904 OPTICS LETTERS / Vol. 35, No. 7 / April 1, 2010

Transmission field enhancement of terahertz pulsesin plasmonic, rectangular coaxial geometries

Xinchao Lu,1 Jiaguang Han,2 and Weili Zhang1,*1School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA

2Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore*Corresponding author: weili.zhang@okstate.edu

Received August 26, 2009; revised February 13, 2010; accepted February 19, 2010;posted February 24, 2010 (Doc. ID 116299); published March 17, 2010

We report on anomalous field enhancement of terahertz transmission in metallic, rectangular coaxial geom-etries. The integration of a particle in the hole not only results in a factor of eight increase in normalizedtransmittance compared to that of the hole-only counterpart, but it also tailors polarization-dependenttransmission discrepancy encountered in arrays of rectangular holes. Our experimental and numerical stud-ies on the impact of geometrical dimensions of the integrated particles indicate that dipolar localized surfaceplasmons of the particles contribute substantially to the terahertz field enhancement through coupling withsurface plasmons and localized surface plasmons of the holes. © 2010 Optical Society of America

OCIS codes: 050.6624, 240.6680, 300.6495.

Recent studies reveal that the field enhancement ofelectromagnetic waves mainly occurs in two types ofplasmonic geometries, i.e., holes or particles of sub-wavelength dimensions [1,2]. Higher than unity nor-malized transmission was observed in periodicallyarranged holes resonating in various spectral re-gimes of electromagnetic waves. The primary at-tribute of this phenomenon has been considered asresonant excitation of surface plasmons (SPs) at theinterface of the metallic holes and dielectric [3–6]. Incontrast, resonance enhancement in the metallic par-ticles appears in the form of anomalous transmissionminimum, owing essentially to resonant excitation ofdipolar localized surface plasmons (DLSPs) [2,7].

Once a particle was integrated into the hole, fur-ther transmission enhancement was achieved in thearray of the resulted coaxials [8–12]. The resonantresponse of the coaxial structures was primarily as-cribed to the contributions of both SPs and the wave-guide TE11 mode at visible frequencies [8]. In theterahertz regime, however, most metals becomehighly conductive. As such, their skin depth remainsapproximately at the same order of that at visible fre-quencies [13,14]. Thus, optically thick terahertzstructures can be made extremely thin comparedwith their resonance wavelengths. Therefore, DLSPsof the inner particles, instead of the waveguide effect,would play an essential role in transmission proper-ties of the coaxial geometries [15–17]. In addition,the advantage of exploring such plasmonic structuresat terahertz frequencies is that the well-developedmicroelectronic processing allows for precise controlover the dimensions of microstructured coaxials,which enables systematic studies of the effect of in-ner particles on the overall behavior of coaxials. Inthis Letter, we present experimental and numericalstudies on the role of DLSPs of the inner particles intransmission properties of terahertz pulses in rectan-gular coaxials. The anomalous field enhancementand the Fano lineshape are characterized in terms ofgeometrical dimensions of the inner particles and the

orientation of the coaxial geometries.

0146-9592/10/070904-3/$15.00 ©

The inset of Fig. 1(a) illustrates a microscopic im-age of a square array of rectangular coaxials com-posed of 100�80 �m2 holes and 80�40 �m2 inte-grated particles with a periodicity 160 �m. The arraywas fabricated by use of conventional photolithogra-phy and metallization processes onto a 190-nm-thickaluminum film with silicon substrate (0.64 mm thick,n-type resistivity �=12� cm). Figure 1(a) showsfrequency-dependent amplitude transmissions of the

Fig. 1. (Color online) (a) Measured frequency-dependentamplitude transmissions of periodic (solid curve) and ran-dom (dash-dotted curve) coaxials with 100�80 �m2 holesand 80�40 �m2 inner particles and the hole-only counter-part (dotted curve), with a periodicity 160 �m and E �x. In-set, microscopic image of the coaxial sample. (b) Simulatedpeak amplitude transmission (diamonds) and normalizedtransmittance (circles) as a function of the length (x axis) ofthe inner particles of 60 �m fixed width. The squares mani-fest the measured peak amplitude transmission. (c) Simu-lated resonance frequencies as a function of the length ofinner particles. The hollow circles are the experimentalresonance frequencies. Simulated electric field distribu-tions of the same coaxial array: (d) at 0.48 THz with E �x

and (e) at 0.51 THz with E �y.

