Advances in Nanoparticles, 2013, 2, 259-265
http://dx.doi.org/10.4236/anp.2013.23036 Published Online August 2013 (http://www.scirp.org/journal/anp)
Conical Nanoparticles for Blood Disease Detection
Luigi La Spada, Renato Iovine, Richard Tarparelli, Lucio Vegni
Department of Engineering, Roma Tre University, Rome, Italy
Received May 6, 2013; revised June 6, 2013; accepted June 14, 2013
Copyright © 2013 Luigi La Spada et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
Metallic nanoparticles play an important role in the design of sensing platforms. In this paper, a new electromagnetic
study for conical metal nanoparticles, working in the Near Infrared and Visible frequency regime, is proposed. The
structures consist of inclusions, arranged in an array configuration, embedded in a dielectric environment. The aim of
this work is to develop new analytical models, in order to describe the nanoparticles electromagnetic behavior in terms
of extinction cross-section (absorption and scattering). The closed-form formulas link the conical nanoparticles geome-
trical and electromagnetic parameters to their resonant frequency properties in terms of wavelength position, magnitude
and bandwidth. The proposed models are compared to the numerical results and to the experimental ones, reported in
literature. Good agreement is obtained. The proposed analytical formulas represent useful tools for sensing applications.
For this reason, exploiting such models a new sensing platform able to detect different blood diseases is obtained. Nu-
merical results confirm the capability of the proposed structure to be used as a sensing platform for medical diagnostics.
Keywords: Conical Nanoparticles; Analytical Models; Sensitivity; Sensing Platform; Blood Diseases
1. Introduction
Nanoparticles are of great scientific interest due to their
potential role in several application fields such as medi-
cine, optics and electronics. When an electromagnetic field
interacts with metal particle, collective electron charge
oscillations arise. Such a phenomenon is called Localized
Surface Plasmon Resonance (LSPR). At the resonant
condition nanoparticles exhibit enhanced electromagnetic
near-field, highly localized in their neighborhood.
Moreover, far-field particle scattering is also enhanced
by the resonance. Light intensity enhancement is a cru-
cial aspect of LSPR structures and localization leads to a
very high spatial resolution. Such particular optical prop-
erties of metallic nanoparticles make them suitable for
several applications involving optical and photonic ones
[1,2], biochemical sensing and detection [3,4], protein
analysis [5,6], cell membrane function [7], biomedical
applications [8,9], food quality analysis [10] and imaging
[11,12]. The use of nanoparticles in medicine offers some
exciting applications, such as drugs delivery, heating the-
rapy techniques, in vivo tumor cell targeting and early
diagnostic techniques [13].
Past researches on metallic nanoparticles have concen-
trated only on two main issues: fabrication processes and
experimental characterization techniques. The literature
is almost silent on metal nanoparticles electromagnetic
properties modeling. Nanoparticles analytical models turn
out to be a useful tool in order to study their optical pro-
perties; in particular how such structures influence and
interact with the surrounding environment, and how to
manipulate, control and design their electromagnetic pro-
perties for specific required applications. Therefore, this
paper attempts to present new design methods for conical
metallic nanoparticles with desired electromagnetic pro-
perties. The findings of this study are expected to provide
a greater understanding of their electromagnetic behavior
and the possibility to use them for sensing applications.
The choice of conical particles is up to their use for bio-
medical applications [14] and Near-Field Optical Micro-
scopy Probes [15]. In addition to this, the tip ensures
stronger electric field localization [16].
The article is structured as follows: first of all the elec-
tromagnetic properties of metallic conical nanoparticles
are evaluated in terms of extinction cross section (ab-
sorption and scattering). For this purpose, new analytical
closed-form formulas, linking the geometrical and the
electromagnetic parameters of such nanoparticles with
their resonant frequency properties, are evaluated. This is
followed by a comparison among analytical, numerical
and experimental results. The capability to manipulate
and control the electromagnetic phenomenon, by exploit-
ing the proposed analytical models, on the nanometer
C
opyright © 2013 SciRes. ANP

