Supporting Information:
Excitation of Terahertz Charge Transfer Plasmons in
Metallic Fractal Structures
Arash Ahmadivand,* Burak Gerislioglu, Raju Sinha, Phani Kiran Vabbina, Mustafa Karabiyik, and Nezih
Pala
Department of Electrical and Computer Engineering, Florida International University, 10555 W Flagler
St., Miami, Florida 33174, USA
*Corresponding Author: [email protected]
Contents
1. Comparing corresponding polarization dependency of equilateral and isosceles FYS structures.
2. E-field enhancement comparison between equilateral and isosceles FYS structures.
3. Comparison between capacitive coupling and direct transfer of charges in fractal assembly.
4. Verification for the behavior of charges at the frequency of CTP resonant mode.
5. Numerically and experimentally obtained absorption cross-section of a fractal assembly.
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1. Comparing corresponding polarization dependency of equilateral and isosceles FYS structures.
To show the influence of polarization variations on the spectral response of the symmetric and
antisymmetric plasmonic FYS structures, we determined the normalized transmission amplitude (NTA)
for both equilateral and isosceles FYS structures with the same dimensions, while the angles between
arms are different. Figure S1 exhibits numerically and experimentally obtained NTA for both plasmonic
structures with the dimensions La=20 μm and Lb=10 μm. The insets in Fig. S1(a) are the top-view pictures
showing the angles between neighbor arms in both symmetric and antisymmetric FYS systems. For the
plasmonic isosceles FYS discussed in the main article, we observed a strong plasmon resonant mode at
~1.1 THz under longitudinal polarization beam (φ=90°), while for transverse polarization (φ=0°), this
transmission dip disappeared and a negligible shallow and broad dip appeared around 1.5 THz. In
contrast, the equilateral FYS (with the angle of 120o between all arms) supports dipolar resonant modes
under both longitudinal and transverse polarizations across 1.5 THz to 1.7 THz. These analyses are
confirmed with the experimental data plotted in Fig. S1(b). The numerically obtained polarizationdependence of the examined structures are shown in Fig. 1S(c). It should be underlined that due to the
large distance between the angled arms and low energy of dipolar modes that appear at the outermost tips,
we do not expect any near-field coupling between the photoexcited E-fields on each arm. This is in
complete contrast with the same structures in nanoscale dimensions in optical systems [1].
Figure S1. (a,b) Numerically predicted and experimentally analyzed NTA for the isosceles equilateral FYS structure with
La=20 μm and Lb=10 μm under longitudinal and transverse polarized beam excitation. (c) Polarization-dependence of the
FYS systems to the incident THz radiation, illustrating the sensitivity of the examined Y-shaped particles to the polarization
direction of the incident beam at the 1 THz for isosceles and 1.6 THz for equilateral Y-shaped fractal structure.
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2. E-field enhancement comparison between equilateral and isosceles FYS structures.
The spectral response of both equilateral and isosceles FYS structures (with the size of La=20 μm and
Lb=10 μm) can be further analyzed by plotting the corresponding E-field enhancement (|Ez|/|E0|, where Ez
and E0 are the amplitudes for the monitored electric-field in the z-direction and incident electric-field,
respectively) profile as a function of the incident THz radiation frequency as shown in Fig. S2(a).
Considering concurrent analysis in the main text, and also NTA profiles, therefore, we expect superior Efield enhancement for the isosceles case compared to the equilateral one under longitudinal polarization
excitation due to symmetry breaking and confining of plasmons at all arms tips at the same time. This
claim can be further analyzed by plotting the corresponding charge distribution profile for an equilateral
FYS structure as shown in Fig. 2S(b). The charges shuttle in the same way as isosceles FYS (see Fig. 2d
in the main text of the article), while the energy of the modes that are concentrated at the arm tips are
lower than the isosceles FYS regime. In the calculated E-field enhancement diagram, the enhancement
extreme for the isosceles FYS is located around 1 THz, while for the equilateral one the peak appears
around 1.35 THz. This difference can be understood easily by plotting 3D E-field map for the
enhancement coefficient which compares the plasmon resonance confinement and near-field regime
between both equilateral and isosceles FYS structures under longitudinal polarization beam at 1.5 THz
Figure S2. (a) Simulated E-field enhancement (|Ez|/|E0|) for both isosceles and equilateral FYS structures as a
function of THz beam. (b) Charge distribution plot for an equilateral FYS structure under longitudinal
polarization excitation. (c, d) Numerically obtained 3D E-field maps for the field enhancement across the
isosceles and equilateral FYS structures, respectively.
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and 1 THz, respectively (see Figs. S2(b) and S2(c)). In the calculated E-field enhancement snapshots, for
the isosceles FYS system, we observed substantial excitation and confinement of plasmonic resonant
modes at the outermost tips under longitudinal polarization THz radiation. On the other hand, for the
symmetric equilateral ones, we observed a drastic decay in the amplitude and confinement of the excited
plasmonic modes at the arms tips.
