Core-shell nanospheres under visible light: Optimal absorption, scattering, and cloaking

Abstract

Discovering peak-performing components, under certain structural and material constraints, is vital for the efficient operation of integrated systems that incorporate them. This becomes feasible by comprehensive scanning of the parametric space for one of the simplest classes of three-dimensional particles used in visible-light metasurface applications: the core-shell nanosphere. For each combination of actual media picked from a long list, the highest-scoring nanoparticles in terms of absorbance, scattering, and cloaking are recorded, while their near-field visualizations unveil the resonance mechanisms that make them so special. The reported results offer additional degrees of freedom in modeling collective meta-atom interactions and contribute to the photonic inverse design by providing the upper limits in the performance for particles of a basic geometry.

Full text

PHYSICAL REVIEW B 99, 075305 (2019)
Core-shell nanospheres under visible light: Optimal absorption, scattering, and cloaking
Arsen Sheverdin and Constantinos Valagiannopoulos*
Department of Physics, School of Science and Technology, Nazarbayev University,
53 Qabanbay Batyr Avenue, Astana KZ-010000, Kazakhstan
(Received 4 December 2018; revised manuscript received 14 January 2019; published 19 February 2019)
Discovering peak-performing components, under certain structural and material constraints, is vital for
the efficient operation of integrated systems that incorporate them. This becomes feasible by comprehensive
scanning of the parametric space for one of the simplest classes of three-dimensional particles used in visible-
light metasurface applications: the core-shell nanosphere. For each combination of actual media picked from a
long list, the highest-scoring nanoparticles in terms of absorbance, scattering, and cloaking are recorded, while
their near-field visualizations unveil the resonance mechanisms that make them so special. The reported results
offer additional degrees of freedom in modeling collective meta-atom interactions and contribute to the photonic
inverse design by providing the upper limits in the performance for particles of a basic geometry.
DOI: 10.1103/PhysRevB.99.075305
I. INTRODUCTION
Placing many identical (or not) small particles across a
surface makes an illusion of extraordinary boundary con-
ditions, which is the principle of metasurfaces with their
countless utilities [1]. Collective operation of these inclusions
placed in lattice configurations can dramatically change the
electric and magnetic field components from both sides of
the lattice, leading to reformulating reflection and refraction
laws, admitting arbitrary field transformations [2]. That abil-
ity to tailor and manipulate local fields in a subwavelength
domain also makes these tiny objects exceptional building
blocks of integrated optical circuits that process information
at the nanometer scale [3]. Suitably selected and carefully
distributed particles can finally build powerful metamaterial
platforms achieving complete control of wave amplitude,
phase with subwavelength spatial resolution, the key feature
behind multiple nanophotonic elements [4].
Among numerous candidate particles, core-shell spheres
are placed prominently for reasons related to analytical solv-
ability permitting efficient optimizations and symmetry dic-
tating angle insensitivity. Such a structure, possessing two
volumes (internal and external), provides the minimal con-
dition to support resonance effects being responsible for any
extremum in the device’s performance. According to rigorous
Mie theory, the response of a small core-shell nanosphere
comprises two terms corresponding to electric and magnetic
dipoles; once each of them gets maximized, the respective
(electric or magnetic) Mie resonance occurs [5,6]. When
both of the terms are small, the particle gives a minimum
overall response which, if appears in the wavelength vicinity
of either of the two maxima, yields to asymmetric line shape,
an identity characteristic of the so-called Fano resonance [7].
Finally, if the permittivities of the core and the shell are of
opposite sign, the well-known surface plasmon resonance [8]
*konstantinos.valagiannopoulos@nu.edu.kz
can manifest itself through large signal concentration on the
plasmonic/dielectric boundary.
Such resonance effects always accompany particle’s
extreme responses in terms of its two basic operations:
scattering and absorption. The scattering from a core-shell
nanosphere determines the way it is perceived by its external
world; thus, it has attracted substantial attention [9] and
helped in the formulation of more general treatments
concerning larger classes of meta-atoms [10]. In particular,
superscattering by spherical nanoparticles has been reported
by superimposing multiple resonances corresponding to
different total angular momenta [11,12] and utilizing nonlocal
coatings [13]. Absorption, on the other hand, is associated
to what is happening inside the lossy particle and is crucial
when conversion of electromagnetic energy to thermal or
other forms is required. As a result, boosting light trapping
by core-shell nanospheres has been extensively examined in
various contexts, involving plasmon-exciton interactions [14]
or total internal reflection in thin films [15]. Importantly, high
losses do not necessarily imply substantial absorptivity since
the field gets “discouraged” from entering the conducting
volume owing to the large impedance mismatch with the
lossless background. That matching condition is also a
prerequisite for cloaking in core-shell particles which dictates
minimum scattering power and very low losses, a rather
challenging combination. The well-established scattering
cancellation technique [16] makes a spherical volume
transparent via coating it with a layer of suitable thickness and
texture but only at a specific frequency; indeed, the cumulative
scattering by an object across the entire electromagnetic
spectrum is an increasing function of its size [17].
The core-shell resonant nanospheres with considerable
absorbing, scattering, or cloaking scores can be used in a
number of different applications. As far as absorption is con-
cerned, similar particles are employed in photovoltaics; broad-
band light collection occurs in the host thin-film solar cells
[18] assisted by developed surface plasmons and followed
by energy conversion into energetic electrons and holes at
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ARSEN SHEVERDIN AND CONSTANTINOS VALAGIANNOPOULOS PHYSICAL REVIEW B 99, 075305 (2019)
the nearby semiconductor [19]. Furthermore, photothermal
therapy, namely, the selective killing of cancer cells through
heat concentration, has been accomplished [20] with highly
absorbing core-shell nanospheres, which can be additionally
used to improve the efficacy of other light-activated biological
treatments [21]. When it comes to spherical particles scat-
tering response, it is the basis of several nanodevice models
for data-storage units facilitated by photon tunable energy-
level upconversion [22] or multicolor labeling and tagging in
optical imaging [23]. When the core-shell spherical geometry
is properly combined with nonlinear materials, one can also
achieve huge scattering switching [24] or enhanced second-
order harmonic generation [25], while filling the core with a
gain medium makes emitters with fast spontaneous emission
feeding plasmonic nanoantennas [26].