L. LA SPADA ET AL.
260
scale, opens up several possible applications. For this
reason, in the second part of this article the use of nano-
particles for sensing applications is presented. In particu-
lar, their sensitivity performances are analyzed and dis-
cussed. Finally, by exploiting the proposed electromag-
netic models a new sensing platform for the detection of
different blood diseases is proposed.
2. Analytical Models and Electromagnetic
Properties of Conical Nanoparticles
In this section the mathematical modeling of conical metal
nanoparticles electromagnetic properties is developed.
First of all, the electromagnetic problem is formulated.
Then, the absorption and scattering cross-section models
are obtained. Finally, in order to verify the proposed ana-
lytical models, a comparison with full-wave simulations
and experimental values, existing in literature, is reported.
2.1. Formulation of the Electromagnetic Problem
The resonant behavior of the individual structure is stu-
died in terms of a quasi-static approximation. In particu-
lar, the general analytical expression of the nanoparticle
polarizability is derived and the dependence of the inclu-
sion polarizability on its geometry, its metallic electro-
magnetic properties, and the permittivity of the surround-
ing dielectric environment, is presented. The proposed
structures consist of resonant metallic conical inclusions,
arranged in an array configuration, whose frequency re-
sponse is modified through the refractive index variation
of the surrounding dielectric environment. Let us assume
that the structure is excited by an impinging electromag-
netic plane wave, having the electric field E parallel and
the propagation vector k perpendicular to the nanoparti-
cle axis, respectively (Figure 1). The geometrical pa-
rameters considered in this study are shown in Figure 1,
being a the bottom radius and h the height of cone. The
nanoparticles electromagnetic properties are revealed in
terms of extinction cross-section. The nanostructure holds
specific resonant frequency properties in terms of posi-
tion, magnitude and bandwidth, depending on its geo-
metrical (shape, dimensions) and on the electromagnetic
Figure 1. Conical nanoparticle geometry: a bottom radius,
h height of cone.
characteristics of the metal it is made of. In order to study
the nanoparticle electromagnetic properties the following
assumption must be done:
 the particle is considered “electrically small”: its size
is much smaller than the operative wavelength in the
surrounding medium [17]. Consequently, its resonant
behavior can be studied in terms of quasi-static ap-
proximation;
 the particle is considered homogeneous and the sur-
rounding dielectric environment is a homogeneous,
isotropic and non-absorbing medium.
2.2. Absorption and Scattering Cross-Section
Analytical Models
Under such conditions the nanoparticles resonant optical
properties can be evaluated starting from their polariza-
bility expressions. It is well known that [18] the polari-
zability component along the z-axis direction (in the limit
of quasi-static approximation) can be expressed as:

ie
ze
ezie
VL






(1)
where V is the particle volume, εe is the surrounding di-
electric environment permittivity, εi is the inclusion di-
electric permittivity and Lz is the depolarization factor.
Therefore, as shown in (1) the inclusion electromagnetic
properties are highly dependent on its geometrical pa-
rameters (V and L), on the metallic material properties (εi)
and on the surrounding environment (εe).
Let us consider now that inclusions permittivity is de-
scribed by a Drude model permittivity as follows:
2
2
p
ij





 (2)
being ε∞ the permittivity at the high frequency limit, ω =
2πf the angular frequency, ωp the plasma frequency and γ
the collision frequency.
Such particles are embedded in a dispersionless and
lossless surrounding environment with permittivity εe. It
is well known that the dipolar polarizability α is maxi-
mized (the nanoparticle is at its resonant condition) when
its denominator goes to zero in both its real and imagi-
nary part [18]. By inserting (2) in the general particle
polarizability expression (1) the resonant behavior of the
nanoparticle is reached when:
42
420
0af af a

 (3)
where f is the resonant frequency with:

2
4
4
22 4
20
2
16π1
8π
4π
zez
z
aLL
a
aaa

24
0
L





 
(4)
We obtain the corresponding resonant wavelength con-

L. LA SPADA ET AL. 261
dition:
2
2042
0
4
2
aaaa
a
c


 (5)
Using (5) it is possible to predict how the particle
geometrical parameters (Lz(a, h)), the metal electromag-
netic properties (ε∞ and γ) and the surrounding dielectric
environment (εe) affect its resonant behavior in terms of
resonant position. To describe the entire nanoparticles
electromagnetic behavior it is necessary to evaluate their
electromagnetic extinction cross section properties, in
terms of scattering and absorption. Separated evaluation
of the absorption and scattering phenomenon for each
nanoparticle is crucial to understand why certain struc-
tures are preferred to others for specific applications. In
other words, by evaluating closed-form formulas for ex-
tinction cross-section properties, it is possible to correlate
the particle electromagnetic properties with its geometri-
cal characteristics, in order to describe its resonant be-
havior, in terms of wavelength position, magnitude and
bandwidth. The analytical electromagnetic solution exists
only for a restricted number of particle geometries, such
as sphere and cylinder [19], cube [20], disc and needle
[21,22]. For any other arbitrary shapes the electromag-
netic solution is given by numerical approaches [23].
It’s known [24] that the corresponding expressions,
linking the inclusion polarizability to its extinction prop-
erties, for absorption cross-section (Cabs) and scattering
cross-section (Csca) read respectively:


