Optics Communications 361 (2016) 130–137

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Optics Communications

http://d0030-40

n CorrHangzh

E-mJohn.Zh

journal homepage: www.elsevier.com/locate/optcom

Design of terahertz metal-dielectric-metal waveguide withmicrofluidic sensing stub

Xiangjun Li a,b,c,n, Jian Song b, John X.J. Zhang c

a Centre for THz Research, China Jiliang University, Hangzhou, PR Chinab College of Information Engineering, China Jiliang University, Hangzhou, PR Chinac Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA

a r t i c l e i n f o

Article history:Received 14 July 2015Received in revised form8 September 2015Accepted 1 October 2015

Keywords:TerahertzMDM waveguideSensing stubMicrofluidics

x.doi.org/10.1016/j.optcom.2015.10.00718/& 2015 Elsevier B.V. All rights reserved.

esponding author at: Centre for THz Reseaou, PR Chinaail addresses: Xiangjun_li@cjlu.edu.cn (X. Li),ang@dartmouth.edu (J.X.J. Zhang).

a b s t r a c t

We design a terahertz (THz) metal-dielectric-metal (MDM) waveguide sensor with embedded micro-fluidic channel suitable for sensing the refractive index variations in liquid. The transmission propertiesare described using transmission line model (TLM) and numerically simulated using finite-differencetime domain (FDTD) method. The sensing characteristics of the structure are systematically analyzedthrough the examination of the transmission spectrum. The results reveal a series of pronounced re-sonance peaks in the transmission spectrum, which has linear relationship with the refractive indexvariation of the material under investigation. For detecting the presence of various cancer cells flowingthrough the microfluidic channel, we designed and optimized the structural parameters of the THz-MDMsensor and achieved a theoretical value of the refractive index detection sensitivity as high as 0.457 THz/RIU for a 20 mμ × 24 mμ cross-section channel. This work shows great promise toward realizing acompact THz refractive index sensor with high sensitivity for identifying the signatures of biologicalsamples in liquid.

& 2015 Elsevier B.V. All rights reserved.

1. Introduction

Terahertz spectroscopy, which covers radiation band ranging100 GHz to 10 THz, has intrigued tremendous interests in thebiological, chemical sciences as well as clinical research commu-nities. Studies have shown that terahertz waves could identifyintermolecular and intramolecular hydrogen bonds in biologicalmaterials such as amino acids [1], polypeptides [2], DNA [3], pro-tein [4], sugars [5], pharmaceuticals [6]. Applications such as pa-thological examinations of tissues [7] and identification of drugs orexplosives in postal packages can also be realized with this real-time, marker-free and non-ionizing technique [8,9].

However, there are a few limitations for applying THz spectro-scopy in biological detection in water solutions. Firstly, water hashuge absorption of THz waves due to the excitation of both waterdipolar moments and the hydrogen bond network. The method ofusing attenuated total reflection can partially solve the problem, butit will encounter the large signal loss from the in and out of thecoupling prism [10]. Second, relatively larger volume of bio-sampleswould be needed for THz analyses based on transmission, since the

rch, China Jiliang University,

wavelength of 1 THz is about 300 mm and the wrist of the corre-spondent Gaussian beam is therefore above 1 mm. Large quantitiesof samples to be studied may be hard to collect in reality. Toovercome such difficulties in sample volume, microfluidic systemshave been proposed for accurate volume control of the solutions toperform THz spectroscopy [11–14].

Alternatively, to address the above limitations, different THzwave manipulation structures such as parallel plate waveguides(PPWGs) or similarly metal-dielectric-metal (MDM) waveguideswere proposed, since they can support modes with deep sub-wavelength scale and high group velocity over a very wide rangeof frequencies extending from DC to visible scale. This is due to theformation of the dispersion-less transverse electro-magnetic(TEM) mode or the similarly MDM fundamental mode (TM0)considering surface plasmon polaritons(SPP) [15]. In THz domain,the highly localized field inside the PPWGs has been used to in-crease the sensitivity of a measurement [16–18]. Furthermore thestub like resonator has been integrated in the THz PPWG as a re-fractive index sensor for liquids in a microfluidic platform [19,20],but they did not use the TM0 mode and the influence of THz SPP atmetal-dielectric interfaces had not been explored though themetals behave almost like a perfect conductor (PEC).