In this work, we regard such a simple but multifunctional
structure as the core-shell nanosphere, illuminated by visible
light and made of actual media with realistic losses. We
consider a set of available materials and, for each core-shell
combination of them, we pick the most efficient designs in
terms of absorption and (high or low) scattering by record-
ing their physical sizes and the operational wavelength. As
our optimization routine scans the visible spectrum, the per-
missible range of the particle’s radius changes accordingly
to capture nanospheres with optical size neither too small,
yielding a non-negligible response, nor too big to support co-
herent operation in metasurface lattices. We report numerous
nanospheres working at various colors of incoming light that
absorb or scatter tenfold the incoming power passing through
their geometrical cross section, while our cloaked meta-atoms
perturb the background field by less than 1%. The variety
of the presented alternative designs combined with their high
fabrication potential through physical [27] and chemical [28]
methods provides additional degrees of freedom in modeling
and realization of multiobjective metasurfaces.
This study tests the limits of a significant class of particles
by exhaustively searching across a quite extended parametric
space including a long list of materials and the entire spectrum
of visible frequencies. Importantly, the optical size of the
considered inclusions is free to vary within a substantial value
range meeting the requirements of practically all metasurface
applications. The proposed optimal designs do not necessarily
correspond to universal maxima in absorbing and scattering
performance of core-shell nanospheres [29]; however, they
certainly hit high scores which can only be surpassed by
more complex designs in structure or texture [30]. Therefore,
we believe that our work contributes to the recent paradigm
shift of photonic inverse design [31,32] by focusing on simple
shapes and actual media.
II. FORMULATION AND METHOD
A. Fields and power
Consider a spherical particle comprised of a core with
radius acovered by cladding of thickness (b−a), illuminated
by visible light in the form of a monochromatic plane wave
(with oscillating frequency ω) traveling into free space [as
in Fig. 1(a)]. The dispersive relative complex permittivities
of the core (r<a) and the shell (a<r<b) are denoted by
ε1=ε1(ω) and ε2=ε2(ω), respectively. The symbols (r,θ,ϕ)
(a)
a/b
b/
λ
0
0.2 0.4 0.6 0.8
0.05
0.1
0.15
0.2
0.25
fixed λ0min
max
(b)
400 450 500 550 600 650 700
0 (nm)
3
4
5
6
7
8
max P/Pinc
(c)
a
b
core
shell
visible
light
0
FIG. 1. (a) The structural model of a core-shell nanosphere il-
luminated by a plane wave of visible light. (b) Typical variation of
absorbed/scattering power metric P/Pinc with respect to aspect ratio
a/band optical size b/λ0for fixed materials and wavelength. (c)
Typical variation of maximum P/Pinc as a function of operational
wavelength λ0for fixed materials.
are used for the related spherical coordinates, while the equiv-
alent Cartesian ones read (x,y,z); the suppressed harmonic
time is of the form e+iωt. For simplicity and without loss
of generality (due to the spherical symmetry), we assume
that the incident wave propagates along the +zaxis and its
electric field vector is always parallel to the xaxis oscillating
with amplitude E0>0 (measured in volts per meter). This
background field can be decoupled into two field terms, each
of which satisfies Maxwell’s laws: one term with no radial
electric component (TE) and another one with no radial
magnetic component (TM). These terms can be expressed
as series of spherical harmonics, which dictate the θ−and
ϕ−dependence of the field quantities in all the regions
defined by the concentric and entire surfaces (rigorous Mie
theory). After imposing the necessary boundary conditions,
the scattered fields for r>b(electric field vector of the TE
set and magnetic one for the TM set) take the forms
ETE
scat =E0
+∞

n=1
STE
nhn(k0r)−ˆ
θcsc θPn(θ) cos ϕ
+ˆ
ϕP
n(θ)sinϕ,
HTM
scat =E0
η0
+∞

n=1
STM
nhn(k0r)−ˆ
θcsc θPn(θ)sinϕ
−ˆ
ϕP
n(θ) cos ϕ,
where Pn(θ) is the Legendre polynomial of first order, degree
n, and argument cos θ, and hnis the spherical Hankel function
of order nand second type. The symbols k0=2π/λ0and
η0stand for the wave number and the wave impedance into
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CORE-SHELL NANOSPHERES UNDER VISIBLE LIGHT PHYSICAL REVIEW B 99, 075305 (2019)
vacuum. The coefficients STE/TM
n,are complex dimensionless
quantities and not shown here for brevity [16].
The power Pscat carried by the TE and TM scattered compo-
nent into vacuum (which constitutes a self-consistent electro-
magnetic field), expresses how much the sphere perturbs the
background field distribution externally to it. It can be easily
computed with the use of Poynting’s theorem and expansions
of hn(k0r) for large arguments k0r1 (in the far region), as
follows (Ref. [33], pp. 102–104):
Pscat =W
+∞

n=1
n2(n+1)2
2n+1STE
n
2+STM
n
2,(1)
where W=πE2
0
k2
0η0>0 is a quantity measured in watts. The
power absorbed by the particle, given the fact that one or
both of the constituent media is lossy, namely, Im[ε1]= 0
or Im[ε2]= 0, is evaluated by applying again Poynting’s
theorem, but for the total field into free space this time. Indeed,
if we integrate the power spatial density across any sphere of
radius r>b(even the infinite k0r→+∞one), we obtain
Pabs =−Pscat −W
+∞

n=1
n(n+1)ReinSTE
n+STM
n.(2)
Obviously, Pscat,Pabs >0, which means that the series in
Eq. (2) should converge to negative values smaller than
(−Pscat /W). In the absence of any losses, we have Pabs =0
and the aforementioned sum is equal to (−Pscat/W).
In order to render the absorbed and scattered power more
meaningful, we should normalize them by suitable quantities.
More specifically, we can use as a reference parameter the
power of the incident illumination passing through the geo-
metrical cross of the scatterer, namely, Pinc =πE2
0b2
2η0. The ratio
Pabs /Pinc is equal to the absorption cross section (Ref. [33],
pp. 69–77) of the particle σabs over the area of the sphere
as seen by the incoming plane wave (πb2). Similarly, Pscat
is normalized by the same quantity and we obtain the metric
Pscat /Pinc which equals the scattering cross section σscat (mea-
sured in square meters) again normalized by (πb2).
