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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 0, 2015 1

A Microstrip Probe Based On ElectromagneticEnergy Tunneling for Extremely Small and Arbitrarily

Shaped Dielectric SamplesR. Ramzan, Senior Member, IEEE, O. Siddiqui, A. Nauroze, and O. Ramahi, Fellow, IEEE

Abstract—An energy-tunneling sensor is fabricated by joiningtwo air-suspended short-circuited microstrip cavities with acommon ground interconnected by a half-wavelength wire. Dueto tunneling, highly concentrated fields are created at the tip ofthe wire. In this work, we propose to exploit these concentratedfields to detect the presence of extremely small and arbitraryshaped samples and their dielectric properties. The simulationand measurement results show respective frequency shifts of 60and 80 MHz in the tunneling frequency when mmsamples of FR4 and Rogers 6006 materials are placed on thewire tip. This kind of energy tunneling probe can bring a specialadvantage in the area of biomedical and forensic analysis where,usually the samples are small in size with no defined shape.

Index Terms—Concentrated EM fields, dielectric sensor, energytunneling in microstrip cavities, sensor probe.

I. INTRODUCTION

T HE tunneling of electromagnetic energy has been reportedin several publications over the recent years [1]–[4]. The

type of energy tunneling discussed here has been identified intwo types of structures. Firstly, it can take place in narrow con-ductive bends and channels filled with hyperbolically dispersivemedia (epsilon-near-zero materials) [1]–[3]. The metallic wires,in this context, have been treated as an effective medium withnegative permittivity in a certain range of frequencies as givenby the well-known relation

Manuscript received January 13, 2015; revised nulldate; accepted March 10,2015. Date of publication March 24, 2015; date of current version nulldate. Thiswork was supported by the United Arab Emirates University under the FacultySeed Grant 21N148.R. Ramzan was with the National University of Computer and Emerging Sci-

ences (FAST-NUCES), Islamabad-44000, Pakistan. He is now with ElectricalEngineering Department, United Arab Emirates University, AlAin-15551, UAE(e-mail: rashad.ramzan@uaeu.ac.ae).

[Please provide postal code.]O. F. Siddiqui is with theElectrical Engineering Department, Taibah University, Madinah, Saudi Arabia(e-mail: omarsiddiqui2@gmail.com).A. Nauroze is with the National University of Computer and Emerging Sci-

ences, Islamabad, Pakistan, Islamabad-44000, Pakistan (e-mail: abdullah.nau-roze@nu.edu.pk).

[Please provide postal code.]O. Ramahi is with theElectrical Engineering Department, University of Waterloo, Waterloo, Ontario,Canada (e-mail: oramahi@uwaterloo.ca).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.2015.2412254

(1)

where is the plasma frequency [5]. Secondly, the electromag-netic energy can also tunnel through the subwavelength wave-guide bends that are filled with wires having the lengths on theorder of half-wavelengths [4]. This dispersion regime has beenreferred to as ‘self-collimation’, ‘Bragg’s refraction’, or ‘canal-ization’ and is identified by diminishing group velocity alongone of the structure’s axes of symmetry and the flatness of thedispersion surfaces [6]–[9]. Numerically, this condition is cal-culated by writing the impedance in terms of the current densityand the dyadic Green function of the probe exciting thewaveguide structure [4], [10]

(2)

where is the surface of the probe inside the waveguide. As-suming a y-directed uniform angular current density

. The tunneling is observedwhen the input impedancein the above equation contains no imaginary part.The latter type tunneling phenomenon offers more flexibility

to achieve tunable resonant cavities without geometrical andstructural modifications of the device itself [4]. Another dis-tinctive feature of the wire-based tunneling structure is veryhigh concentration of the electric field around the wire tips atthe entrance and exit points of the tunneling wave. The con-centrated fields are produced because of the tunneling channelin this case only comprises of a thin wire whose width can bediminishing small. Exploiting the wire-tunneling, a dielectricsensing set-up has been fabricated and reported earlier [11]. Itimplements rectangular waveguide, an array of wires, and largedielectric samples that cover the entire wire dimensions. Intu-itively, one would expect more sensitivity to an external pertur-bation if the array of wires is replaced by a single wire fed by awave-guiding channel comparable to its diameter. This is pos-sible because in such a case, the same amount of energy wouldtunnel through a single wire, resulting in stronger field concen-trations within a small volume around the wire tip. Therefore, asshown in this work, such a single-wire tunneling probe woulddetermine the presence and dielectric properties of very smallperturbations comparable to the size of the wire tip. Note that

1536-1225 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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2 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 0, 2015

Fig. 1. (a) 3-D view of proposed energy tunneling based air-suspended mi-crostrip wire-loaded structure. (b) 2-D back view of the microstrip structure andposition of the dielectric sample.

