Broadband resonant terahertz transmission in a

composite metal-dielectric structure

Jiaguang Han1, 3,*

, Jianqiang Gu2, 3

, Xinchao Lu2, Mingxie He

3,

Qirong Xing3, and Weili Zhang

2

1 Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore 2 School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA

3 Center for Terahertz waves and College of Precision Instrument and Optoelectronics Engineering, Tianjin

University, P. R. China

* phyhanj@nus.edu.sg

Abstract: We present a systematic numerical study of a metal-dielectric-

metal sandwich plasmonic structure for broadband resonant transmission at

terahertz frequencies. The proposed structure consists of periodic slotted

metallic arrays on both sides of a thin dielectric substrate and is

demonstrated to exhibit a broad passband transmission response. Various

design considerations have been investigated to exploit their influence on

the transmission passband width and the center resonance frequency. The

structure ensures a broadband transmission over a wide range of incident

angles.

© 2009 Optical Society of America

OCIS codes: (300.6270) Spectroscopy, far infrared; (240.6680) Surface Plasmons; (310.4165)

Multilayer design

References and links

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#113672 - $15.00 USD Received 1 Jul 2009; revised 24 Aug 2009; accepted 31 Aug 2009; published 1 Sep 2009

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1. Introduction

The recent studies on metamaterial and plasmonic structures have been gaining enormous

interest experimentally and theoretically in a broad range of disciplines [1–3]. The initial

research has paved a way for a series of fundamental understandings of the rich phenomena

and thus has raised the possibility of delivering unique structures unavailable in natural for

controlling electromagnetic waves. Continued interest in the subject is fueled by various

promising applications in nanofabrication, biochemical sensing, integrated devices, and so on

[4–6].

Among these, the research into optical devices at terahertz (THz) frequencies gathered a

great attention due to the unique and important applications of THz technology, which has a

large impact on various research fields such as material characterizing, security detection,

molecule sensing, imaging, and etc [7–9]. A THz device is desired to control the pulsed or

continuous-wave freely propagating THz radiation. Depending on the application, the

frequency, bandwidth, transmission power and modulation scheme of THz radiation may vary

widely. Typical THz devices usually include resonant filters, polarizers, compensators and

modulators [10]. There is an increasing demand for a THz bandpass resonant filter to be

designed for ensuring high tolerances to manufacturing parameters and multi-frequency

operations. In this study, we report on a strategy to create a novel structure that combines a

metal-dielectric-metal (MDM) sandwich with a periodic slot structure to perform an

ultrabroadband THz resonant filter with flatter transmission top. Such a device may provide a

desirable filtering method and operation to select frequency band in the THz regime and thus

lead to most practical applications.

2. Analysis and numerical results

Variant of the metallic subwavelength hole arrays related to unique extraordinary resonant

transmission had been discussed broadly at THz frequencies [11–13]. However, few attempts

were made to provide a filter with a wideband transmission based on such a metallic hole

array design. Motivated by this, our design for the resonant THz bandpass filter is a sandwich

structure consisting of periodic square-loop hole array. Figure 1(a) illustrates the schematic of

a unit cell of the chosen structure with normal incident electromagnetic field orientations. A

pair of 200-nm thick patterned metallic cladding layers sandwiches a dielectric layer of

thickness d. Each metallic layer was perforated with an array of square-loop-shaped slots with

dimensions: linewidth W, periodicity P and length L, as shown in Fig. 1(b). The chosen

square-loop slot pattern is a simple and symmetric structure, which exhibits excellent

transmission performance and is also easy for fabrication in practice. Such a MDM structure

is typically of linear dimensions in the THz community [14,15]. Simulations of the spectral

response were performed using a 3D full-wave solver employing CST Microwave studio TM.

