Transition from capacitive coupling to directcharge transfer in asymmetric terahertzplasmonic assembliesARASH AHMADIVAND,1,* RAJU SINHA,1 BURAK GERISLIOGLU,1 MUSTAFA KARABIYIK,1

NEZIH PALA,1 AND MICHAEL SHUR2

1Department of Electrical and Computer Engineering, Florida International University, 10555 W Flagler St., Miami, Florida 33174, USA2Center for Integrated Electronics, Rensselaer Polytechnic Institute, 110, 8th St., Troy, New York 12180, USA*Corresponding author: aahmadiv@fiu.edu

Received 10 October 2016; revised 20 October 2016; accepted 21 October 2016; posted 21 October 2016 (Doc. ID 278457);published 14 November 2016

We experimentally and numerically analyze the chargetransfer THz plasmons using an asymmetric plasmonicassembly of metallic V-shaped blocks. The asymmetricdesign of the blocks allows for the excitation of classical di-polar and multipolar modes due to the capacitive coupling.Introducing a conductive microdisk between the blocks, wefacilitated the excitation of the charge transfer plasmonsand studied their characteristics along with the capacitivecoupling by varying the size of the disk. © 2016 OpticalSociety of America

OCIS codes: (300.6495) Spectroscopy, terahertz; (250.5403)

Plasmonics; (220.4000) Microstructure fabrication.

http://dx.doi.org/10.1364/OL.41.005333

Direct manipulation of charges via redistribution, transfer, andquantum tunneling has been studied theoretically and experi-mentally for nanoscale plasmonic systems [1]. With a differentmechanism compared with classical capacitive resonance cou-pling, the direct transfer of excited charges allows for designingadvanced plasmonic nanosystems with exquisite features.Metallic subwavelength particles and blocks are particularlypromising candidates to support and manipulate ultrastrongplasmonic resonant modes across a wide spectrum range span-ning from the ultraviolet to microwave frequencies [2]. Thespectral properties of the localized plasmon resonant modesstrongly rely on the shape and geometry of the sustaining com-ponents. These resonant modes can be classified into superra-diant bright modes [3], subradiant dark modes [4] (recognizedas asymmetric line shapes, such as the electromagnetically in-duced transparency [5], and Fano resonances [6]), and chargetransfer plasmons (CTPs) [1]. Classical plasmonic sub- andsuperradiant modes have been broadly used for several appli-cations, including all-optical and optoelectronic devices[7,8]. In contrast, the applications of CTPs are primarilylimited to the fundamental analysis of the quantum physicsbehind the process at visible spectrum energies [9,10].

The CTP resonant modes that have been observed in nano-scale systems with the reduced offset gaps down to atomic sizeswere explained by direct quantum tunneling [10] and indirectFowler–Nordheim tunneling [11] principles. The CTP modespossess attractive features across low energies below <0.9 eV.However, shifting the CTP resonant modes to the mid- and far-infrared domain with high tunability is a challenge. Realizingthis feature across low energies would allow for tailoring novelactive plasmonic devices, such as single-molecule sensorsand high-responsivity optoelectronic devices. Despite havingunique plasmonic features, metallic nanoparticles and assem-blies suffer from destructive losses under low-energy beam ex-posure ranging at mid- and far-infrared and terahertz (THz).This is caused by weak capacitive coupling between the proxi-mal blocks, causing a substantial localization of the plasmonsin the micro-gaps. Conversely, the direct transfer of chargesbetween the metallic structures delivers unique abilities to turnon and off the charge shuttling by varying the intensity ofthe incoming beam, which could be used for developmentof functional THz plasmonic devices.