Fig. 2. (a) E-field distribution of the upper side of wire without dielectricsample (b) E-field distribution with mm FR4 dielectric sample.

in the other contemporary cavity-perturbation techniques [12],[13], the waveguide natural modes are excited and perturbed.Hence the required sample sizes are comparable to the wave-guide dimensions.

II. SIMULATION RESULTS

To demonstrate the intuitions presented in Section I, a tun-neling structure comprising of two short-circuited air-filled mi-crostrip transmission lines sharing a common ground plane issimulated in full-wave simulation software Agilent’s HFSS. Thesimulation set-up, as presented in Fig. 1, consists of a single wireconnecting the two cavities through a hole which is drilled closeto the conducting back plane. The structure is dimensioned suchthat the tunneling takes place around 7GHz. The simulated elec-tric field plot, depicted in Fig. 2(a), shows that indeed the highestfields are concentrated around the wire tips. The strong fields arethen perturbed by placing a mm FR4 sample be-tween the trace and the wire tip. As shown in Fig. 3, a significantfrequency shift of 60 MHz is detected between the location ofthe perturbed and unperturbed resonance peaks.The resulting electric field plot (Fig. 2) also shows that the

FR4 sample channels the dominant electric fields, thus causingthe effective wire length to increase. Consequently, the tun-neling frequency shifts to a lower value. As seen from theplot, the full energy transmission is not achieved because ofthe considerable radiation loss from the half-wavelength wirepresent in an air cavity. The radiated fields can be minimizedby using dielectric filled in the gap between the signal trace andthe ground.With the use of dielectric, the gap between the signaltrace and the ground can be reduced for the same line impedanceso that the electric fields stay confined. Nonetheless, in this ap-plication, the electric field concentration at a specific frequency

Fig. 3. Simulated and response of the microstrip structure with19.3 mm wire with and without dielectric sample.

Fig. 4. Photograph of manufactured air suspended microstrip structure ma-chined out of a single aluminum block. The tunneling wire, dielectric sample,and measurement setup is shown in inset.

is more important than the energy transfer so that the shift in theresonance peak in the frequency response can be detected.

III. THE PHYSICAL ENERGY TUNNELING MICROSTRIP SENSOR

The fabricated microstrip based structure along with the mea-surement setup is shown in Fig. 4. The top and bottom mi-crostrip is 60 mm long and 4.2 mm wide and suspended inair at 10 mm height from the ground plane. The characteristicimpedance of themicrostrip is close to 160 at 7 GHz. The highcharacteristic impedance was chosen instead of 50 , as the dif-ference between the microstrip width and diameter of SMA be-comes very large (40 and 0.5 mm, respectively) at 7 GHz whichwould make it very difficult to launch energy. Moreover, sincethe microstrip is shorted at far end; matching at the tunnelingfrequency is naturally achieved and the mismatch at other fre-quencies does not affect the results at tunneling frequency.A copper strand of 0.5-mm diameter and 19.3-mm length is

used to load the microstrip cavity as shown in Fig. 1(b). A tinypiece of adhesive insulation paper tape is placed on the bottomof the microstrip in order to avoid the accentual short betweenthe wire and the microstrip. A small plastic jacket is placed inthe middle of the wire so as to fit the 1.5 mm ground hole for

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RAMZAN et al.: MICROSTRIP PROBE BASED ON EM ENERGY TUNNELING FOR DIELECTRIC SAMPLES 3

Fig. 5. Measured S11 and S21 response of the microstrip structure with19.3 mm wire with and without dielectric sample.

mechanical support without an electric connection. All the sidewalls are 3-mm thickness and the thickness of the ground planeis 2.4 mm. Further thickness reduction is recommended, but wasnot possible due to the limited capability of the available millingmachine.