In this paper, we proposed a compact (several tens of micro-meters width and several hundreds of micrometers length) andhighly sensitive liquid refractive index sensor based on a two layers

X. Li et al. / Optics Communications 361 (2016) 130–137 131

THz MDM stub structure. To make optimized designs, we not onlyemployed the numerical technique such as the finite difference-time domain method (FDTD), but also generated the transmissionline model (TLM) for the proposed sensing structure. TLM is a fastand reliable analytical approach investigated for optical bands [21–24], but few applications are reported in the THz band. The char-acterization of the impedance of the MDM by TLM can be useful fora better understanding of the MDM based THz components. TLManalytical modal also provides a design tool to generate complexplasmonic structures since the amount of calculation will dramati-cally drop when the optimization is necessary compared with EMpopular full wave numerical methods such as FDTD and FEM. Themodel allows us to rapidly and precisely simulate the transmissionspectra of THz MDM stub sensor considering SPP. The sensingcharacteristics of the proposed THz MDM stub structure wereanalyzed in detail. The result show that THz MDM stub integratedwith a microfluidic channel can be a very promising for both mo-lecular and cellular analyses towards point-of-care type of biologicalsensing.

2. Structure and method

The proposed THz MDM wave guide with a two layers stubstructure is schematically shown in Fig. 1(a) and (b), in which thestub includes a solid spacing dielectric layer and a liquid bioma-terial sample layer. Consider the possible applied scenario in Fig. 1(a) where the thickness t of the structure is thick enough to sim-plify the sensor into a 2D scheme in Fig. 1(b). The channel ( airε )width is d. The two layers stub with width w includes a dielectricspacing layer ( dε ) with height h1 and a biomaterial sample layer( sε ) with height h2. When the biomaterial sample is liquid flowingin tens of microns microfluidic channel, the solid dielectric spacinglayer is necessary in an integrated system.

It has been revealed that the transmission of an MDM wave-guide can be described using the analogy between single-mode

Fig. 1. Design of a THz MDM waveguide with a two layers stub including a dielectric sp(b) 2-D Schematic; (c) the equivalent transmission-line representation, and (d) its simp

MDM waveguides and microwave transmission lines [21–24].Then, the waveguide of width d is replaced by a transmission lineof characteristic impedance

Z dd d

k 10

β ηε

( ) = ( )( )

where dβ ( ) is the SPP propagation constant at wavelength λ, dε isthe relative permittivity of the dielectric in the MDM, η is the waveimpedance in the dielectric, and k 2 /0 π λ= . The analogy will be ef-fective under the quasi-static approximation with d λ≪ in whichonly single fundamental mode (TM0) can be supported. The dβ ( )can be calculated by the dispersion relationship for the TM-SPP ora simplified approximation [25]

d kk d

22

d dd m

m0

0β ε ε

ε εε

( )= −−

( )

where dε and mε are the relatively permittivity of dielectric andmetal respectively. When ?mε →∞ the d k n k neff d d0 , 0β ( )= ≅ , whereneff d, is the effective index of the MDM with the dielectric of therefractive index nd.

In Fig. 1(b) the characteristic impedance of the wave guide ofair Zair can be obtained from Eq. (1) by substituting vacuum fordielectric. At the same time the stub sections of the waveguide onthe spacing dielectric and the sample can be represented by twofinite-length transmission lines of characteristic impedance Zd andZs with the corresponding relatively permittivity dε and sε , andreplacing d by w.

The whole THz MDM wave guide with two layers stub consistsof the three transmission line segments, which need to be con-nected in parallel in Fig. 1(c). The equivalent network presentationshown in Fig. 1(d) . The part of transmission corresponding to thetwo layers stub can be replaced by effective impedance

Z ZZ jZ hZ jZ h

tantan 3

stub dL d d

d L d

1

1

ββ

=′ + ( )

+ ‵ ( ) ( )

acing layer and fluidic layer with samples under investigation. (a) 3-D Schematic;lified circuit model.

Fig. 2. Comparison of transmission for the THz MDM wave guide with a two layers stub. (a) TLM versus FDTD simulations, where red circle and solid line represent theresults of TLM from Eq. (5) and FDTD based on PEC model, and blue square and dash line represent the results of TLM and FDTD based on Drude model. (b) The evolution oftransmission with h1. Note: the size parameters are d¼w¼h2¼20 μm, h1¼10 μm and L¼200 μm, and the metal is gold, the channel is filled with air, the spacing dielectric isSi, the sample is water. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

X. Li et al. / Optics Communications 361 (2016) 130–137132

where dβ is the SPP propagation constant in the spacing dielectriclayer, and ZL′ is the effective impedance for the biomaterial samplelayer

Z ZZ jZ hZ jZ h

tantan 4

L sL s S

s L S

2

2

ββ

‵ =+ ( )+ ( ) ( )

where Sβ is the SPP propagation constant in the sample layer ZL isthe impedance of the stub end that becomes short-circuited (Z 0L= )[24] with the approximation of PEC when mε →∞ that most ofmetals meet the condition between 0.1 and 3.0 THz.