Figure 2(a) shows the simulated transmission of a typical MDM structure with

dimensional parameters: P = 120 µm, L = 100 µm, W = 20 µm and d = 21 µm, where the

simulated model assumes that the metal is chosen as Aluminum and the middle dielectric is

Mylar of relative permittivity εd = 2.89. For comparison, a MD structure with only one single

metallic layer of the same square-loop hole array as that in MDM is also presented by the blue

curve. Inspection of the transmission clearly shows that the MDM structure of double metallic

layers has a much flatter transmission top as compared to that in MD. Clearly, the additional

#113672 - $15.00 USD Received 1 Jul 2009; revised 24 Aug 2009; accepted 31 Aug 2009; published 1 Sep 2009

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second array has the significant effect of flattering the transmission top and thus leads to an

ultrawide passband. The resonance top in the MDM structure is pulled broadly by the two

resonance frequency fi = 0.95 THz and fa = 1.28 THz away from each other, and the simulated

passband response centers at f0 = 1.12 THz.

Fig. 1. (a) The unit cell of the sandwich metal-dielectric-metal structure with normal incident

electromagnetic field. (b) Schematic of a square array of square-loop-shaped slots with a period

of P, linewidth W and length L. The thickness of the middle dielectric substrate is d.

Recently, a lot of works have been reported to explore the interaction of electromagnetic

wave with periodically arranged subwavelength structures [3,16,17]. For example, the

extraordinary optical transmission through subwavelength hole arrays was demonstrated and

often explained in terms of the resonant excitation of surface plasmons, where the excitation

of surface plasmons is widely believed responsible for resonant transmission based on the

interference of multiple electromagnetic wave scattered by periodically arranged holes. For

our case, we noticed that lower resonance frequency fi is located near the resonance frequency

of the MD structure, as shown in Fig. 2(a). The excitation of the surface plasmons by the

periodically arranged slot arrays in the MD structure is considered to be responsible for this

resonant peak. The electric field distributions in Fig. 2(b) also represent this feature clearly.

Because the excitation occurs in the single-layer MD structure, namely within one plane, we

call such a resonance an in-plane resonance. On the other hand, however, fa is located at a

higher frequency. When we search the origin of the resonance fa, it is interesting to notice that

the resonance fa is close to the resonance frequency excited in a sandwich metallic patch, as

shown in Fig. 2(a). The localized surface plasmons are excited in the metallic patch in each

plane, and when two-metallic-patch interfaces are brought together, the resonance modes

around each interface start to interact and couple together and thus produces the resonance fa.

The coupling between the front and back patch can be seen obviously through the electric

field distributions in Fig. 2(c). Considering that the resonance involves two planes, we call fa

an out-of-plane resonance. Therefore, in a complete MDM structure, it is no doubt these two

kinds of resonances, which are dominated respectively by surface plasmons and coupled

localized surface plasmons, interact each other and then give rise to the broad transmission

band. For convenience, we define ∆f = fa - fi to characterize such a unique resonant passband

transmission top and indicate the center resonance frequency as f0 [18–20].

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Fig. 2. (a) Comparison of the transmission spectra of the chosen MDM with the MD structure

of only one single metallic layer, as well as the sandwich patch array. The parameters are: L =

100 µm, P = 120 µm, W = 20 µm, d = 21 µm and εd = 2.89. The metal is Aluminum of

thickness 200 nm. (b) and (c) are electric field distributions at lower resonance frequency for

the MD and MDM structures, respectively.

For such a MDM filter design, the permittivity εd and the thickness d of the substrate

dielectric and the main geometry parameters of the slot naturally influence the optical

response. In following, we investigate the effect of these factors and aim to provide a greater

control and optimized design. Because the variation of periodicity P only induces slight

changes of both f0 and ∆f, P is assumed the fixed value of 120 µm throughout the

aftermentioned simulations. To illustrate interaction between metallic arrays, the transmission

of the chosen sandwich MDM structure at normal incidence for different spacing d are plotted

in Fig. 3(a), while the changes of f0 and ∆f as a function of d are summarized in Fig. 3(b).