In the present work, we analyze the plasmonic response ofan asymmetric four-member assembly of V-shaped metallicblocks (VSMBs), which are placed head-to-head close to eachother. Both numerical and experimental analysis are carried outto investigate and demonstrate the capacitive coupling anddirect charge transfer between VSMBs at THz frequencies.To this end, four different regimes are considered to monitorand evaluate excitation of dipolar, quadrupole modes, andCTPs resonances across the THz domain. It is shown that pres-ence of a conductive disk between VSMBs in touching regimefacilitates efficient transfer of charges along the blocks leadingto a distinguished CTP resonant mode at lower energies.Such an asymmetric design is used to employ its geometricalfeatures to induce dipolar and multipolar modes. In contrastwith conventional bowtie antennas and analogous structureswithout antisymmetry features, the proposed assembly allowsfor inducing low energy modes such as multipolar dips acrossthe THz spectrum.

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0146-9592/16/225333-04 Journal © 2016 Optical Society of America

The plasmonic assembly were fabricated by photo-lithography technique on a high resistivity silicon wafer(>10; 000 Ω:cm) (to provide the required transparency inthe THz domain [12]). Two layers of the positive photoresists(LOR 3B and S1805) with the total thickness of 2.6 μm weredeposited and patterned. Employing the e-beam evaporation,we then deposited the 750 nm of titanium (Ti) layer at therate of 5 Å/s (99.99% purity, pressure 7.6 × 10−7 Torr). Theliftoff was performed by immersing in remover PG for120 min at 70°C followed by IPA and DI water rinse.The assembly arrays were fabricated in the area of 1500 μm ×1500 μm with the periodicity of 80 μm. The SEM picturesshown along the Letter were obtained using the JEOL 7000tool. The THz characterization was performed using a THzTDS setup with the beam bandwidth of 10 GHz to4.5 THz with the average power of ∼100 μW. For the numeri-cal modeling, the FDTD method (Lumerical 2016) was usedwith the PML layers as the workplace boundaries for radiationdirection (z axis) and periodic boundaries for x and y axes.A plane wave pulse of 2.6 ps served as an external THz source.The Ti dielectric function Ti was taken from the empiricallydefined values by Palik [13].

Figure 1(a) shows a schematic profile for the V-shapedassembly (not to scale). The gap between the VSMBs was12 μm. Figure 1(b) specifies the geometrical parameters ofthe plasmonic system. The corresponding geometrical sizesare described in the figure caption. The normalized transmis-sion amplitude (NTA) for the plasmonic assembly is shown inFig. 1(c). The capacitive coupling plays a major role in theemergence of distinct dips along the curve. The deeper mini-mum around 1.75 THz correlates with the dipolar resonantmode, while the quadrupole mode appears as a weaker diparound 2.35 THz. The inset is the SEM image of the fabricatedTHz plasmonic assembly. Figure 1(d) shows the appliedelectro-optical signal amplitude as a function of time delay.One should note that reducing the gap distance betweenVSMBs helps to make the peaks narrower, leading to a higherquality-factor [11]. The comparison with the simulated curvesallows us to interpret the charge transfer plasmon resonances.Figures 1(e) and 1(f ) illustrate the E-field map and vectorialcharge distribution, respectively, for the plasmon resonanceexcitation and concentration in the junction area of theVSMBs at the frequency of the dipole dip. The charges aremainly concentrated at the tips of the blocks (VSMBs apexes),which are parallel to the incident beam polarization. Reducingthe gap distance between VSMBs is a typical strategy to narrowthe transmission dips; however, achieving significant dips

requires small offset gaps. The fabrication of thin 3D micro-structures with small gaps is highly challenging [14].