Two forms of the transmission of the MDM waveguide coupledto a single stub are given by [24,26]

⎛⎝⎜

⎞⎠⎟T

ZZ

LL

12

exp5

stub

air SPP

2

= + −( )

−

⎛⎝⎜

⎞⎠⎟T

S S R iR R i

LL

exp1 exp

exp6

inin out dS

out dS SPP

2ϕϕ

= − ( )− ( )

−( )

where, L is the length of the waveguide, and LSPP is the characteristicdecay length of the SPP mode in the waveguide. In Eq. (5) the firstpart with the modulus accounts for interference between the in-cident wave and the wave reflected from the stub. The exponentialfactor describes attenuation of SPP and the signal intensity decays ona length scale of the characteristic propagation length of the SPP

mode, L Im2 .SPP1β=( ( ))− In Eq. (6), Tin

ZZ Z

22air

d air= + , RdS

Z Z

Z ZL d

L d= ′ −

′ +, Rin

ZZ Z2

d

d air= +

,

SinZ

Z Z2d

d air= +

, SoutZ

Z Z2

2air

d air= + are transmission, reflection and scattering

coefficients. And h arg R2r d dS1ϕ ϕ ϕ βΔ = + = + ( ) is the round tripphase difference in the dielectric stub. In Eq. (6). if m2 1ϕ πΔ = ( + )(m¼0,1,2,…) is satisfied the transmission minima frequency is de-termined as follows:

⎡⎣⎢

⎤⎦⎥

fc m

n h

2 1

4 7m

R

eff d

arg

, 1

dS( )

=+ −

( )

π

Though most of metals can be seen as a PEC at 0.1–3.0 THzcovered by popular THz time-domain spectroscopy (THz-TDS), butthere is still an obvious difference between a real metal and a PECmodel in THz wave band. To investigate such a real scenario, wetake gold as a real metal assuming its classic Drude conductivitywith a dielectric function i1 / /m p

2 2ε ω ω ω τ= − ( + ). A plasma fre-quency of /2 2080 THzpω π = and a carrier scattering time of

18 fsτ = is taken from [27]. At the same time, we selected the highresistance silicon ( 11.66dε = ) [28]as the spacing layer that is pop-ular in microfluidic system manufacture and almost lossless in

0.1–3.0 THz and the biological sample is replaced by water with aDebye–Lorentz function at 296 K [29]

j jA

j1 1 8s

s

s s

1

1

2

22 2ε ω ε

ωτεωτ ω ω ωγ

ε( ) = Δ+

+ Δ+

+− +

+( )

∞

where the first and second terms are the Debye-type slow and fastrelaxation mode with relaxation strengths 73. 91ε∆ = , 1. 562ε∆ =and relaxation times 8. 76 ps1τ = , 0. 224 ps2τ = . The third termshows the Lorentz-type intermolecular stretching vibration withamplitude A / 2 35. 1 THzS

2 2π( ) = , resonant frequency/2 5. 30 THzSω π = and damping constant /2 5. 40THzSγ π = . The last

term 2. 34ε =∞ is the higher frequency limit in the real part.

