IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 12, 2013 631

Wideband Tuning of the Tunneling Frequencyin a Narrowed Epsilon-Near-Zero Channel

Miranda Mitrovic, Branka Jokanovic, Member, IEEE, and Nebojsa Vojnovic

Abstract—We propose a design of foam epsilon-near-zero (ENZ)waveguide with - and -plane step discontinuities at the samewaveguide cross section. This enables using channel dielectric per-mittivity greater than the permittivity in input waveguides, whichis required for foam ENZ waveguide realization. A method forwideband tuning of tunneling frequency by changing the length oftwo longitudinal slots was also proposed and experimentally veri-fied. Simulated tuning range is 1.06 GHz, which is in a good agree-ment with experimentally achieved 0.99 GHz. This tuning range isaccompanied by amplitude decrease of 1.6 dB.

Index Terms— - and -plane step discontinuity, epsi-long-near-zero (ENZ) metamaterial, frequency tuning, rect-angular waveguide.

I. INTRODUCTION

E NERGY tunneling through a very narrow channel ob-tained by reducing the height of a rectangular waveguide

has attracted great attention of the scientific community inthe past several years. It has been theoretically shown that itis possible to obtain transmission of electromagnetic wavesexcited in an input waveguide through a very narrow channeldespite the significant -plane discontinuity between thesetwo waveguides [1]. It was further explained [2] that thisunusual effect called energy tunneling takes place just belowthe cutoff frequency in the channel, when its effective per-mittivity becomes close to zero (epsilon-near-zero, ENZ). Inaddition to the tunneling frequency, the ENZ channel supportspropagation at one more frequency above the cutoff, known asthe Fabry–Perot (FP) resonance, which strongly depends on thelength of the channel.Propagation wavelength at the tunneling frequency ap-

proaches infinity, so the wave propagation can be consideredquasi-static, even at a great distance, which means that it doesnot depend on the length of the channel. This kind of behavioris characteristic for the left-handed zero-order resonator, sothe tunneling frequency can be addressed as a zero-orderresonance (ZOR). This is why the ENZ channel can be usedto enhance the efficiency of the energy transfer through thewaveguide discontinuities, as well as for energy confinement

Manuscript received February 20, 2013; revised April 24, 2013; acceptedApril 26, 2013. Date of publication May 01, 2013; date of current version May16, 2013. This work was supported by the Ministry for Education, Science andTechnological Development, Republic of Serbia, under Projects TR32024 andIII 45016.The authors are with the Institute of Physics, University of Belgrade,

11080 Belgrade, Serbia (e-mail: miranda@ipb.ac.rs; brankaj@ipb.ac.rs;nebojsav@ipb.ac.rs).Color versions of one or more of the figures in this letter are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/LAWP.2013.2261046

below the diffraction limit [1]. Other applications involvedielectric sensing [3], as well as multiband filtering and tunablehigh directivity [4] or omnidirectional antennas [5].ENZ behavior was accomplished either by using the dis-

persion characteristic of the rectangular waveguide near thecutoff [6], or by adding complementary split-ring resonatorsinside the channel [7]. If the channel width is equal to the widthof input waveguides (which is usually the case), the dielectricpermittivity in the ENZ channel ( ) should be lower thanin the input waveguides ( ) in order to provide tunneling.Here, we have proposed a more flexible design of the ENZwaveguide that consists of -step discontinuity added at thesame cross section as -step to reduce the channel width withrespect to input waveguides. This design allows to begreater than , which is the case in our letter.A method of tuning the tunneling frequency by changing the

capacitance of a varactor diode placed across the channel wasrecently proposed [8]. However, the achieved frequency shiftis followed by considerable decrease of transmission amplitudeas well as the -factor, which are the main drawbacks of thisapproach. Here, we have proposed and experimentally verifieda method of tuning the tunneling frequency using two longitu-dinal slots on the broad side of the narrowed channel. The tuningrange of the tunneling frequency is optimized by changing theoffset and length of two longitudinal slots. This way of tuningthe tunneling frequency has little influence on transmission am-plitude and can be efficiently applied to a very thin channel,which is not the case in the only previously reported methodof tuning the tunneling frequency [8]. Frequency tuning canbe done continuously by means of sliding backshort, or dis-cretely by using p-i-n diodes across the slots. Proposed tuningmethod can be used to widen the frequency range of ENZ sen-sors for measurements of dielectric permittivity [9], as well asin a design of tunable multiband filters using multilayered struc-ture [10], but with narrowed channels instead of the wire media.

II. FOAM ENZ WAVEGUIDE

A novel design of foam ENZ waveguide that consists ofa thin microwave substrate Taconic TLY-5A ( ,

), which serves as an ENZ channel and also asa carrier of the input waveguides, is shown in Fig. 1. The useof a microwave substrate in the channel is very advantageoussince it allows precise control of channel height and roughness( ) of the metal coating ( m, MS/m),which can significantly increase the losses in the channel if welower channel height below a certain point, or the roughnessis too high [11]. Input waveguides are made of foam dielectricROHACELL 200 WF ( , ), whichis easily shaped and cut.