B. Maximization scheme
Our aim is to consider numerous bulk media which are
available for applications in the visible part of the wavelength
spectrum, 400 <λ
0<700 nm, by taking into account their
frequency-dispersive behavior. The materials are selected
based on their electromagnetic diversity and experimental
relevance as usual [34]. From this large set of employable
materials, we would like to pick those combinations, in
suitably sized core-shell nanospheres, which overdeliver in
terms of absorption and scattering. Our results could serve
as a directory of maximal performances under the condition
of using real media in simple two-layered structures and as
benchmarks for smarter designs to pass.
We follow a systematic approach that scans all the re-
garded wavelengths λ0and, for each of them, selects the
configuration of dimensions (a,b) giving maximal Pabs /Pinc or
Pscat /Pinc. In the optimization, we do not avoid homogeneous
spheres solely made of one material (a/b→0,1) and thus
0<a/b<1; for the size of the nanosphere, on the contrary,
we pose an upper bound of half wavelength and exclude too-
small structures (0.05 <b/λ0<0.25). A typical variation
of our metrics P/Pinc on an (a/b,b/λ0) map is depicted
in Fig. 1(b) at fixed λ0. From several local maxima, we
select the strongest one and we store it (together with the
dimensions of the regarded design) as the best performance
that can be achieved by a specific pair of materials for the
considered operational wavelength λ0. The aforementioned
global maximum corresponds to one point in the graph of
Fig. 1(c), where the highest scores P/Pinc for each wavelength
are shown as a function of λ0. Potential abrupt changes
of the curve are attributed to the fact that the represented
quantity max{0<a/b<1,0.05λ0<b<0.25λ0}P/Pinc is an outcome of
maximization and thus no smooth behavior is necessarily
expected. From the graph of Fig. 1(c), we pick only one ul-
traperforming design for absorption or scattering with certain
frequency preference.
It should be stressed that, unlike the inequality 0 <a/b<
1 that is imposed by the structure, the constraint 0.05 <
b/λ0<0.25 is an artificial one. In particular, extremely small
sizes b/λ0→0 usually give very weak scatterers and ab-
sorbers, while nanospheres bigger than λ0/2 cannot serve as
unit cells for collective operation in metasurfaces, arrays, and
networks [35]. As has been mentioned [36], no lower limit
for bmeans that the best performance emerges for a reso-
nant atom with its extremely tiny size. Therefore, on certain
occasions, the largest value of P/Pinc across the rectangular
plane of Fig. 1(b) is recorded for the low limit b/λ0=0.05,
which means that the true maximum is exhibited for a small
particle outside of the considered map. If the maximum of the
curve in Fig. 1(c) happens for such a case, we check secondary
peaks to neighboring (or not) wavelengths. Therefore, the
reported overdelivering structures always correspond to an
interior (not boundary) extremum to the map of Fig. 1(b),
which sometimes emerges for b/λ0∼
=0.05.
Our search for optimal designs contains several mate-
rials including bulk metals, semiconductors, and inorganic
dielectrics, for which permittivity profiles are obtained from a
well-known material database [37], containing measurements
from established references [38,39]. In the following, we
assume that the dielectric constants ε1and ε2of our media
remain the same at a specific wavelength λ0, regardless of
the layer thicknesses. Certain corrections to the damping of
metals by taking into account the shape and the size of the
samples are possible [40]; however, given the relatively large
diameter of the particles (at least 40 nm or 10% of the
operational wavelength), we assume such an influence to be
of restricted importance.
The two materials in such a simple design should be chosen
as different as possible (Re[ε1]Re[ε2]<0); otherwise the
conditions for resonance [3] cannot be fulfilled. Therefore,
from the aforementioned available media, we have concluded
that the most remarkable performances related to absorption
and scattering emerge for combining a metal in the visible
with a nonplasmonic material, regardless of their relative po-
sition (shell or core). This placement-indifference feature can
be attributed to the way that the field “embraces” the sphere as
a finite-size scatterer which, unlike the infinite nanowire case
[41], supports symmetric interplay between the response from
any two antipodal points of its surface. By trying every single
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ARSEN SHEVERDIN AND CONSTANTINOS VALAGIANNOPOULOS PHYSICAL REVIEW B 99, 075305 (2019)
TABLE I. Optimally absorbing nanospheres with metallic cores (ε1, different rows) and dielectric shells (ε2, different columns).
Performance Pabs /Pinc at specific wavelengths λ0(indicated also by the corresponding color of the visible spectrum) and optimal geometric
sizes (a,b) for each combination of the available materials at which the proposed core-shell sphere of Fig. 1(a) absorbs maximally the
incident field. Shaded boxes denote poor performance.
ABSORPTION
Core/Shell
Aluminium
antimonide
(AlSb)
Cadmium
sulfide
(CdS)
Iron(III)
oxide
(Fe2O3)
Iron(II,III)
oxide
(Fe3O4)
Gallium
arsenide
(GaAs)
Gallium
phosphide
(GaP)
Titanium
oxide
(TiO2)
Silver
(Ag)
6.50 @ 670 nm
b/λ0=0.070
a/b =0.66
6.70 @ 530 nm
b/λ0=0.070
a/b =0.54
4.64 @ 625 nm
b/λ0=0.086
a/b =0.62
9.63 @ 420 nm
b/λ0=0.052
a/b =0.80
4.48 @ 515 nm
b/λ0=0.082
a/b =0.86
10.40 @ 530 nm
b/λ0=0.051
a/b =0.73
10.31 @ 470 nm
b/λ0=0.051
a/b =0.66
Gold
(Au)
5.92 @ 700 nm
b/λ0=0.074
a/b =0.70
4.21 @ 585 nm
b/λ0=0.086
a/b =0.68
5.89 @ 685 nm
b/λ0=0.074
a/b =0.62
4.18 @ 590 nm
b/λ0=0.090
a/b =0.66
Copper
(Cu)
5.93 @ 690 nm
b/λ0=0.073
a/b =0.72
4.67 @ 600 nm
b/λ0=0.082
a/b =0.64
4.90 @ 630 nm
b/λ0=0.082
a/b =0.72
6.374 @ 64 nm
b/λ0=0.069
a/b =0.70
4.65 @ 605 nm
b/λ0=0.082
a/b =0.60
combination of media, we check the behavior of the device
across all the operating wavelengths λ0and, through the
optimization process described above, we conclude to a single
design working at a specific wavelength. In this way, the tables
presented in the following are populated and contain the best
cases corresponding to each core-shell pair of materials. It
should be stressed that we may miss a highly performing
design for a certain wavelength because a better one appears
at another wavelength; however, the obtained results cover the
entire visible part of the frequency spectrum.