3. Results and discussion

To illustrate the developed transmission line model by com-paring the metal models by PEC and Drude, we considered the THzstub waveguide with the following set of parameters L¼200 mμ ,h2¼w¼d¼20 mμ , and h1¼10 mμ . The metal is gold, the channel isfilled with air, the spacing dielectric is Si, and the sample is waterby the model in Eq. (8). The geometry parameters are typical inapplications such as PCR [30] and circulation tumor cell (CTC)detection [31–35]. We examined the accuracy of the TLM model bycalculating the waveguide transmittance with FDTD. In numericalFDTD simulations, both the MDM waveguide and the stub aredivided into the computational domain containing uniform Yeecells with Δx¼Δy¼1 mμ and surrounded by all perfectly ab-sorbing boundaries. To calculate transmission of the MDM withthe stub(T¼Pout/Pin), incident power of Pin and transmitted powerof Pout were monitored at positions of x¼0 and x¼L respectively inFig. 1(b). Fig. 2(a) shows the comparison of transmissions calcu-lated by TLM (assuming Z 0L= ) from Eq. (5) (solid and dash lines)and by FDTD (circle and square symbols) with the metal describedby PEC (red) and Drude model (blue). The results illustrated thatthe prediction of the TLM has relatively good agreement withFDTD method especially considering the SPP effect using Drudemodel. It is also to be noted that PEC model is not accurate enoughto estimate the transmission of our proposed THz MDM stubstructure when the length of MDM wave guide is more thanseveral hundred micrometers. Fig. 2(b) shows the influence of h1the height of the silicon spacing layer in the stub on the trans-mission by TLM. It reveals that when h1 increase from 0 to 30 mμ ,and there will be more resonance peaks on the transmissionspectra that can be used in sensing. The reason for this variationcould be revealed by Eq. (7) that the distance between neighborresonances will decrease with h1 increasing, which also reducesthe width of the resonance dip at the same time.

Fig. 3. The density plots of electric fields (in relative scale) corresponding to the fundamental antisymmetric SPP mode of the THz MDM stub structure at (a) f¼0.2 THz,(b) 0.76 THz, (c) 2.0 THz and (d) 3.0 THz by FDTD. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

X. Li et al. / Optics Communications 361 (2016) 130–137 133

To further investigate the behavior of the stub as sensing ele-ment, the profiles of the transverse electric field (Ey) is plotted inFig. 3(a)–(d) for f¼0.2, 0.76, 2.0, 3.0 THz by FDTD. We see that theenergy of electric field is focused at the stub area, and the field instub at the f¼0.76 THz reaches the highest among four frequencieswhere the transmission is at the minimum. The ratio of thehighest density at 0.76–0.2 THz where the transmission is at themaximum is more than 7.5 times. It is the enhancement of electricfield in the stub play the main role in the sensing functions.

In order to character the sensing features of the proposedstructure, the transmission spectra are calculated by the TLM inFig. 4. with same geometric parameters in Fig. 2 when the metal isgold, the spacing dielectric is Teflon (a), HDPE (b), Quartz (c) andSilicon(Si) (d), and the refractive index of the sample is increasingfrom 1.0 to 2.0. Four spacing materials are low loss in THz bandwhich is widely used in THz system building and the real part of

Fig. 4. The transmission spectra calculated by TLM for the spacing dielectric as (a) Teflonthe size parameters are d¼w¼h2¼20 μm, h1¼10 μm and L¼200 μm, and the metal is gofrom 1.0 to 2.0.

their average refractive index are only considered in the calcula-tion with 1.45 for Teflon, 1.57 for HDPE, 1.95 for Quartz and 3.417for Si [28,36,37]. The calculation errors from the approximation ofthe refractive indices on these spacing materials should be negli-gibly small compared with those errors from fabrication andmeasurement [38]. The resonance dips of resonances are nar-rowing because distances between neighbor resonances will de-crease with nd increasing derived from Eq. (7). It is obvious thatthe resonant frequencies show linearly red shifts with the in-creasing refractive index of the sample in Fig. 5(a). If we take thedefinition of the sensitivity as the shift in the resonant frequencyper unit change of refractive index (THz/RIU), we determine thesensitivity by linearly fitting the resonant frequency curve. Thesensitivities for air and the four spacing materials are 0.838 THz/RIU, 0.451 THz/RIU, 0.383 THz/RIU, 0.233 Hz/RIU and 0.052 THz/RIU respectively. So the spacing dielectric material has obvious

(n¼1.45), (b) HDPE (n¼1.57), (c) Quartz (n¼1.95) and (d) Silicon (n¼3.417) whenld, the spacing dielectric is Si with the refractive index of the sample nS is increasing

Fig. 5. Characteristics of THz MDM Sensor. (a) The refractive index of the sample versus the resonant frequency with the spacing dielectric as Air, Teflon, HDPE, Quartz andSilicon; (b) the sensitivity of the sensor versus the refractive index of the spacing dielectric.

Fig. 6. The sensitivity of the proposed structure versus the spacing layer height h1 in (a), the spacing layer height h2 in (b), the MDM width d in (c) and the stub width w in(d) with h1¼10 mμ and h2¼w¼d¼20 mμ when the spacing dielectric is Air (green), Teflon (red), HDPE (blue), Quartz (purple) and Silicon (black). (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version of this article.)

