic field had not changed

significantly, although the values of the electric field were sig-

nificantly higher in the multi-layered antenna, which seems to

indicate that the higher electric fields in the multi-layered

antenna partially explain the higher impedance of the multi-

layered antenna. If we consider that the intrinsic impedance of

free-space is about Z0¼ 377 X and that the reflectance can be

estimated by R ¼ j ZL�Z0

ZLþZ0j2 (ZL is the impedance of the nano-

antenna), then the reflectances for single and multi-layered

antennas are 6.63% and 66.17%, respectively. The reflectance

formula R ¼ j ZL�Z0

ZLþZ0j2 assumes that the source is solely excit-

ing the antenna, and for a small source placed close to the

antenna, we got reflectance values close to the calculated

ones. Given this initial estimate, it seems that impedance

matching does not provide a good explanation for the larger

electric field in the multi-layered structure.

However, in many practical situations, an array of nano-

antennas will be fabricated and illuminated by a source with

a large spot-size diameter (e.g., coming from a laser source),

meaning that the source will also illuminate regions with no

nano-antennas. We have calculated the reflectance for an

array where the antennas are separated by 10 lm in a square

array (this distance is chosen so that the antennas do not cou-

ple with each other), and the calculated reflectances for the

single and multi-layered antennas are 3.01% and 4.08%,

respectively (it is true that this reflectance will strongly

depend upon how you configure the array, but we have just

used the array as an example). The significant lower reflec-

tance for the multi-layered antennas can be explained by the

fact that the source with a large spot diameter is illuminating

mostly the silica substrate and the antennas are small struc-

tures on top of the substrate.

FIG. 10. Distribution of Frel along the lateral direction in the gap of the

nano-antenna at y¼ 250 nm and z¼ 0 for the optimum parameters:

H¼ 500 nm, FF¼ 50%, a¼ 90�, l¼ 211 nm, w¼ 422 nm, and g¼ 50 nm.

FIG. 11. Favg as a function of wavelength for the optimum parameters:

H¼ 500 nm, FF¼ 50%, a¼ 90�, l¼ 211 nm, w¼ 422 nm, and g¼ 50 nm.

FIG. 12. Effect of the gap width (g) on Favg at the wavelength of 1053 nm

by keeping other parameters constant as H¼ 500 nm, FF¼ 50%, and

a¼ 90�.

133106-7 Morshed, Khaleque, and Hattori J. Appl. Phys. 121, 133106 (2017)

It is true that the impedance matching could be

improved by using tapers45,46 or other impedance matching

techniques, for example, a proper choice of parallel load

(i.e., different permittivity materials in the gap) can be used

for a good matching between the antenna and the feeder

without changing the dimension.47 However, it would add

further complexity to our devices which are generally

excited through the vertical direction.41 It might also be chal-

lenging to fabricate the impedance matching structures on

top of the existing antennas, leading to complicated multi-

step fabrication processes. In addition, given the small area

of the antennas, most of the reflected fields will likely be

scattered into different directions rather than returning to the

laser source.

IV. CONCLUSION

In conclusion, we have designed a bowtie-composite

structure by using gold and silica materials and examined how

to optimize antenna parameters to get the highest electric field

enhancement factor. For the optimum parameters, the proposed

antenna reached a relative and average electric field enhance-

ment factor of 32.3 and 17.2, respectively, which are six and

about four times higher compared to a pure gold bowtie nano-

antenna for the gap width of 50 nm at the wavelength of

1053 nm. Due to the improved performance of the nano-

antenna, it might be useful for different applications such as

surface enhanced Raman spectroscopy and nano light emitting

diode (nano-LED) sources. Moreover, its smaller spot size

than the subwavelength gap can help single molecule detec-

tion. Although the antenna has been optimized with a fixed air

gap between the two arms, the smaller the gap is, the larger the

electric field enhancement factor is (although very small gaps,

i.e., g< 30 nm, are hard to be fabricated in practice).

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial

support of the University of New South Wales (Canberra

Australia). We also acknowledge the financial support from

the Asian Office of Aerospace Research and Development

(AOARD)-USAF (FA2386-15-1-4064) and the Australian

Research Council (ARC) (LP160100253).

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