2010 Optical Society of America

April 1, 2010 / Vol. 35, No. 7 / OPTICS LETTERS 905

coaxials and the counterpart hole-only array. Thedata were recorded by terahertz time-domain spec-troscopy (THz-TDS) under normal incident radiationwith electric field parallel to the longer axis of thestructure, E �x [4,18]. The amplitude transmission isdefined as �t����= �Es��� /Er����, where Er��� and Es���are the Fourier-transformed amplitudes of the tera-hertz pulses transmitted through the reference, ablank silicon wafer identical to the array substrate,and the array, respectively. It is interesting to notethat the measured transmission of the coaxials (0.92)exhibits a significant increase over that of the hole-only array (0.47) at the Si–Al �±1,0�, plasmonicmode. In addition, the resonance frequency of the co-axials reveals noticeable redshift.

Such resonant properties are systematically char-acterized in a series of coaxial structures with vari-ous dimensions of inner particles but fixed periodicityand dimensions of holes. Figure 1(b) shows the peakamplitude transmission and normalized transmit-tance as functions of particle length (along the x axis)obtained from measurements and numerical simula-tions using a finite integration technique. The nor-malized transmittance was obtained by normalizing�t����2 over the open area of the coaxial. The dielectricproperties of Al were characterized by the Drudemodel in the simulations. The particle length showsan extensive influence on the field enhancementwhen the particle width (along the y axis) is fixed at60 �m. The calculated amplitude transmission andnormalized transmittance at the Si–Al �±1,0�, plas-monic mode approach their maxima at lengths of 70and 90 �m, respectively. The measured normalizedtransmittance reveals a value of 5.64 at length80 �m, which is eight times of that in the hole-onlycounterpart, showing a good consistency with the cal-culation. In Fig. 1(c) we show that the resonance red-shifts with increasing length of the particles.

The observed transmission properties of the co-axial structures are essentially a result of resonantexcitations of DLSPs of the particles and their cou-pling with SPs, localized surface plasmons (LSPs) ofthe holes, and direct scattering. The increased par-ticle length along electric field strengthens its DLSPresonance, which gives rise to resonance enhance-ment and redshift through coupling with SPs andLSPs of the holes [7,19]. The effect of direct scatter-ing is also revealed from Fig. 1(a), where the nonreso-nant background of the coaxials is noticeably reducedcompared with that of the hole-only array due tomodification of direct scattering by the addition ofthe particle.

Figure 2(a) shows the measured amplitude trans-mission with terahertz electric field switched to E �y.As expected, the hole-only array exhibits much stron-ger peak transmission (0.85) than that of E �x owingto the polarization-dependent nature of the rectangu-lar holes [4]. As such, when the 80�40 �m2 particleis integrated in the hole, although a factor of 1.67 en-hancement in normalized transmittance is achieved,no obvious modification is shown in the amplitudetransmission. However, when the particle dimension

is changed to 60�60 �m2, a nearly perfect transmis-sion, 0.99, is achieved owing to enhanced DLSP reso-nance along the y axis. The measured highest nor-malized transmittance for E �y is again obtained inthe coaxial array with 80 �x axis��60 �y axis� �m2

particles, having a value 6.20 at 0.47 THz. The reso-nance shift, similar to that of E �x, is closely relatedto the particle length along the terahertz electricfield. It is also interesting to note that the extensivepolarization-dependent transmission discrepancy inthe rectangular holes is very well compensated byDLSPs of the integrated particles through couplingwith SPs and LSPs of the holes in the coaxials. Forexample, the measured peak amplitude transmis-sions in the coaxial array with the 80�60 �m2 innerparticles for E �x and E �y are 0.84 and 0.88, respec-tively, while the values are 0.47 and 0.85 for the hole-only array.

The asymmetric resonance lineshape of the coaxialgeometries is analyzed by use of the Fano model,which describes the interaction between the discreteresonant state and the continuum scattering state[7,8,20–23]. Here, contributions to the discrete reso-nant state include DLSPs of the particles, SPs, andLSPs of the holes. The Fano transmittance can bewritten as IFano=Ia+Ib�1+�vq� /����2 / �1+ ���1/����2�,where ���= ��−��� / �� /2�, Ia is a slowly varyingtransmittance, Ib is the continuum transmittance co-efficient that couples with the discrete resonantstates, �� /2 is resonance frequency, � /2 is line-width, and q� is the Breit–Wigner–Fano coupling co-efficient for the �th discrete state. As shown in Fig.3(a), the experimental transmittance of the coaxialarray with the 80�40 �m2 inner particles at E �x iswell fit by the Fano model, indicating that both Al–Si�±1,0�, and �±1, ±1� resonances are resulted fromthe contributions of DLSPs of the particles, SPs,LSPs of the holes, and the direct scattering.