The aforementioned optimization approach can be em-
ployed in more general inverse design schemes with alterna-
tive metrics [instead of the scattering (1) or absorbed power
(2)] related to the examined response like the epsilon-near-
zero (ENZ) features of the considered particles, which accom-
pany numerous interesting interactions [42,43]. Moreover, the
presented methodology may be modified to detect not only ul-
traperforming isolated core-shell nanospheres but also meta-
surfaces made of many of them, working collectively; indeed,
the collective polarizability of a meta-atom is analytically
expressed in terms of the individual one [44]. Further minor
adjustments can be made if the particles are not free standing
but the background incorporates other passive structures, like
a dielectric substrate, commonly utilized when a metasurface
is actually fabricated.
C. Available fabrication techniques
Prior to introducing the results of the proposed optimiza-
tion, it is worth briefly discussing the potential fabrication
methods of core-shell particles, made from a number of
media. Even in the visible, there are several ways of shaping
multilayered nanospheres [45], given the fact that spherical
geometry provides a minimum surface area for a given vol-
ume, a rather natural preference.
One large set of methods in fabricating core-shell nanopar-
ticles concerns chemical reactions that occur across the sur-
face of the core producing the suitable engulfing cladding.
In particular, oxide shells of controllable thicknesses are de-
veloped around metallic spheres via hydrolysis of the related
precursors [28], while the metal passivation method followed
by deposition of surface active agents leads to construction of
similar meta-atoms [46]. Furthermore, an efficient two-step
process of coat synthesis on plasmonic colloids has been pro-
posed, yielding to stable particles able to get transferred into
any solvent [47]. In addition, nanospheres in dimer pairs can
be also self-assembled, since different substances tend to ad-
here to each other, mutually react, and form hybrid structures
[48]. Moreover, colloidal meta-atoms with controlled density
can be grown on thin films via the Langmuir-Schaefer tech-
nique [49] or electron-beam-induced deposition [50], which
do not necessarily concern nanoparticles of spherical shape
[50,51].
Apart from the aforementioned techniques, one can fol-
low physical fabrication methods by directly depositing the
desired media around spherical cores without relying on
chemical reactions. More specifically, core-shell nanoparti-
cles can be prepared through a solution-based template wet-
ting method by exploiting the different interaction degree of
the two comprising media with water [27]. Finally, gas-phase
synthesis makes a low-cost alternative approach according to
which the core gets combusted and its molecules are sprayed
with the suitable covering medium in gas form [52].
In most of the cases described above, the core is metallic,
which is quite a common choice; however, note that designs of
plasmonic shells are also realizable. In particular, metal col-
loids can be deposited around oxides with help from suitable
acidic layers placed in-between [53,54] or by employing pi-
cosecond laser and ultrasonic wave generation in a deionized
water bath [55].
III. OPTIMAL ABSORPTION
In Table I, we show the best designs for each combi-
nation of metallic cores (ε1) and semiconducting or dielec-
tric coats (ε2) operated at specific wavelengths whose color
paints the corresponding cell. Shaded boxes correspond to
poor absorption performance. One directly notices that silver,
due to its low losses and strong plasmonic nature [56], can
adjust itself to resonate with all the available claddings and
at different visible wavelength each time. In general, the
moderate magnitude of losses, even for the semiconducting
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CORE-SHELL NANOSPHERES UNDER VISIBLE LIGHT PHYSICAL REVIEW B 99, 075305 (2019)
TABLE II. Optimally absorbing (maximum Pabs /Pinc) nanospheres with dielectric cores (ε1, different columns) and metallic shells
(ε2, different rows).
ABSORPTION
Shell/Core Air
Aluminium(III)
oxide
(Al2O3)
Cadmium
sulfide
(CdS)
Iron(III)
oxide
(Fe2O3)
Iron(II,III)
oxide
(Fe3O4)
Gallium
phosphide
(GaP)
Titanium
oxide
(TiO2)
Silver
(Ag)
8.53 @ 520 nm
b/λ0=0.050
a/b =0.67
7.06 @ 690 nm
b/λ0=0.053
a/b =0.78
8.88 @ 445 nm
b/λ0=0.050
a/b =0.56
7.79 @ 535 nm
b/λ0=0.050
a/b =0.55
8.60 @ 415 nm
b/λ0=0.051
a/b =0.41
Gold
(Au)
8.93 @ 610 nm
b/λ0=0.050
a/b =0.863
8.40 @ 665 nm
b/λ0=0.051
a/b =0.84
4.41 @ 590 nm
b/λ0=0.078
a/b =0.640
5.46 @ 700 nm
b/λ0=0.061
a/b =0.74
6.07 @ 700 nm
b/λ0=0.057
a/b =0.70
5.37 @ 615 nm
b/λ0=0.070
a/b =0.69
Copper
(Cu)
7.41 @ 590 nm
b/λ0=0.054
a/b =0.82
5.29 @ 590 nm
b/λ0=0.070
a/b =0.72
8.42 @ 690 nm
b/λ0=0.051
a/b =0.80
5.28 @ 695 nm
b/λ0=0.062
a/b =0.72
4.51 @ 700 nm
b/λ0=0.070
a/b =0.80
5.93 @ 700 nm
b/λ0=0.058
a/b =0.70
8.42 @ 695 nm
b/λ0=0.051
a/b =0.80
coats, gives diversity in optimal operational frequency. That
is why CdS and TiO2coats exhibit considerable flexibility
in their frequency preference in proportion to what is the
metallic core inside. On the contrary, AlSb works always
better with red color illumination regardless of the plasmonic
medium that is paired. By inspection of Table I,itisalso
inferred that designs with the highest efficiency tend to be
smaller since the incident power passing through their cross
section is accordingly lower, which is the reason that very thin
meta-atoms are excluded from the adopted scheme [36].