Increasing d from 5 to 65 µm, f0 is reduced from 1.26 to 0.91 THz, accompanying an increase

of ∆f from 0.23 to 0.35 THz. For spacing above 21 µm, ∆f stays approximately the same with

increasing d, but the resonance occurring above 1.5 THz is seen to be enhanced obviously,

which is related to a higher-order excitation of surface plasmons.

The effect of linewidth W of the square loop can be seen in Figs. 3(c) and 3(d). With

increase of W from 5 to 25 µm, we can see that the center resonance frequency f0 blueshifts

from 0.84 to 1.44 THz, approximately twice variations. Meanwhile, ∆f is significantly

broadened from 0.16 to 0.47 THz, corresponding 294% variations. Although both f0 and ∆f

are enhanced with increasing W, the variations are not linear. We now consider the influence

of the length L in the square loop. Similar as the case of changing W, L also affects the

transmission profile of the MDM structure remarkably. The pronounced feature can be seen

from Figs. 3(e) and 3(f) that f0 is reduced from 1.82 to 1.24 THz if L becomes longer from 70

to 100 µm. However, it is of interest to notice that a maximum value of ∆f is achieved when L

equals to 85 µm, and further increased L leads to a decrease of ∆f. This may suggest an

optimum length for device design for performance at various center resonance frequencies

with different passbands.

In practice, except for the aforementioned dimensional parameters that influence the

transmission profile naturally, we can deduce that variation of permittivity εd of the dielectric

spacer has a similar effect on the response of the MDM structure. Actually, the permittivity of

substrate dielectric is flexible depending on the material selection and at THz frequencies we

also have various dielectric substrates with good transparent features such as Mylar, Quartz,

Teflon, Zitex (a kind of porous Teflon) and so on. The transmission of the MDM structure

with different dielectrics is plotted in Fig. 4. The primary effect of varying the dielectric is to

tune the center frequency f0 and ∆f. Decreasing the permittivity εd, f0 is blueshifted and ∆f is

broadened. The decrease of εd also makes the transmission top flatter.

#113672 - $15.00 USD Received 1 Jul 2009; revised 24 Aug 2009; accepted 31 Aug 2009; published 1 Sep 2009

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Fig. 3. (a) Computed transmission spectra of MDM structure with P = 120 µm, L = 100 µm, W

= 20 µm, and εd = 2.89 for various d. (b) ∆f and center resonant frequency f0 as a function of d.

The solid line is the fitting. (c) and (d) are effect on the transmission using different linewidth

W of the slot, where other parameters are fixed as: P = 120 µm, L = 100 µm, d = 50 µm, and εd

= 1.50. (e) and (f) are effect of various L on the transmission of the MDM structure with P =

120 µm, W = 20 µm, d = 50 µm, and εd = 1.50.

The preceding discussion concerning the effect of various dimensional parameters and

permittivity of middle dielectric on the response of the presented MDM structure

demonstrated that these parameters are essentially that of making the resonant transmission

curve broader, or flatter, or making the center resonance frequency shift. All may be taken as

optima in the practical device designs owing to their simplicity in fabrications. The

appropriate choice of these parameters of the MDM structure thus provides to obtain desired

center frequency and bandwidth, but if an analytical model can be given, it is of more help.

An analytical model for the center resonance frequency can be developed approximately in a

similar way as that proposed in Ref [20]. based on a circuit theory approach of microstrip

patch antennas, given as:

0 .( , , )

eff

cf

P L Wξ ε= (1)

The approximation by Eq. (1) to f0 primarily takes both substrate and geometry parameters of

slots into account and can be used to give the supplement to the numerical method for

determining desirable design. Here c is the velocity of light in free space. ( , , )P L Wξ depicts

#113672 - $15.00 USD Received 1 Jul 2009; revised 24 Aug 2009; accepted 31 Aug 2009; published 1 Sep 2009