Our goal is to demonstrate THz CTPs using the directtransfer of charges between VSMBs. To this end, we insertedconductive disks with the same thickness and material asVSMBs with the varying diameters to follow the transitionfrom the capacitive coupling to the direct transfer of charges.First, the disk with the diameter of 7 μm was used, while thegap between disk and VSMBs apexes was reduced to 2.5 μm oneach side. According to Mie’s theory, a particle with the size ofthe considered disk is able to support dipolar modes at THzresonances [2]. In this regime, the central disk sustains astrong dipolar mode enhancing the quality of the observedtransmission line shapes via the dipole–dipole interaction [1].Figure 2(a) depicts the effect of this geometrical variation. Inthe NTA profile, both dipole and quadrupole dips wereenhanced and shifted to the smaller THz frequencies, while thisenhancement is more appreciable for the dipolar dip. The ex-perimental data is in complete agreement with the numericalpredictions. By increasing the diameter of the central conduc-tive disk, we provided a path for shuttling of the charges be-tween VSMBs. In this regime, keeping the other geometries thesame and increasing the diameter of the conductive disk to12 μm (touch the tips of each block) provided a conductivebridge for the charges. Figure 2(b) exhibits the correspondingNTA spectra for the asymmetric cross design with the centraldisk touching the VSMBs apexes. The inset is the SEM imageof the fabricated assembly. The major difference compared withthe prior case is elimination of the multipolar mode and emerg-ing of the CTP dip around 0.5 THz. Due to the formation of asmall pathway between the blocks, we expect direct shuttling ofcharges in the same way as in the optical nanoscale systemscharacterized by quantum transition [15]. However, in the ex-amined microstructure for the touching regime, the connectedsmall parts can support a limited number of transportingcharges across the assembly. Increasing the size of the centralconductive disk to the overlapping regime leads to a sensibleshift in the position of the induced resonant modes to thesub-THz spectra, while both dipolar and CTP dips becamenarrower and deeper. Increasing the size of the overlappingregion causes a dramatic damping in the energy of both modesreflecting the electrical properties of the disk that will bediscussed in the following. Figure 2(c) illustrates the NTAprofile for the overlapping regime for both simulation andexperimental analysis. The inset is the corresponding SEM pic-ture of the fabricated assembly. The corresponding E-fieldsnapshots illustrate the effect of the conductive disk in the

Fig. 1. (a), (b) Schematic and tip view pictures of the assembly, respectively. (c) Calculated and measured NTA for the capacitive coupling forthe following dimensions: a∕b∕c∕d � 10∕25∕10∕35 μm. Inset is an SEM image of the plasmonic assembly. (d) Applied electro-optical signalamplitude (mV) as a function of time delay (ps). (e), (f ) E-field map and charge distribution profiles across the asymmetric assembly underlongitudinal polarization excitation, respectively.

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formation of the CTP mode. Figure 2(d) presents the structurewith a nontouching disk in between, where the plasmons areconcentrated at the tips and in the gap areas between the diskand the VSMB apexes. For the touching and overlapping con-ditions shown in Figs. 2(e) and 2(f ), respectively, the E-fieldconcentration at the middle section of the assembly (disklocation) is nearly zero, while the charges are transported tothe left and right sides of the VSMBs parallel to the THz beam.The charges that are transported to the perpendicular blocks arenegligible. This effect is highly distinct for the overlappingregime, and the charges being nearly zero for both the centraldisk and perpendicular VSMBs are consistent with the opticalcharge transfer studies for nanoscale systems [16].

The cross-sectional analysis of the E-field plot along theassembly provides a better understanding for the distributionof the charges across the structure. Figure 3 shows the E-fieldmaps and diagrams (jE j) as functions of the assembly position(x axis) for different regimes. When the intermediate disk isabsent, the field localization is concentrated at the apex tipsof the VSMBs. Adding the conductive disk to the central partand increasing its diameter from a nontouching to overlappingcondition transfers the localization of the E-field from thecentral region to the arms’ tips with the field at the conductivedisk becoming nearly zero. The overlapping areas help inducesharper and enhanced plasmonic dipolar and CTP modes. Thegeometry of the overlapping areas allows us to trade-off thecharges between the VSMBs of a standalone assembly. Thiscan be described by defining the resistance (R) of the diskas a function of the junction geometry [17]