In Table II, we present nanoparticles with notable absorb-
ing performances when the metallic material plays the role
of the coat surrounding a dielectric sphere. Since the metal
is sandwiched between two dielectrics (one of which is air),
two surfaces between opposite-sign permittivities are formed
and the field concentration around the external boundary
(r=b) excites a similar surface plasmon around the internal
one (r=a); therefore, the field in the lossy regions remains
high, leading to substantial absorption. One can also notice
that the majority of the presented meta-atoms in Table II are
working better under red-colored illumination. Indeed, when
the incident wave, traveling towards the nanosphere, meets the
metallic layer, its penetration to the structure gets hindered
by the mismatch of the oppositely signed Re[ε]; therefore,
maximal absorption occurs for large λ0, overcoming such a
skin effect (red color). Special mention can be made of the
case of hollow plasmonic “nanobubbles” whose cores are
empty (air inside) and which demonstrate high Pabs /Pinc due to
the narrowly placed conformal surfaces, both separating metal
from air. Finally, we note that silver’s multicolor optimal re-
sponse depending on what is the paired medium holds even if
it plays the role of cladding (Table II) instead of core (Table I).
We notice that all the ultra-absorbing designs of Table I
support a near-field distribution of the electric field magnitude
|E|(normalized by the incident one), similar to the one shown
in Fig. 2(a), when operated at the desired wavelength. In
particular, we observe a large local field concentration along
the xaxis at the external boundary (between the dielectric
and air), which sharpens the discontinuity of the normal (x)
electric field component, happening due to material change.
Furthermore, the field in the metallic core is not homogeneous
(as in the static case) because of the substantial |Im[ε1]|of the
used metals at the optimal frequencies. Obviously, the contour
plot is symmetric with respect to the zaxis, unlike what is
happening around the xaxis, where the single-sided excitation
biases the distributions. The arrows on the map show the
direction of the electric field components (−ˆ
y×(ˆ
y×E))
being parallel to the (z,x) plane and it is interesting that the
in-plane electric field changes direction into the metallic core.
In Fig. 2(b), we consider the same particle and represent the
typical variation of total |H|on the (z,x) plane (which, unlike
|E|, is continuous), while the vector field corresponds to
(−ˆ
y×(ˆ
y×H)). One directly observes the two hotspots along
the zaxis at the interface between the plasmonic core and the
dielectric coat, which is a manifestation of a localized surface
plasmon [8]. It is also remarkable that, under the maximal
absorption condition, the zcomponent of the magnetic field
into the core is much stronger than the xone and even larger
than the main yone.
When it comes to the highly absorbing nanospheres em-
ploying a metallic shell and a semiconducting core referred to
in Table II, a representative electric field response is shown in
Fig. 3(a). Again, the signal is maximized at x=±bbut, unlike
in Fig. 2(a), the dielectric cavity sustains significant intensity
due to its nonplasmonic (Re[ε1]>0) nature. In addition, the
electric field in the low-loss core is almost homogeneous
and parallel to the incident component (x), which reminds
us clearly of the static solution (unlike the highly damped
-0.08 -0.04 0 0.04 0.08
-0.08
-0.04
0
0.04
0.08
0
2
4
6
8
10
12
(
a
)
-0.08 -0.04 0 0.04 0.08
-0.08
-0.04
0
0.04
0.08
0
2
4
6
8
10
12
(
b
)
FIG. 2. Typical spatial distribution of the normalized magnitude
of (a) total electric field |E|and (b) total magnetic field |H|on
the (z,x) plane for most core-shell designs of Table I. The specific
outputs belong to Cu/GaP nanospheres at λ0=640 nm. The arrows
show the direction of the in-plane components of the corresponding
fields.
075305-5

ARSEN SHEVERDIN AND CONSTANTINOS VALAGIANNOPOULOS PHYSICAL REVIEW B 99, 075305 (2019)
-0.06 -0.03 0 0.03 0.06
-0.06
-0.03
0
0.03
0.06
0
2
4
6
8
10
(a)
-0.06 -0.03 0 0.03 0.06
-0.06
-0.03
0
0.03
0.06
0
2
4
6
8
10
(b)
FIG. 3. Typical spatial distribution of the normalized magnitude
of (a) total electric field |E|and (b) total magnetic field |H|on the
(z,x) plane for most shell-core designs of Table II. The specific
outputs belong to a GaP/Au nanosphere at λ0=700 nm. The arrows
show the direction of the in-plane field components of the corre-
sponding fields.
case of Fig. 2(a)). In Fig. 3(b), where |H(z,x)|is represented,
we notice again [as in Fig. 2(b)] the localized plasmon at
z=±a, but this time the signal magnitude at the rear side
(z=a) is stronger than the one at the front side (z=−a),
contrary to what is recorded for the nanosphere with plas-
monic core. Importantly, the dielectric internal texture of the
meta-atom flips the direction of the dominant magnetic (z)
component compared to Fig. 2(b), while the density remains
homogeneous.
In Fig. 4(a), we show the metric Pabs/Pinc as a function of
the working wavelength λ0for selected optimally absorbing
designs of Table I. It is noteworthy that all four nanospheres,
which are picked based on their large performance and oper-
ated at various frequencies, have a silver core (as indicated by
the corresponding multicolored row of Table I). Furthermore,
we verify the well-known conclusion that the higher is the
maximum at a resonance (Ag/GaP design, green color), the
more narrow-band it is; in this way, highly selective filtering
or switching is feasible with use of the respective particles. On
the other hand, responses of less efficient designs (Ag/AlSb
nanosphere, red color) give lower quality factors and support
relatively high absorption for a wider range of wavelengths.
In Fig. 4(b), the frequency response of various nanospheres
with dielectric core and metallic cladding from Table II is
represented with different colors corresponding to the opti-
400 450 500 550 600 650 700
0
2
4
6
8
10
12
(a)
400 450 500 550 600 650 700
0
2
4
6
8
10
(b)
FIG. 4. Normalized absorbed power Pabs/Pinc as a function of op-
erational wavelength λ0for the best designs picked from (a) Table I,
corresponding to nanospheres with metallic core and dielectric coat,
and (b) Table II, corresponding to nanospheres with dielectric core
and metallic coat.
mal visible-light frequency. The selected designs for green
(Ag/CdS) and violet (Ag/TiO2) illumination yield very sharp
transfer functions; however, the responses become smoother
for devices operated at larger wavelengths.
IV. OPTIMAL SCATTERING
In Tables III and IV, we repeat the optimization process
illustratively described in Figs. 1(b) and 1(c) for various
combinations of materials, most of which are employed in
Tables Iand II, but in a quest for maximum scattering
efficiency Pscat/Pinc this time. Once again, we try metallic
cores combined with semiconducting coatings, whose optimal
designs are included in Table III (in direct analogy with Table I
for absorption), and dielectric spheres covered by metals,
whose results are shown in Table IV (similarly to Table II for
absorption).