IV. MEASUREMENT RESULTS

The transmission and reflection coefficients are measured byusing a Rohde & Schwarz, ZVL13 Vector Network Analyzer.Two dielectric samples FR4 ( ) and Rogers Duroid 6006( ) are inserted into the cavity and carefully at the wiretip. The resulting transmission and reflection coefficients are de-picted in Fig. 5. As in simulation, a 60MHz shift in the tunnelingfrequency is observed for the FR4 sample. When the structure isperturbed by a higher permittivity Duroid sample, an increase inthe wire’s effective length causes a further 20 MHz shift in thetunneling frequency. Considering the size of the sample whichis only mm , the frequency shift is large enoughand can be easily detected by any sensitive commercial demod-ulator.The 3 dB difference between the measurement and simula-

tion transmission coefficients is mainly due to the conductorlosses present in the 2-mm-thick walled fabricated structure.The HFSS setup, on the other hand, implements perfect elec-trical and magnetic boundaries to decrease the simulation times.The difference in the measured resonant frequency is due to theeffective reduction in the wire length due to the presence of thethick ground plane. As shown in Fig. 4, the open structure witha large air gap between trace and ground bears resemblance toan antenna system in which a half dipole is fed by a microstriptransmission line. The structure, therefore, is prone to high ra-diation losses which is evident from a 9-dB transmission loss at

the resonance. To verify this assumption, the structure was cov-ered by an adhesive copper tape from all sides. The measuredtransmission loss in this case was reduced to only dB.

V. SUMMARY AND CONCLUSIONS

This work presents a sensitive microstrip probe, which is ableto detect minimal changes in the dielectric composition of ma-terials. The sensitivity is obtained by exploiting the energy tun-neling phenomenon in which strong concentrated electric fieldsare created at the tip of a wire fed by a high impedanceguiding channel. When mm samples of FR4 andRogers Duroid materials were placed at the probe tip, respectiveshifts of 60- and 80-MHz shift were detected from the centerfrequency of 7.6 GHz. The structure, size can be easily scaledby changing the center frequency and the feeding mechanismto make it suitable to the desired application. Considering theresolution offered by the proposed probing technique, it can bepotentially used in biomedical and crime scene forensic anal-ysis.

REFERENCES[1] A. Alu and N. Engheta, “Light squeezing through arbitraily shaped

plasmonic channels and sharp bends,” Phys. Rev. B, vol. 78, pp.035440–035445, Jul. 2008.

[2] A. Alu, M. Silveirinha, and N. Engheta, “Transmission-line analysisof epsilon-near-zero (ENZ)-filled narrow channels,” Phys. Rev. E, vol.78, Jul. 23, 2008, Art. ID. 016604.

[3] M. G. Silveirinha and N. Engheta, “Theory of supercoupling,squeezing wave energy, and field confinement in narrow channels andtight bends using near-zero metamaterials,” Phys. Rev. B., vol. 76,no. 24, Dec. 2007, Art. ID. 245109.

[4] [Please provide issue number.]O. Siddiqui, M.Kashanianfard, and O. Ramahi, “Frequency-selective energy tunnelingin wire-loaded narrow waveguide channels,” Progr. Electromagn. Res.Lett., vol. 15, pp. 153–161, 2010.

[5] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Lowfrequency plasmons in thin-wire structures,” J. Physics: CondensedMatter, vol. 10, no. 22, pp. 4785–4809, Jun. 1998.

[6] J. Witzens, M. Loncar, and A. Scherer A, “Self-collimation in planarphotonic crystals,” IEEE J. Sel. Topics Quantum Electron., vol. 8, no.6, pp. 1246–1257, Nov.–Dec. 2002.

[7] O. F. Siddiqui and G. V. Eleftheriades, “Resonant modes in continuousmetallic grids over ground and related spatial-filtering applications,” J.Appl. Phys., vol. 99, pp. 083102–083110, May 2006.

[8] P. Belov, C. Simovski, and P. Ikonen, “Canalization of subwavelengthimages by electromagnetic crystals,” Phys. Rev. B, vol. 7, no. 19, pp.193105–193108, May 2005.