In Fig. 3(b), we show the measured angle-resolvedtransmission spectra of the same coaxial array atE �x. The Al–Si �±1,0�, plasmonic mode at 0.46 THzexhibits angle-independent behavior owing to adominant contribution of DLSPs of the particles. Thehigh frequency Al–Si �±1, ±1� plasmonic mode near

Fig. 2. (Color online) (a) Measured frequency-dependentamplitude transmissions of periodic coaxials (Cox) and ran-dom coaxials (RCox) with various inner particles (Ptc) andthe hole-only array (dotted curve) at E �y.

0.80 THz, however, experiences resonance splitting

906 OPTICS LETTERS / Vol. 35, No. 7 / April 1, 2010

with incident angle greater than 10°, owing to a weakeffect of DLSPs but a primary contribution of the SPresonance. Based on the angle-resolved experiment,we further characterize the coupling mechanism be-tween different states of the coaxials by use of aHamiltonian, H=H1+H2+H3+ V, where the eigen-states H1, H2, and H3 stand for the DLSP resonanceof the particle, the Al–Si SP �−1,0� mode, and thecontributions of both LSP of the hole and direct scat-tering [22], respectively, and V is the coupling termbetween these eigenstates represented by oupling co-efficients �12, �13, and �23. The corresponding eigenfrequencies, �1 /2 and �2 /2, are the DLSP and SPresonance frequencies, respectively, given by theirdispersion relations [7,22], and �3 /2 is resultedfrom both LSPs of the holes and direct scattering[22]. The variables, i.e., �3, �12, �13, and �23, are ob-tained by diagonalizing H using the angle-resolvedtransmission data in Fig. 3(b). At E �x, the calculatedcoefficients are ��12�=8.03�10−3, ��13�=0.103, and��23�=9.70�10−3, indicating that the coupling be-tween DLSPs and LSPs primarily contributes to thefield enhancement, which further explains the angel-independent behavior of the Al–Si �±1,0�, mode ob-served in Fig. 3(b). This behavior is also evidencedfrom the computed electric field distribution of the co-axials, as illustrated in Fig. 1(d), where strong fieldenhancement is observed in the particle and the openarea of the coaxial. In addition, this is consistent withthe measured amplitude transmission of a nonperi-odic counterpart array composed of same numberdensity of coaxials. As shown in Fig. 1(a), the minordifference in the transmissions between the periodicand nonperiodic arrays indicates that SPs play lessimportant role than DLSPs of particles and LSPs ofthe holes.

At E �y, the calculated coefficients are ��12�=0.151,��13�=5.00�10−4, and ��23�=2.35�10−2, manifestingthe dominant role of the coupling between DLSPsand SPs. This is also consistent with the electric fielddistribution shown in Fig. 1(e), in particular, the elec-

Fig. 3. (Color online) (a) Measured (open circles) and Fanofit (solid curve) transmittance of the coaxials with innerparticle 80�40 �m2, periodicity 160 �m, and E �x. The fit-ting parameters are Ia=0, Ib=0.0013, q1=24.5, 1 /2=0.11, �1 /2=0.4485, q2=1.35, 2 /2=0.07, �2 /2=0.7680, q3=1.8323, 3 /2=0.25, and �3 /2=1.1852. (b)Measured angle-resolved transmission of the same coaxialarray at E �x. The dashed curves represent the resonancemodes.

tric field along the surface of metal in the vicinity of

the coaxials is much enhanced than that at E �x. Thedrastically reduced transmission in the nonperiodicarray, as shown in Fig. 2, also reveals that SPs playan important role in the transmission field enhance-ment at E �x.

In conclusion, anomalous transmission propertiesof rectangular coaxial geometries are investigated byuse of THz-TDS and numerical simulations. In par-ticular, the impact of geometrical dimensions of theinner particle is systematically exploited, whichshows that a number of factors contribute to the ob-served field enhancement, including DLSPs of theparticles, SPs, LSPs of the hole, and direct scatter-ing. The unique resonant characteristics make thecoaxial structures an excellent candidate in develop-ing active and passive terahertz components.

The authors acknowledge S. Zhang for his help innumerical simulations. This work was partially sup-ported by the National Science Foundation (NSF).

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