Im
abs
Ck

 (6)
42
6π
sca
k
C

 (7)
where k = 2πn/λ is the wave-number, λ is the wavelength
and n = √ε is the refractive index of the surrounding di-
electric environment.
Then, by following the same procedure in [24] and
considering the electric field polarization and the particle
geometry, the absorption and scattering cross-section
analytical models have been developed and here reported,
respectively:


2
πIm
3
ei e
abs
econe ie
ha
Ck L
 

 




(8)


2
2
4
π
3
6π
ei e
sca
econe ie
ha
k
CL
 





(9)
where Lcone reads:
2
2
11
1
241
cone
L
a
h











(10)
In Figure 2 a comparison between analytical and nu-
merical results [25], for extinction cross-section spectra,
is presented. In particular:
 for gold nanoparticles, experimental values [26] of
the complex permittivity function have been used;
 the surrounding dielectric medium is considered to be
vacuum.
2.3. Comparison between Analytical Model,
Numerical Simulations and Experimental
Values
The proposed analytical models are verified through the
comparison with full-wave numerical simulations, and
the experimental data existing in literature for gold [15],
silver [27] and copper [28] conical particles, for different
geometrical parameter values as shown in Table 1, where
the relative errors are evaluated and reported. Good
agreement among all three results was reached. The rela-
tive errors are expressed as:
analitical numerical
numerical
an
E




 (11)
analitical experimental
experimental
ae
E




 (12)
3. Sensitivity Analysis
In this paragraph the sensitivity properties of conical
nanoparticles are evaluated. Sensitivity is commonly de-
Figure 2. Comparison between numerical and analytical
model for extinction cross-section (a = 20 nm; h = 20 nm).

L. LA SPADA ET AL.
262
Table 1. Comparison of resonant wavelengths for gold, silver and copper conical particles: analytical, numerical and ex-
perimental values (gold [15], silver [27] and copper [28]).
Resonant wavelength (λ [nm])
Particle Size [nm]
Analytical values Numerical values Experimental values
Ea−n (%) Ea−e (%)
a = 45, h = 25 540 570 550 5.263 1.818
a = 45, h = 50 560 590 570 5.085 1.754
gold
a = 45, h = 100 620 650 610 4.615 1.639
a = 28, h = 93 650 670 650 2.985 0
a = 46, h = 100 580 600 586 3.333 1.024
silver
a = 70, h = 115 582 610 588 4.590 1.020
a = 190, h = 20 750 780 764 3.850 1.83
a = 190, h = 40 720 740 713 2.70 0.98
copper
a = 190, h = 60 660 700 685 5.71 3.65
fined as S = Δλ/Δn, expressed in nm/RIU (Refractive
Index Unit). Typically, if the refractive index variation
range is sufficiently narrow, both analytical results (Fig-
ure 3(a)) and full-wave simulations (Figure 3(b)) high-
light that the input-output relation between refractive in-
dex and resonant wavelength position can be considered
linear. A test material, surrounding the nanoparticle, with
a varying refractive index n in the range 1 - 3 has been
chosen.
In Table 2, instead, analytical, numerical and experi-
mental sensitivity for gold [29], silver [30] and copper
[31] conical particles are compared.
4. The Nanocone-Based Sensor
(a)
In this section the design of a gold conical nanoparticle
array is proposed. As it will be shown by numerical re-
sults, the proposed structure can be used as a sensing
platform for the detection of blood diseases.
Dielectric properties of biological samples can be de-
scribed by the complex refractive index as:
cr
nnjk (13)
where nr is the real part and k is the imaginary part of
refractive index of the sample. Its electromagnetic prop-
erties are related to the real and imaginary part of the
refractive index as a function of the frequency. Tissue
dielectric properties and their frequency response are the
results of the interaction between the electromagnetic
radiation and their constituents at molecular and cellular
level. These variations imply significant changes in their
electromagnetic properties.
(b)
Figure 3. Variation of the resonant wavelength as a function
of the refractive index of the surrounding medium (a = 20
nm; h = 20 nm, gold nanoparticle): (a) analytical values; (b)
full-wave simulations results.
It’s well known that hematological diseases induce
structural, biochemical and mechanical changes in Red
Blood Cells (RBCs) [32]. The structural variations imply
significant changes in cell electromagnetic properties.
part. As a result it is possible to detect such differences
by permittivity measurements on the considered sample.
The refractive indices of different kind of RBCs, in the
optical frequency range, differ in their real and imaginary