X. Li et al. / Optics Communications 361 (2016) 130–137134

effect on the sensor's sensitivity and the relationship betweenthem is shown in Fig. 5(b). It can be seen that the sensitivity isexponentially declining with the refractive index of the spacingdielectric increasing. It is concluded that the lower the refractiveindex of the spacing dielectric the better the sensor's sensitivity isand the highest sensitivity will be achieved when the refractiveindex is 1. The phenomenon can be attributed to the higher re-fractive index of the spacing dielectric causing higher reflection ofthe electrical-magnetic wave to the coupling MDM wave guidewith air. The sensitivity of our sensor will have better performancethan the similar THz PPWG resonant cavity sensor offered byMttleman's group with TE mode [20] if we take the lower re-fractive index spacing dielectric like Teflon, HDPE and Quartz oreven smaller at a very thin thickness. The possible ideal solution isusing the porous polymers film as the spacer. Their sensor has a

sensitivity of 91.25 GHz/RIU when it is working at TE1 mode. Atthe same time the widths of their PPWG at 1mm and resonantcavity at 472 mμ are much bigger than ours.

Finally, the structural parameters of the device impact onsensing sensitivity are analyzed in order to improve the perfor-mance. It is clear that the geometry parameters of the proposedsensor such as h1, h2, d and w will dominate the sensitivity of oursensor. By utilizing the TLM method in Eq. (5), we now study thesensing performance when one of the above four geometryparameters of h1¼10 mμ and h2¼w¼d¼20 mμ is changing withkeeping other three ones invariable in Fig. 6. At the same weconsider the effect of the spacing materials by choosing Air, Teflon,HDPE, Quartz and Si as examples. Fig. 6(a) shows the relationshipbetween the sensitivity and h1 that the sensitivity is exponentiallydeclining with the height h1 of the spacing dielectric increasing,

Fig. 7. The d dnFOM Max / /FWHMλ= ( ) of the proposed structure versus the spacing layer height h1 in (a), the spacing layer height h2 in (b), the MDM width d in (c) and thestub width w in (d) with h1¼10 mμ and h2¼ w¼d¼20 mμ when the spacing dielectric is Air (green), Teflon (red), HDPE (blue), Quartz (purple) and Silicon (black). (Forinterpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 8. THz Permittivity of the 4 different liquid samples are modeled by experimental measurement including distilled water (black), and three cultured human cancer cellsincluding DLD-1 (red), HEK293 (green) and HeLa (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of thisarticle.)

X. Li et al. / Optics Communications 361 (2016) 130–137 135

which is very similar with the relationship between the sensitivityand the refractive index of the spacing dielectric in Fig. 5(b) sincetheir changing are physically equivalent. The above results alsocould be illuminated by Eq. (6), where the height of h1 and therefractive index of the spacing dielectric in the round trip phasedifference h arg R k n h arg R2 2d dS d dS1 0 1ϕ βΔ = + ( ) ≅ + ( ) are each af-fecting the resonant peaks of T in an exponential relationship.Fig. 6(b) shows the relationship between the sensitivity and h2that there is an optimized height for the sample layer to reach thehighest sensitivity. By Eq. (6). the transmission resonant peakobviously depends on the phase of the reflection RdS from the

sample to the spacing layer which is affected by h2 and nS at thesame time. On the curved surface of transmission resonant peakson h2 and nS , there is the maximum gradient of the resonant peaksalong nS with h2 variation. The optimized height is increasingwhen the refractive index of spacing materials is increasing. Theoptimized heights of Air, Teflon, HDPE, Quartz and Silicon arecalculated as 15 mμ , 24 mμ , 26 mμ , 38 mμ and 85 mμ , and corre-sponding sensitivities are 0.875 THz/RIU, 0.457 THz/RIU,0.396 THz/RIU, 0.267 THz/RIU and 0.092 THz/RIU respectively.Fig. 6(c) and (d) shows the relationship between the sensitivityand the widths of the coupling MDM and the resonant stub. The

Fig. 9. The transmission spectra by (a) TLM and (b) FDTD for distilled water (black), and three cultured human cancer cells including DLD-1 (red), HEK293 (green) and HeLa(blue) when the spacing material are Teflon with optimized geometry parameters of h1¼10 mμ , h2¼24 mμ and w¼d¼20 mμ . (For interpretation of the references to color inthis figure legend, the reader is referred to the web version of this article.)