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632 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 12, 2013

Fig. 1. Foam ENZ waveguide with relevant dimensions: mm,mm, mm, and mm. Outer metal coating is

removed so the dielectric layers can be seen.

Fig. 2. Equivalent circuit of a narrowed ENZ waveguide.

The propagation of the first-order mode ( ) in a narrowchannel can be described as a propagation of the TEM mode ina parallel-plate waveguide with effective permittivity, which isgiven as [3]

(1)

It can be seen that the effective permittivity equals zeroat the channel cutoff frequency at which the tunneling ofenergy appears

(2)

The frequency range in which energy tunneling may occur iswithin the passband of the input waveguide, i.e., between cutofffrequency of mode and the frequency at which the firsthigher mode appears ( ). In order to fitthe tunneling frequency in this passband, we can keep the samewidth of the channel and the input waveguides, but put dielec-tric with smaller relative permittivity in the channel, or we cannarrow the channel with respect to the input waveguides, so itsrelative permittivity can be equal or even greater than the rela-tive permittivity in the input waveguides. This can be describedby defining a condition [12]

(3)

The equivalent circuit of the proposed ENZ waveguide isgiven in Fig. 2. -step discontinuity between the input wave-guide and the channel is modeled by parallel capacitance [13],while the -step discontinuity, i.e., the change in the channelwidth is modeled by parallel inductance [13]. The tunnelingfrequency, as well as the Fabry–Perot resonance, come from theresonating nature of the obtained circuit. The propagationconstant in input waveguides filled with microwave substrateand foam dielectric is , where is givenas [13]

(4)

Fig. 3. Comparison of (thin lines) and (thick lines) parameters ob-tained by full-wave simulation (with markers) and equivalent circuit (withoutmarkers) for (a) two different channel widths ( mm—light lines and

mm—dark lines) and (b) two different channel lengths (mm—light lines and mm—dark lines). The channel cutoff fre-

quencies are denoted with arrows.

It should be pointed out that ZOR resonance appears abovethe channel cutoff frequency, which is not the case with ENZwaveguide based only on -plane step discontinuity. Sincethe step in -plane can be represented as capacitance, andthe channel characteristic impedance has an inductive naturebelow the cutoff, the tunneling in this case is forced to occur atthe frequency that is just below the channel cutoff in order toprovide the necessary inductance for resonator.Using the proposed equivalent circuit, we are able to predict

the frequency of tunneling and Fabry–Perot resonance quite ac-curately, without any full-wave simulation. This is illustrated inFig. 3(a) and (b), which shows the comparison of andcoefficients obtained using an equivalent circuit and a full-waveanalysis for the different widths and lengths of the channel,respectively. The small discrepancy in results obtained usingequivalent circuit comes from the fact that the expressions forand [13] are valid only for mode propagation. Since

the input waveguides are composed of two layers, that causesa hybrid mode to arise. However, the height of one layer in re-gard to the other one is very small, so we can approximate it bya mode.

III. METHODS OF TUNING

According to expression (2), the tunneling frequency is fixedfor the given channel geometry since it depends only on channelwidth and dielectric permittivity in the channel. However, in thisletter, we have shown that it is possible to shift the tunnelingfrequency down by changing the length of two longitudinal slotsplaced on the broad face of the ENZ channel (see Fig. 4).It is well known that a longitudinal slot whose length is nearly

equal to the half free-space wavelength is a commonly used

MITROVIC et al.: WIDEBAND TUNING OF TUNNELING FREQUENCY IN NARROWED EPSILON-NEAR-ZERO CHANNEL 633

Fig. 4. ENZ channel with coaxial connectors for signal excitation and longitu-dinal slots with length for frequency tuning. The slot displacement from thechannel centerline (offset) is denoted with .

Fig. 5. Simulated tuning range versus slot offset, for the different slot lengths, and 8 mm, respectively, in the direction of the arrow.