3. Comparison between capacitive coupling and direct transfer of charges in fractal assembly.
The effect of charge transfer plasmons (CTPs) on the spectral response of the designed fractal antenna can
be understood by comparing the effect of plasmon resonance coupling and direct transfer of charges
across the quadratic FYS antennas (see Fig. S3(a)). To this end, we first extracted the spectral response of
a four-member FYS structures that are located apart with an offset gap in between, consisting of four FYS
structures with La=20 μm and Lb=10 μm as shown in Fig. S3(b). In this regime, having a gap between
FYS arms allows for formation of capacitive coupling between the excited resonant plasmonic modes. In
Figure S3. (a) The schematic top-view profile for a systematic configuration of four FYS structures located with
an offset gap distance (Doffset) apart. (b, c) Normalized transmission amplitude (NTA) spectra for FYS structures
with variant offset spot as a function of incident THz beam. Both dipolar and quadrupolar dips are indicated
inside the profiles by dotted circles.
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Figure S4. (a, b, and c) The near-field snapshots for a systems composed of four FYS structures that are located
with offset gap distances with the size of 10 μm, 5 μm, and 2 μm, respectively, showing the capacitive coupling
between excited plasmonic modes between arms.
numerical analysis, for a gap distance of 10 μm and under longitudinal polarization beam radiation, we
observed a sharp dipolar peak around 2.25 THz, which is attributed to the weak coupling between
resonant modes. Reducing the gap distance to 5 μm and 2 μm, we observed stronger capacitive coupling
between the excited resonant modes. The effect of this interference is excitation of an additional small
minimum in longer THz band with a red-shift for both dips. The smaller dip correlates with the
quadrupolar mode due to the interference between arising modes corresponding to the closely spaced
arms. In addition, by bringing the FYS systems closer to each other, the sharpness and depth of the
absorption lineshapes increased substantially. For smaller distances, the quadrupolar lineshape became
deeper due to efficient coupling between low energy modes (Fig. S3(c)) including a red-shift toward the
sub-THz band. Figure S4 illustrates the near-field maps of the plasmon resonance excitation and coupling
in the capacitive coupling regime. The major difference between capacitive coupling and transfer of
charges can be seen in the E-field snapshots. Accordingly, a large field of the excited plasmons
accumulates at the gap spot area between neighboring arms, and leads to drastic decay of charges at the
opposite arms tips. The obtained results are in accordance with the previously studied regimes for both
THz and mid-infrared domains [2-6].
4. Verification for behavior of charges at the frequency of CTP resonant mode.
By reducing the gap spot distance (Doffset) between FYS arms to “zero” and hence, achieving contacting
regime, a conductive pathway is provided for the excited charges to transit across the fractal antenna to
the outermost part of the arms that are parallel to the polarization direction of the incident THz radiation.
In this regime, as shown in the manuscript, the multipolar dip (in the right side) is eliminated, while
another dip corresponding to the dipolar mode is enhanced, and also a CTP mode is excited at the left side
of the dipolar minimum (at lower energies). According to Wen et al. [7] for charge transfer mechanism in
nanoscale at both visible and near-infrared spectra, the position and depth of CTP resonant mode strongly
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Figure S5. (a) A top-view of the plasmonic structure with the description for Lt. (b) Numerically calculated
transmission amplitude which is focusing on the behavior of CTP and dipolar modes while the length of
conductive path (Lt) is varying between 50 μm to 70 μm. The red-shift in the position of the dip is demonstrated
by a dashed line. The dashed-dotted line illustrates the drastic decay in the quality of dipolar dip. (c) Normalized
transmission amplitude for the variations in Lb, while the other geometries are fixed as La=15 μm. The width of
the conductive path is varying between 7.5 μm to 12.5 μm. The blue-shift in the position of CTP dip is
substantial including a sensible intensification in the corresponding narrowness and depth. The dipolar dip also
blue-shifted to the higher energies with the same quality.
depend on the conductance of the metallic junction. To verify that the induced dip at the sub-THz band is
a CTP mode, we carried out some numerical simulations to show how the behavior of the CTP dip by
geometrical modifications.
As shown in Fig. S5(a), we altered the length (Lt) of the horizontal arm and monitored the plasmonic
response of the structure. It should be underlined that we changed the length of the arm that is parallel to
the incident THz beam polarization. By increasing the entire length of the conductive pathway (Lt) from
50 μm to 70 μm, the conductance decreases (see Eqn. 1 in the manuscript), and the charge shuttling time
increases significantly. Consequently, position of the CTP mode red-shifts to lower energies while its
amplitude remains unchanged [8]. Numerically plotted normalized transmission spectra in Fig. S5(b)
shows the shift of the CTP mode with the variations in Lt for FYS3 which showed the deepest CTP and
dipolar resonant modes. Classical dipolar and multipolar modes present substantial dependence on the
geometrical dimensions. Therefore, subtle variations in the geometry of subwavelength plasmonic
structures can be accompanied with appearing and disappearing of resonant modes. This is clearly visible
in Fig. S5(b) for dipolar dip, which decayed significantly as Lt increased. Continuous increase in the
length of the arm leads to formation of a significant distance between Y-shape arms of neighbor FYSs,
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Figure S6. (a) E-field snapshot for the excitation of plasmonic modes at the CTP frequency including
accumulation of charges at the FYS arms. (b) Logarithmic scale for the E-field excitation in fractal antenna. (c),
(d) The vectorial illustration for the direction of charges across the fractal antenna for the resonance peak
located at the dipolar and CTP modes frequencies, respectively.
resulting a drastic decay in the dipolar resonant mode. As a result, the dipolar dip weakened and decayed
gradually by increasing the length of the variant arm including a subtle red-shift to the lower energies.