An important feature of Tables III and IV, which is absent
in the case of absorption (Tables Iand II), is that they are
partially populated by homogeneous, instead of core-shell,
particles. In particular, our optimization for specific material
pairs shows that spheres solely filled by a single substance
make more efficient designs rather than any alternative core-
shell geometrical variant. For this reason, in Tables III and IV,
we have repetitive occurrence of the same configurations
comprising only one material. For example, one of the most
highly scattering objects is a homogeneous GaP sphere when
illuminated by blue light.
As usual, silver, due to its strong plasmonic features
combined with low losses, gives very efficient core-shell
nanospheres operated at various colors of the visible spec-
trum. It outperforms (Pscat /Pinc ∼
=11.2) all its competitors
working with violet light, when it is suitably covered by
TiO2(Table III) and most remarkably scatters notably green
(Pscat /Pinc ∼
=9.6) and red (Pscat /Pinc ∼
=9.8) illumination when
used as an external coating to Al2O3and CdS cores, respec-
tively (Table IV). As far as the orange and yellow light is
concerned, one can achieve significant scattering efficiencies
by using copper spheres wrapped by Al2O3layers (orange
color, Table III) or copper claddings around CdTe cores
(yellow color, Table IV).
In Fig. 5(a), we show the electric field magnitude variation
|E|on the (z,x) plane as in Figs. 2(a) and 3(a) but for
a representative case of maximally scattering homogeneous
dielectric spheres. We notice again the two substantial signal
concentrations along the xaxis at the external boundary of
the shell indicating discontinuity of the normal (x-directed)
components. The internal distribution is almost symmetric
azimuthally with a slight shift, as an outcome of the unilateral
excitation, giving a dark point close to the origin. As far as the
direction of the in-plane Eis concerned [arrows in Fig. 5(a)],
one can observe vortices [57] around that dark point which
extend across the considered cross section of the sphere.
Most of the other optimal core-shell nanoparticles of
Tables III and IV are scattering light like a vertical (along
the xaxis) electric dipole operated at its resonance as shown
in Figs. 2(a) and 3(a), while their magnetic fields Hform
the well-known localized surface plasmon (along the zaxis)
depicted in Figs. 2(b) and 3(b). The same effects occur and
are even more enhanced when the optimization concludes
075305-6

CORE-SHELL NANOSPHERES UNDER VISIBLE LIGHT PHYSICAL REVIEW B 99, 075305 (2019)
TABLE III. Optimally scattering (maximum Pscat /Pinc) nanospheres with metallic cores (ε1, different rows) and dielectric shells
(ε2, different columns).
SCATTERING
Core/Shell
Aluminium(III)
oxide
(Al2O3)
Aluminium
antimonide
(AlSb)
Cadmium
sulfide
(CdS)
Cadmium
telluride
(CdTe)
Gallium
phosphide
(GaP)
Titanium
dioxide
(TiO2)
Silver
(Ag)
9.35 @ 400 nm
b/λ0=0.098
a/b =0.86
8.54 @ 700 nm
b/λ0=0.10
a/b =0.74
9.61 @ 540 nm
b/λ0=0.010
a/b =0.67
7.80 @ 400 nm
Ag only
b/λ0=0.12
11.45 @ 485 nm
b/λ0=0.19
a/b =0.20
11.17 @ 425 nm
b/λ0=0.086
a/b =0.86
Gold
(Au)
4.85 @ 605 nm
b/λ0=0.15
a/b =0.80
8.09 @ 700 nm
AlSb only
b/λ0=0.13
6.80 @ 680 nm
b/λ0=0.13
a/b =0.65
10.13 @ 475 nm
GaP only
b/λ0=0.13
7.08 @ 400 nm
TiO2only
b/λ0=0.18
Copper
(Cu)
5.14 @ 605 nm
b/λ0=0.146
a/b =0.78
8.09 @ 700 nm
AlSb only
b/λ0=0.13
7.01 @ 645 nm
b/λ0=0.126
a/b =0.70
4.91 @ 610 nm
b/λ0=0.142
a/b =0.92
10.13 @ 475 nm
GaP only
b/λ0=0.13
7.08 @ 400 nm
TiO2only
b/λ0=0.18
to a single metallic sphere since they keep their internal
electric field very low. On the contrary, the design examined
in Fig. 5(b) (Ag/GaP at λ0=485 nm) makes an exception in
terms of its near-field pattern since its small core leaves the
dielectric mantle to support two maxima along the zaxis into
its volume. In addition, the vector (−ˆ
y×(ˆ
y×E)) follows
again a dipolar pattern but the field lines depart from and
arrive at points with small field intensity. As a result, there is
a remarkable inversion of the background local electric field
in the vicinity of the meta-atom, which can be attributed to
the considerable electrical size of our sphere combined with
its high scattering efficiency.
In Fig. 5(c), we have picked some efficient scatterers from
Tables III and IV which require a single medium (dielectric)
and examine the variation of their performance Pscat/Pinc as
a function of oscillation wavelength λ0operated at several
colors of the visible spectrum (indicated by the color of the
respective curves as in Fig. 4). One clearly notices the well-
known trade-off between the magnitude and the bandwidth of
the resonance which gives a quite selective transfer function
for the GaP nanosphere and a wideband response for a ho-
mogeneous CdS particle. Similarly, in Fig. 5(d), we consider
various core-shell designs and we realize that the one with
the near field of Fig. 5(b) (Ag/GaP) supports an extremely
sharp resonance which renders it suitable for switching and
filtering applications. When it comes to the rest of the setups,
their operations are more narrow band compared to their
homogeneous counterparts, while their maximum Pscat is kept
close to tenfold the incident power Pinc.
V. OPTIMAL CLOAKING
In this section, we repeat the optimization process de-
scribed in Sec. II B and executed in Sec. IV by aiming at
the minimization of Pscat /Pinc instead of the maximization
of it. In other words, we are searching for pairs of media
which make core-shell nanospheres exhibit very low scatter-
ing efficiencies while having a non-negligible optical diameter
2b/λ0. As imposed by the principles of a scattering cancella-
tion cloak [16], opposite signs of permittivities are required
(Re[ε1]Re[ε2]<0) in order for the entire particle to become
transparent. However, in this study we do not follow exactly
the scattering cancellation paradigm [16] due to the constraint
for minimum size (b>0.05λ0) and inevitable losses. Indeed,
in the lossless limit, the true minimum is Pscat →0 and occurs
for an extremely tiny sphere b/λ0→0, which is rejected by
TABLE IV. Optimally scattering (maximum Pscat/Pinc ) nanospheres with dielectric cores (ε1, different columns) and metallic shells
(ε2, different rows).