Fig. 6. Tuning slot ( mm, mm) with marked positions of p-i-ndiodes.

radiator in antenna systems. It can be represented by a shuntadmittance that mainly depends on the slot offset, i.e., the slotdisplacement from the channel centerline. For tuning the tun-neling frequency, we have proposed two very short longitudinalslots whose length ranges from to , and whichare placed far from the channel centerline in order to increase thetuning range. The tuning range of the tunneling frequency de-pends on the length of the slot and also on its offset. Changing ofthe slot length can be done either continuously by sliding planarbackshort, or discretely by using p-i-n diodes across the slots.Simulated tuning range as a function of offset and slot

length for continuous tuning is shown in Fig. 5. It can beseen that the slots with different lengths exhibit the maximumtuning range for the same displacement, which is slightly apartfrom the channel ends (offset mm). The maximumsimulated frequency shift of 1.18 GHz is achieved in the range7.03–5.85 GHz (16.8% of the tuning range) using slots withthe length mm.For the discrete tuning, we can place a finite number of p-i-n

diodes across the slots, as it is shown in Fig. 6. We have simu-lated the influence of a p-i-n diode switch, which is reflected ina way that the OFF state of the diode has no influence on the slot,and the ON state short-circuits the slot. This is how the slot ef-fectively becomes divided into two parts, from which the longerone is predominantly responsible for the frequency shift. There-fore, the position of the diode with respect to the -step canbe determined using corresponding slot length from Fig. 5. toachieve desired frequency shift. This has been verified in Fig. 7(see curves ii–iia and iii–iiia). The minimal frequency shift isobtained when the slot is short-circuited in the middle, and as a

Fig. 7. Simulated (thin lines) and (thick lines) parameters for discretetuning using p-i-n diodes across the slot in the case of: i) both diodes turned OFF;ii) only PIN2 switched ON; iii) only PIN1 switched ON, compared to the resultsobtained using slots without diodes of the length: iia) mm; and iiia)

mm. For comparison of discrete ( ) and continuous ( ) tuningranges, the case iv) without slots is also given.

consequence, we have a discrete tuning range ( ), which issmaller than the frequency range for continuous tuning ( ),as it is shown in Fig. 7.

IV. EXPERIMENTAL VERIFICATION

We have experimentally verified continuous tuning methodusing silver conductive paste to shorten the slots. For the exper-iment, the input waveguides were excited by coaxial connectorswhose position with respect to the channel and backshorts, aswell as the length of pins, has been optimized to obtain the bestimpedance matching near the tunneling frequency.Comparison between the measured and simulated andparameters around the tunneling frequency (ZOR) as a func-

tion of the slot length for slot offset mm is given in Fig. 8.The simulated tuning range is 1.06 GHz, which is in a goodagreement with experimentally achieved 0.99 GHz. This tuningrange is accompanied by an amplitude decrease of 1.6 dB. How-ever, the maximum achievable tuning range is about an oc-tave, i.e., between cutoff frequencies of mode and the firsthigher mode of input waveguides. To achieve such a widetuning range, it is necessary to excite ZOR without tuning slotsbelow, but near to the cutoff frequency of mode of theinput waveguides.The ENZwaveguide is a dual-band device because it supports

two transmission bands: ZOR and FP. By tuning the tunnelingfrequency by means of longitudinal slots, the FP resonance isshifted down simultaneously, but this shift is smaller than theZOR one. Experimentally achieved tuning range is 0.78 GHz,while theoretical prediction gives 0.86 GHz, as can be seen inFig. 9. Obtained results show that there is no degradation of theamplitude of FP resonance during the frequency tuning due tobetter matching of input ports at lower FP frequencies.The experimental model with coaxial connectors is shown in

Fig. 10.

V. CONCLUSION

We have proposed a more flexible design of ENZ waveguidewhich includes both - and -step discontinuity at the samecross section of the rectangular waveguide. In this way, dielec-tric permittivity required for energy tunneling can now be

634 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 12, 2013

Fig. 8. Comparison of the experimentally obtained and parametersand the simulated ones for ZOR resonance for different slot lengths: i) withoutslots; ii) mm; iii) mm; iv) mm; v) mm;and vi) mm. Slot offset is mm.

Fig. 9. Comparison of the experimentally obtained and parametersand the simulated ones for FP resonance for different slot lengths: i) withoutslots; ii) mm; iii) mm; iv) mm; v) mm;and vi) mm. Slot offset is mm.

Fig. 10. Side view of fabricated ENZ waveguide with coaxial connectors.

greater than the dielectric permittivity in input waveguides,which is useful for the design of foam waveguides. We havealso proposed the method of tuning the tunneling frequency bymeans of two longitudinal slots placed along the ENZ channel.The method is experimentally verified for continuous variationof the slot length, and the tuning range of approximately 1 GHzis obtained. The maximum achievable tuning range can be aswide as an octave, i.e., between cutoff frequencies of and

modes of input waveguides. This design and the proposedfrequency tuning method using p-i-n diode switch is suitablefor multiband filters with agile, real-time frequency-tuningcapabilities, while continuous tuning with sliding backshortis more useful for sensors for wideband measurements ofdielectric permittivity.

ACKNOWLEDGMENT

The authors would like to thank Prof. F. Medina andDr. R. Rodriguez-Berral for useful discussion through bilateralcooperation PRI-AIBSE-2011-1119, and the Institute IMTELin Belgrade, Serbia, for the fabrication of ENZ waveguides.They also thank Evonik Industries for providing ROHACELLsamples.

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