X. Li et al. / Optics Communications 361 (2016) 130–137136

results show that the sensitivity keeps almost invariable when dand w changing between 10 mμ and 70 mμ in which the singlefundamental mode up to 2.1 THz is only supported. It is because dand w have no effects on the positions of resonant peaks sincethey are not present at the expression of the round trip phasedifference ϕΔ .

However these widths will affect the Full Width Half Maximum(FWHM) of transmission spectrums. The factor of merit (FOM)defined by d dnFOM Max / /FWHMλ= ( ) will reveal such influencesin Fig. 7. The FOMs are exponentially decreasing with h1 in-creasing in Fig. 7(a) and exponentially increasing with an upperlimit on h2 in Fig. 7(b). The growing of d will improve the FOMs inFig. 7(c), but the growing of w reduces them shown in Fig. 7(d). SoFOM is more indicative than sensitivity used for evaluating asensor for it takes the bandwidth of resonant peak into con-sideration, which is crucial for determining the resolution orprecision of the measurement. If we fixed the h1¼10 mμw¼20 m and d 50 mμ = μ to ensure that only transverse magneticmode excited up to 3 THz [39], we can get the maximum sensi-tivity of 0.457 THz THz/RIU with Teflon spacer at the optimizedheight h2¼24 mμ with FOM¼3.1 in an applicable scenario.

To demonstrate the potential of our proposed structure as aliquid refractive index sensor, we choose four samples includingdistilled water, and three cultured human cancer cells such asDLD-1, HEK293 and HeLa as application examples. In Fig. 8 theirpermittivity by Debye–Lorentz functions in 0.1–3.0 THz were ta-ken from [10] by THz attenuated total reflection spectroscopy withthe monolayer of the cancer cells cultured in incubation chamberon the ATR prism at 310 K. We calculated transmissions of thesefour samples in Fig. 9. when the spacing material are Teflon withoptimized geometry parameters of h1¼10 mμ , h2¼24 mμ andw¼d¼20 mμ . The result shows that there are the most apparentdifferences between four samples when the spacing material isTeflon. The resonant frequencies are 1.254 THz, 1.279 THz,1.264 THz, 1.247 THz by TLM in Fig. 9(a), and 1.213 THz, 1.245 THz,1.234 THz, 1.217 THz by FDTD in Fig. 9(b) for water, DLD-1, HEK293and HeLa respectively. And their absorptions also are relativelydifferent which can be further studied as detection indicators.There is still large potential to improve the sensitivity of thestructure by changing the geometry parameters. In real scenario itis probably difficult to directly recognize the cancer cells by thesimple shifting amplitudes of the resonant frequencies. But ourproposed structure have the potential to build the single cell basedmodels by statistical analysis of resonant peak features in futureresearch. The models can be applied in recognition and classifi-cation of real cancer cells in liquids. The proposed structure hasthe potential to detect the presence of single cancer cells, based onthe large population screening capabilities offered by the

microfluidics coupled with statistical analyses, which will be ap-plied to correlate the resonant frequency shift with the cellspresented.

4. Conclusion

In summary, we introduce the design of a compact THz MDMwaveguide-coupled microfluidic stub structure for the detection ofrefractive index variations in liquid. TLM method is proved as anefficient and reliable analytical approach to design the sensorstructure on deep THz sub-wavelength MDM waveguide. The re-sonant wavelength of the sensor has a linear relationship with therefractive index of the sample under investigation. The sensitivityof the sensor can be further optimized by narrowing the heightand reducing the refractive index of the spacing dielectric material.In addition, the width of THz MDM and the stub also play a roleinfluencing the sensitivity. The simulation results show that thesensitivity of the structure can exceed 0.457 THz/RIU with a20 mμ × 24 mμ cross-section channel if further properly designed.We show the potential application in cancer cell detection in li-quid, using the Debye–Lorentz models. The simplicity of thestructure makes the potential implementation possible using thestate-of-the-art microfabrication technologies for the device fea-ture size needed for THz detection. The proposed design andmodeling serves as an important guidance to realizing a fully in-tegrated microfluidic sample manipulation integrated with thehigh-resolution chemical and biological detections through THzsensing.

Acknowledgments

Our work has been financially supported by the NonprofitTechnology Research Programs of Zhejiang Province of China un-der Grant no. 2013C31088 (Li), National Science Foundation CA-REER Award under Grant no. 0846313 and DARPA Young FacultyAward under N66001-10-1-4049 (Zhang).

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