SCATTERING
Shell/Core
Aluminium(III)
oxide
(Al2O3)
Aluminium
antimonide
(AlSb)
Cadmium
sulfide
(CdS)
Cadmium
telluride
(CdTe)
Gallium
phosphide
(GaP)
Titanium
dioxide
(TiO2)
Silver
(Ag)
9.62 @ 530 nm
b/λ0=0.082
a/b =0.78
8.09 @ 700 nm
AlSb only
b/λ0=0.13
9.82 @ 700 nm
b/λ0=0.083
a/b =0.83
7.80 @ 400 nm
Ag only
b/λ0=0.12
10.13 @ 475 nm
GaP only
b/λ0=0.13
9.71 @ 650 nm
b/λ0=0.086
a/b =0.80
Gold
(Au)
7.00 @ 700 nm
b/λ0=0.11
a/b =0.84
8.09 @ 700 nm
AlSb only
b/λ0=0.13
4.39 @ 565 nm
Au only
b/λ0=0.15
10.13 @ 475 nm
GaP only
b/λ0=0.13
7.08 @ 400 nm
TiO2only
b/λ0=0.18
Copper
(Cu)
6.92 @ 700 nm
b/λ0=0.10
a/b =0.84
8.09 @ 700 nm
AlSb only
b/λ0=0.13
6.38 @ 590 nm
CdS only
b/λ0=0.19
4.47 @ 590 nm
Cu only
b/λ0=0.15
10.13 @ 475 nm
GaP only
b/λ0=0.13
7.08 @ 400 nm
TiO2only
b/λ0=0.18
075305-7

ARSEN SHEVERDIN AND CONSTANTINOS VALAGIANNOPOULOS PHYSICAL REVIEW B 99, 075305 (2019)
-0.24 -0.16 -0.08 0 0.08 0.16 0.24
-0.24
-0.16
-0.08
0
0.08
0.16
0.24
0
0.5
1
1.5
2
2.5
3
3.5
4
(a)
-0.24 -0.16 -0.08 0 0.08 0.16 0.24
-0.24
-0.16
-0.08
0
0.08
0.16
0.24
0
1
2
3
4
5
6
7
8
(b)
400 500 600 700
0
2
4
6
8
10
12
(c)
400 500 600 700
0
2
4
6
8
10
12
(d)
FIG. 5. (a, b) Spatial distribution of the normalized magnitude
of the total electric field |E|for (a) typical homogeneous dielectric
sphere maximal scattering design (AlSb alone at λ0=700 nm) and
(b) optimal particle with silver core and GaP shell (at λ0=485 nm).
The arrows show the direction of the in-plane electric field vector.
(c, d) Normalized absorbed power Pscat /Pinc as a function of op-
erational wavelength λ0for certain designs picked from Tables III
and IV.
our scheme. Our objective is not to cloak a specific volume of
radius aand permittivity ε1but to propose nanospheres of ex-
ternal radius bthat scatter a negligible portion of the incoming
power corresponding to their geometrical cross section (πb2).
Finally, it is important to clarify that our method does not give
efficient designs with dielectric core and metallic cladding due
to the mismatch of the wave in vacuum with the plasmonic
coat, which gives rise to a skin effect and prevents the incident
wave from “seeing” the volume average of the structure.
In Table V, we show the least scattering nanoparticles with
plasmonic core coated by semiconducting mantles for each
combination of the considered media. Once again, we notice
the substantial ability of silver spheres to provide optimal
designs (scattering less than 0.5% of Pinc ) at different colors
metal
dielectric
core-shell
(a) (b)
-0.08 -0.04 0 0.04 0.08
-0.08
-0.04
0
0.04
0.08
0
1
2
3
4
5
6
(
c
)
-0.08 -0.04 0 0.04 0.08
-0.08
-0.04
0
0.04
0.08
0
2
4
6
8
10
12
(
d
)
FIG. 6. (a, b) The radiation patterns [r2pscat(r,θ,ϕ)/Pinc ]for
spherical nanoparticles of the same external radius: homogeneous
metallic (blue), homogeneous dielectric (green), and cloaked core-
shell (red). (c, d) The respective near-field spatial distributions of |E|;
the arrows represent the in-plane vector of electric field. Panels (a)
and (c) correspond to the Ag/GaP pair (at λ0=645 nm) and panels
(b) and (d) to the Ag/TiO2combination (at λ0=525 nm ) of Table V.
of the visible spectrum depending on what is the dielectric
cladding that contains them. Furthermore, the nanoparticles
with gold and copper core working for red color are almost
identical regardless of the coating (Fe2O3or GaAs) since
the two metals have similar permittivities at λ0∼
=700 nm:
ε1∼
=−18 −i0.85.
In Fig. 6(a), we pick a specific low-scattering design
(Ag/GaP at λ0=645 nm) from Table Vof size (2b) and
represent certain radiation patterns, namely, the power density
pscat (r,θ,ϕ) (which is obviously inversely proportional to
r2), multiplied by r2to neutralize the effect of the distance,
and divided by the incident power Pinc. In other words, we
TABLE V. Optimally cloaked (minimum Pscat/Pinc ) nanospheres with metallic cores (ε1, different rows) and dielectric shells
(ε2, different columns). The scattering cancellation cloak [16] under realistic losses in the visible.