R�Ω� � 2

σ�ω�tπ ln

�2dδx

�; (1)

where σ�ω� is the frequency-dependent conductivity, t is thethickness of structure, d is the length between junctions, and δxis the contact width at the junctions. The conductivity is givenby σ � nTie2τ∕me [18], where nTi is the electron density forTi (4.44 × 1028 m−3), e is the elementary charge, τ is the mean

time between collisions, and me is the electron mass. Increasingthe diameter of the overlapping disk extends the length betweenjunctions, and the corresponding resistance increases accord-ingly. In this limit, while charges would be able to travelthrough the pathway, the dissipative losses can be substantialdue to the disk resistance. When incident THz radiation is res-onant with the transmission line shape, the intense localizationof charges across the lossy metallic components causes a dra-matic energy dissipation. By increasing the diameter of the in-termediate disk, the induced dips shift to the lower energies dueto the enhanced dissipative absorption cross section. This is incontrast with the CTP resonant shift observed in dimers at op-tical frequencies [16]. We compared the absorption spectra fordifferent regimes in Fig. 3(e), which is showing monotonicallygrowing absorption spectra with increasing the size of the over-lapping disk. This can be explained by the resistance increase asa function of the disk diameter [Fig. 3(f )]. The inset exhibitsthe position of the CTP mode as a function of the disk diam-eter, which is consistent with the experimental results.Obviously, by increasing the size of the middle disk (diameter>16 μm), the absorption extreme correlating with the CTPpeak is vanished due to strong damping in the correspondingCTP peak, while the absorption at the dipole position is un-changed. Next, changing the polarization of the THz radiationto transverse mode (φ � 90°) results in nearly similar plas-monic response with subtle variations in the amplitude ofthe dipolar dip. For the capacitive coupling, we expected sameresonant modes with lower amplitude of dips. For the presenceof an overlapping disk, the same CTP peak is expected, whilethe dipolar dip becomes broader and shallower in comparisonwith the longitudinal case.

We also quantified the dephasing time for the inducedCTP dip at the THz band using the proposed method basedon Fourier transformation. The Cauchy–Lorentz distributionwas used to define the damped harmonic oscillator [19].Thus, the dephasing time for the induced CTP dip for the pres-ence of overlapping disk is given by T CTP � 2ℏ∕FWHM,

Fig. 2. Characterized and simulated NTA profiles for the asymmetric THz assembly for the presence of (a) a nanodisk between gaps, (b) atouching disk to the VSMBs, and (c) an overlapping nanodisk. Insets are the corresponding SEM pictures for nanodisk variations. (d)–(f )Corresponding E-field maps for different studied regimes for the CTP mode. The charge transfer is plotted inside the numerically defined maps.

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where ℏ is the reduced Planck’s constant. For the deepestCTP dip at 0.58 THz, the dephasing time is estimated as5.49 × 10−12 s (∼5.5 ps).

In conclusion, we have systematically studied the transitionof plasmonic charges across an antisymmetric four-memberassembly of THz VSMBs using both experimental and numeri-cal analysis. Comparing the plasmon response of the assemblyin both capacitive and bridged regimes, we showed that thepresence of a conductive path between plasmonic blocks givesrise to different sub-THz resonant modes. Providing a signifi-cant tunable spectral response across the low energies helps indeveloping a novel platform for geometrically tunable THzplasmonic devices.

Funding. National Science Foundation (NSF) (0955013);Army Research Laboratory (ARL) Multiscale MultidisciplinaryModeling of Electronic Materials (MSME) CollaborativeResearch Alliance (CRA) (W911NF-12-2-0023, ProgramManager: Dr. Meredith L. Reed).

Acknowledgment. Raju Sinha gratefully acknowledgesthe financial support provided through a dissertation yearfellowship by the University Graduate School (UGS) atFlorida International University.

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Fig. 3. (a)–(d) Cross-sectional E-field maps and field concentration diagrams for capacitive coupling, presence of a nontouching disk, presenceof a touching disk, and presence of an overlapping disk, respectively. (e) Comparative absorption profiles for the VSMBs assembly with theabsence and presence of intermediate disk with various diameters. (f ) Resistance variations as a function of the intermediate disk diameter.Inset is the CTP position as a function of conductive disk diameter.

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