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the contribution of dimensional parameters to the resonant transmission and is calculated

from:

( , , ) ,i i

i

P L Wξ β ζ ζ= + ∆∑ (2)

where we define i = 1, 2, 3 and thusi

ζ corresponds to P, L and W. iβ is the coefficient of each

dimensional parameters denoting the contribution to the resonant transmission and ζ∆ is the

Fig. 4. (a) Computed transmission spectra for various permittivity εd of the middle dielectric

substrate. (b) Dependence of the simulated values of the center resonance frequency f0 with

corresponding ∆f on εd. The solid line shows the fitting result.

correction index. effε is the effective permittivity considering an effective contribution of

the middle dielectric and air, and can be calculated from [14]:

(1 ) ,eff d air

d d

d dε ε ε

λ λ= + − (3)

where airε = 1.0 is the permittivity of air and

dλ is the critical thickness. The best fits to the

center resonance frequency by the model for various cases are presented by the solid lines in

Figs. 3(b), 3(d) and 3(f) and 4(b) with 1

1.36β = , 2

6.32β = − , 3

1.88β = and 90d

mλ µ= .

Figures 5(a) and 5(b) show the computed transmission curves of the MDM structure in the

H- and E-planes, respectively, for various angles of incidence θ. For TE-incidence, the

passband stays almost the same over wide angles of wave incidence. For TM-incidence, the

higher resonance frequency fa is shifted towards lower frequency slightly with increasing

incident angles. The simulated ∆f is 0.36 THz for normal incidence and 0.17 THz for TM 45°,

respectively. Hence, the presented MDM structure normally provides a stable resonant

passband with incident angles.

#113672 - $15.00 USD Received 1 Jul 2009; revised 24 Aug 2009; accepted 31 Aug 2009; published 1 Sep 2009

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Fig. 5. The 3D profile of simulated transmission response for various incident angles θ in (a)

TE polarization and (b) TM polarization, respectively. The parameters are: P = 120 µm, L =

100 µm, W = 20 µm, d = 50 µm, and εd = 1.50.

We now consider the effect of placing multiple layers. In Fig. 6(a), we compare the

simulated transmission of the design of different MDM layers, where up to four layers are

cascaded. It was not found significant effect when stack more layers, and the passband keeps

approximately the same as that of the two-array configuration, although more arrays causes

increased ripple and slightly broaden ∆f. The ripple may be due to the scattering of different

layers. Finally, as an extension, we present the simulated transmission of a complementary

structure of the chosen MDM structure in Fig. 6(b), namely, a metallic square-ring array

printed on both sides of the middle dielectric substrate, where a broad stopband can be found.

This provides a good choice for stopband THz devices and our recent research also

demonstrate such a structure exhibit a negative index in the THz regime [21].

Fig. 6. (a) Effect on the transmission response using various MDM layers. (b) Comparison of

the MDM structure with its complementary structure. The used dimensional parameters are as

same as those in Fig. 5.

3. Conclusion

In conclusion, a unique plasmonic sandwich configuration has been considered to produce a

structure having a broad passband at THz frequencies. We found that the geometry

parameters, as well as the permittivity of the dielectric substrate, have visible influence on the

transmission width and the center resonance frequency, which are capable of giving us the

versatility required in the practical device design. The stability in the passband transmission

response of the proposed structure is also obtained over wide angles of wave incidences, as

#113672 - $15.00 USD Received 1 Jul 2009; revised 24 Aug 2009; accepted 31 Aug 2009; published 1 Sep 2009

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well as in placing a multiple-layers case. The structure could lead to potential applications in

THz optical devices, such as filters, etc.

Acknowledgments

The author acknowledges financial support from the MOE Academic Research Fund of

Singapore and the Lee Kuan Yew Fund.

#113672 - $15.00 USD Received 1 Jul 2009; revised 24 Aug 2009; accepted 31 Aug 2009; published 1 Sep 2009

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