CLOAKING
Core/Shell
Aluminium(III)
oxide
(Al2O3)
Cadmium
sulfide
(CdS)
Iron(III)
Oxide
(Fe2O3)
Iron(II,III)
Oxide
(Fe3O4)
Gallium
arsenide
(GaAs)
Gallium
phosphide
(GaP)
Titanium
dioxide
(TiO2)
Silver
(Ag)
0.018 @ 425 nm
b/λ0=0.12
a/b =0.32
0.004 @ 535 nm
b/λ0=0.075
a/b =0.35
0.023 @ 635 nm
b/λ0=0.076
a/b =0.39
0.054 @ 515 nm
b/λ0=0.11
a/b =0.39
0.024 @ 700 nm
b/λ0=0.074
a/b =0.52
0.002 @ 645 nm
b/λ0=0.064
a/b =0.43
0.003 @ 525 nm
b/λ0=0.070
a/b =0.32
Gold
(Au)
0.034 @ 600 nm
b/λ0=0.11
a/b =0.44
0.024 @ 685 nm
b/λ0=0.077
a/b =0.39
0.034 @ 695 nm
b/λ0=0.090
a/b =0.64
0.031 @ 595 nm
b/λ0=0.10
a/b =0.44
Copper
(Cu)
0.018 @ 605 nm
b/λ0=0.094
a/b =0.42
0.021 @ 685 nm
b/λ0=0.079
a/b =0.40
0.033 @ 700 nm
b/λ0=0.090
a/b =0.64
0.019 @ 605 nm
b/λ0=0.094
a/b =0.42
075305-8

CORE-SHELL NANOSPHERES UNDER VISIBLE LIGHT PHYSICAL REVIEW B 99, 075305 (2019)
400 450 500 550 600 650 700
10-3
10-2
10-1
100
FIG. 7. The variation of Pscat /Pinc with respect to operational
wavelength λ0for several optimally cloaked nanoparticles picked
from Table Vworking at different colors of the visible spectrum.
Asymmetric (Fano) resonances [7] occur.
have 2π
0π
0[r2pscat/Pinc]sinθdθdφ=Pscat /Pinc and show
the variation of the quantity in the brackets at the maximum
cross section plane. We consider three objects of the same ex-
ternal radius band accordingly the same normalization power
Pinc : two homogeneous spheres filled either with the used
plasmonic material (Ag, ε1) or with the employed dielectric
(GaP, ε2) and the core-shell design which optimally combines
these two (ε1,ε
2) media to make a practically cloaked object
with identical dimensions. The latter polar plot is negligible
in magnitude compared to the two former ones and that is
why we show only parts from the radiation patterns of the
two homogeneous spheres. In Fig. 6(b), the same process
of Fig. 6(a) is repeated but for the particle with silver core
and TiO2cladding. As indicated in Table V, the core-shell
scattering is slightly larger that time, but simultaneously vastly
smaller than the Pscat /Pinc from silver or TiO2homogeneous
spheres of radius b∼
=37 nm at λ0=525 nm.
In Figs. 6(c) and 6(d), we show the near-field distributions
|E|for the cloaked objects examined in Figs. 6(a) and 6(b),
respectively. In both designs we note the almost homogeneous
electric field outside of them which is also xdirected as
indicated by the in-plane arrows. In other words, the incident
plane wave is practically unperturbed not only in the far region
[as shown in Figs. 6(a) and 6(b)] but also in the vicinity of the
external surface r=b, implying an almost perfect scattering
cancellation cloak with realistic losses. In addition, the signal
is homogeneous into the core, as dictated by the spherical
symmetry, and quite strong, as a result of electric dipole
resonances that develop almost opposite (Re[ε1]Re[ε2]<0)
and mutually neutralized polarizations at the two domains of
the particle.
In Fig. 7, as in the other sections, we select some of the best
designs of the related Table Vand test them in the vicinity
of their optimal operational frequency. Some of the optimal
particles (like Ag/GaP under red light) retain their notable
performance at much smaller λ0giving wideband cloaks.
However, it is remarkable that, in all cases, the minimal-
scattering bands are followed by “bright zones” at slightly
larger wavelengths resulting in an asymmetric line shape that
unveils the Fano-resonant nature [7] of the cloaking effects
reported in Table V. In this way, one obtains a dramatic two-
decimal-order upsurge of Pscat (Ag/TiO2design under green
light) if increases the oscillating wavelength only by a few
nanometers.
VI. CONCLUSIONS
An exhaustive search for core-shell spherical particles
that exhibit substantial efficiency in terms of absorption and
scattering of the incoming light has been presented. Numer-
ous plasmonics, semiconductors, and dielectrics have been
considered as potential homogeneous fillings of the two do-
mains comprising the nanospheres. For each pair of media,
we scan the entire visible wavelength spectrum and select
the sizes that give maximal performance to the regarded
simple architecture. These optimal designs are reported in
several tables, in proportion to the objective they serve, while
their near-field representations reveal the underlying wave
interactions. By inverse logic, we quest after poor (minimal)
scattering efficiency corresponding to invisible objects; as
a result, many realistic scattering-cancellation cloaks under
actual losses have been obtained.
The major mechanisms behind almost any performance
maximization of both isolated particles and collective meta-
surfaces are the various types of resonances. Since the em-
ployed materials are lossy and the behavior of the meta-atoms
is strongly dependent on the optical sizes, no closed-form
conditions for resonance can be derived and, thus, the pro-
posed technique is required to detect the occurrence of similar
effects by optimizing the considered metrics. Therefore, in the
cases of most ultraperforming designs, we observe electric or
magnetic Mie resonances corresponding to maximal dipolar
terms in the sums of the canonical solutions. Needless to
say, quadruple or higher-order resonances emerge as long as
the electrical radius of the particles increases, and multiple
non-negligible canonical terms support strong local maxima.
Furthermore, our method frequently stumbles on optimal
nanospheres with field hotspots attributed to localized surface
plasmon resonances developed at boundaries of opposite-sign
permittivity domains. Such plasmonic effective behavior is
also a prerequisite for the particle to be seen as transparent,
namely, to demonstrate invisibility with vanishing scattered
power. These minima in the output can appear at wavelengths
neighboring to corresponding maxima, yielding to frequency
responses with asymmetric shape indicating Fano resonances.
This work detects the limits of a simple particle configura-
tion into a parametric space, permitting it to be employed in
virtually all metasurface applications in the visible. The pre-
sented designs provide performance benchmarks of what one
can achieve with core-shell geometry and, simultaneously,
set the bars that one must pass by utilizing more complex
structures and artificial media. However, even a plain increase
in the number of concentric shells will render the full, “brute-
force” optimization of the system computationally challeng-
ing, and thus should be assisted by more elaborate techniques
like the implementation of machine learning algorithms.
075305-9

ARSEN SHEVERDIN AND CONSTANTINOS VALAGIANNOPOULOS PHYSICAL REVIEW B 99, 075305 (2019)
ACKNOWLEDGMENT
This work was partially supported by Nazarbayev Uni-
versity Small Grants with the project entitled “Super trans-
mitters, radiators and lenses via photonic synthetic matter”
(Project No. 090118FD5349). Funding from the MES RK
state-targeted program BR05236454 is also acknowledged.
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