L. LA SPADA ET AL. 263
Table 2. Sensitivity values for gold, silver and copper coni-
cal particles: comparison among analytical, numerical and
experimental values (gold [29], silver [30] and copper [31]).
Sensitivity [nm/RIU]
Particle Analytical
sensitivity
Numerical
sensitivity
Experimental
sensitivity
gold 300 275 239
silver 200 210 197
copper 280 250 200
Therefore the main purpose of this paragraph is to
correlate the sensor electromagnetic properties with the
ones of the substance under test.
To detect the aforementioned changes (corresponding
to different blood pathological states) a new sensing plat-
form is proposed. In Figure 4 the sensing system opera-
tion pattern is shown. The sensor, without any Material
Under Test (MUT), has a specific resonant frequency.
Once the material to study is placed, the system “sensor-
MUT” is illuminated by an electromagnetic field. The
nanoparticle-based sensor (yellow) is in direct contact
with the biological sample (green). In this configuration,
the MUT electromagnetic properties play a crucial role in
the variation of the total effective permittivity and of the
sensing platform scattering properties. The signal detected
(scattering cross-section) will have the resonant wave-
length position, magnitude and bandwidth depending on
the electromagnetic characteristics of the overall system
“sensor-MUT”. In particular, this sensor consists of gold
conical nanoparticles arranged in an array configuration,
deposited on a SiO2 substrate as shown
in Figure 4.

2
SiO 2.08
 

The possibility to implement metallic cones on flat di-
electric substrates is well established in literature, several
kind of fabrication techniques are possible, for example:
nano-imprint lithography and electron beam evaporation
[33], electron beam induced deposition [34], templating
approach [35] and nanotransfer printing (nTP) method
[36].
By using the analytical models proposed in the previ-
ous section, a new sensing platform has been designed to
resonate in the range 900 - 1200 nm.
To describe the electromagnetic behavior of the bio-
logical sample under test, RBCs refractive index models
proposed in [37] have been exploited. The scattering co-
efficients properties of the sensor change their position,
depending on the different RBCs structural modifications
(Figure 5). As a result, the sensor is capable to detect
human red blood cells structural modifications, allowing
us to detect different blood diseases, by refractive index
measurements.
As shown in Figure 5 different spectral responses
have been reported in order to show the sensor capability
Figure 4. Sensing system operation pattern.
Figure 5. Scattering cross-section spectra for different struc-
tural changes in RBCs (a = 20 nm; h = 100 nm).
to distinguish healthy RBCs from specific diseases such
as Schizont and Trophozoite malaria.
5. Conclusions
In this paper a new study on metallic nanoparticles elec-
tromagnetic properties modeling was proposed. The con-
sidered structures were metallic cones, embedded in a
surrounding dielectric environment, working in the In-
frared and Optical frequency regime.
The electromagnetic modeling of nanoparticles was ob-
tained in order to design new sensing platform. In this
regard, new analytical models describing absorption and
scattering cross-section properties, in terms of wavelength
position, magnitude and amplitude width, were deve-
loped. Such new design formulas link the nanoparticles
resonant properties with their structural and electromag-
netic parameters. Then, the proposed models were com-
pared to numerical simulation results and experimental
data. A good agreement among analytical, numerical and
experimental values was obtained. The sensitivity of the
nanoparticles was studied and discussed. The possibility
to control nanoparticles electromagnetic properties, by
exploiting the proposed analytical models, paves the way
to several possible applications. In particular, the pro-
osed structure was designed in order to detect different

L. LA SPADA ET AL.
264
blood diseases. Numerical results have demonstrated the
capability of conical particles array to be used as a sens-
ing platform for medical diagnostics.
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