On the other hand, Lb is the other geometrical parameter that has a direct relationship with the
corresponding AC conductance of the conductive pathway (see Eqn. 1 in the manuscript). Figure S5(c)
exhibits the transmission amplitude profile for Lb variations (in the range of 7.5 μm to 12.5 μm), while the
length of the Y-shaped arms is fixed at La=15 μm. Increasing the width of the pathway leads to increasing
conductance and significant intensification in the quality of the CTP dip including a blue-shift in the
position of the resonant mode to the higher energies. On the other hand, the dipolar resonant minimum
also demonstrated a trivial blue-shift to the higher energies due to intensified dipolar coupling arisen from
the outermost adjacent Y-shaped arms.
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The behavior of the charges at the CTP frequency can be better understood by drawing the
corresponding charge distribution profiles shown in Fig. S6. Here, the opposite charges are concentrated
at two different FYS arms (Fig. S6(a)). Figure S6(b) shows the logarithmic scale profile (Log |Ez|) for the
plasmon resonance excitation in the fractal antenna, exhibiting absence of charges at the center of the
antenna. Figures S6(c) and S6(d) illustrate the vectorial map of the electron oscillations at the dipolar and
CTP modes frequencies, which clearly demonstrates the unique behavior of the modes.
Figure S7. Numerically (solid) and experimentally (dashed) determined NTA profiles for the fractal
assemblies with three different geometries based on defined sizes for (a) FYS1 (b) FYS2, and (c) FYS3.
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5. Numerically and experimentally obtained absorption cross-section of a fractal assembly.
Underlying the specific features of the proposed plasmonic system, we also calculated and plotted
corresponding absorption cross-section for the examined antenna to verify the quality of the incident light
absorption correlating with the transmission dips (see Fig. S7). We used the proposed method in the main
manuscript to calculate the absorption spectra [6]. Considering the smaller size of the entire antenna
compared to the incoming THz beam, in the quasi-static limit, we expect the plasmonic response
including both transmission dips and correlating absorption cross-section due to geometry-dependence
and not radiative losses. As shown in the absorption spectra, the deeper the transmission minimum is, the
higher the absorption curve is. From the plotted spectra, numerical calculations are in good agreement
with the experimental data for the absorption cross-section.
References
1 S. Gottheim, H. Zhang, A. O. Govorov, and N. J. Halas, “Fractal nanoparticle plasmonics: The
Cayley tree,” ACS Nano vol. 9, no. 3, pp. 3284-3292, Feb. 2015.
2 B. Cerjan, X. Yang, P. Nordlander, and N. J. Halas, “Asymmetric aluminum antennas for selfcalibrating surface-enhanced infrared absorption spectroscopy,” ACS Photonics vol. 3, no. 3, pp.
354-360, Feb. 2016.
3 X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang,
“Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual
excitation pathways of the dark mode,” Appl. Phys. Lett. vol. 100, no. 13, p 131101, Mar. 2012.
4 G. C. Dyer, G. R. Aizin, S. Peru, N. Q. Vinh, S. J. Allen, S. J. Reno, and E. A. Shaner, “Inducing
incipient terahertz finite plasmonic crystal in coupled two dimensional plasmonic cavities,” Phys.
Rev. Lett. vol. 109, no. 12, p. 126803, Sep. 2012.
5 D. R.; Chowdhury, R. Singh, M. Reiten, J. Zhou, A. J. Taylor, J. F. O’Hara, “Tailored resonator
coupling for modifying the terahertz metamaterial response,” Opt. Express vol. 19, no. 11, pp.
10679-10685, May 2011.
6 B. Auguie, and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev.
Lett. vol. 101, no. 14, p. 143902, Sep. 2008.
7 F. Wen, Y. Zhang, S. Gottheim, N. S. King, Y. Zhang, P. Nordlander, and N. J. Halas, “Charge
transfer plasmons: Optical frequency conductances and tunable infrared resonances,” ACS Nano,
vol. 9, no. 6, pp. 6428-6435, May 2015.
9
8 O. Pérez-González, N. Zabala, A. G. Borisov, N. J. Halas, P. Nordlander, and J. Aizpurua,
“Optical spectroscopy of conductive junctions in plasmonic cavities,” Nano Lett. vol. 10, no. 8,
pp. 3090-3095, Jul. 2010.
10