[9] P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwaveimaging using an array of parallel conducting wires as a lens,” Phys.Rev. B, vol. 73, pp. 033108–033111, Jan. 2006.

[10] R. Collins, Field Theory of Guided Waves, 2nd ed. New York, NY,USA: Wiley–IEEE, 1991, pp. 471–483.

[11] O. F. Siddiqui and O. Ramahi, “A novel dielectric detection systembased on wire-loaded waveguides,” IEEE Microw. Wireless Compon.Lett., vol. 21, no. 2, pp. 113–115, Feb. 2011.

[12] M. Santra and K. Limaye, “Estimation of complex permittivity of arbi-trary shape and size dielectric samples using cavity measurement tech-nique at microwave frequencies,” IEEE Trans. Microw. Theory Techn.,vol. 53, no. 2, pp. 718–722, Feb. 2005.

[13] J. Sheen, “Measurements of microwave dielectric properties by anamended cavity perturbation technique,” Measurement, vol. 42, no. 1,pp. 57–61, Jan. 2009.

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 0, 2015 1

A Microstrip Probe Based On ElectromagneticEnergy Tunneling for Extremely Small and Arbitrarily

Shaped Dielectric SamplesR. Ramzan, Senior Member, IEEE, O. Siddiqui, A. Nauroze, and O. Ramahi, Fellow, IEEE

Abstract—An energy-tunneling sensor is fabricated by joiningtwo air-suspended short-circuited microstrip cavities with acommon ground interconnected by a half-wavelength wire. Dueto tunneling, highly concentrated fields are created at the tip ofthe wire. In this work, we propose to exploit these concentratedfields to detect the presence of extremely small and arbitraryshaped samples and their dielectric properties. The simulationand measurement results show respective frequency shifts of 60and 80 MHz in the tunneling frequency when mmsamples of FR4 and Rogers 6006 materials are placed on thewire tip. This kind of energy tunneling probe can bring a specialadvantage in the area of biomedical and forensic analysis where,usually the samples are small in size with no defined shape.

Index Terms—Concentrated EM fields, dielectric sensor, energytunneling in microstrip cavities, sensor probe.

I. INTRODUCTION

T HE tunneling of electromagnetic energy has been reportedin several publications over the recent years [1]–[4]. The

type of energy tunneling discussed here has been identified intwo types of structures. Firstly, it can take place in narrow con-ductive bends and channels filled with hyperbolically dispersivemedia (epsilon-near-zero materials) [1]–[3]. The metallic wires,in this context, have been treated as an effective medium withnegative permittivity in a certain range of frequencies as givenby the well-known relation

Manuscript received January 13, 2015; revised nulldate; accepted March 10,2015. Date of publication March 24, 2015; date of current version nulldate. Thiswork was supported by the United Arab Emirates University under the FacultySeed Grant 21N148.R. Ramzan was with the National University of Computer and Emerging Sci-

ences (FAST-NUCES), Islamabad-44000, Pakistan. He is now with ElectricalEngineering Department, United Arab Emirates University, AlAin-15551, UAE(e-mail: rashad.ramzan@uaeu.ac.ae).

[Please provide postal code.]O. F. Siddiqui is with theElectrical Engineering Department, Taibah University, Madinah, Saudi Arabia(e-mail: omarsiddiqui2@gmail.com).A. Nauroze is with the National University of Computer and Emerging Sci-

ences, Islamabad, Pakistan, Islamabad-44000, Pakistan (e-mail: abdullah.nau-roze@nu.edu.pk).

[Please provide postal code.]O. Ramahi is with theElectrical Engineering Department, University of Waterloo, Waterloo, Ontario,Canada (e-mail: oramahi@uwaterloo.ca).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.2015.2412254

(1)

where is the plasma frequency [5]. Secondly, the electromag-netic energy can also tunnel through the subwavelength wave-guide bends that are filled with wires having the lengths on theorder of half-wavelengths [4]. This dispersion regime has beenreferred to as ‘self-collimation’, ‘Bragg’s refraction’, or ‘canal-ization’ and is identified by diminishing group velocity alongone of the structure’s axes of symmetry and the flatness of thedispersion surfaces [6]–[9]. Numerically, this condition is cal-culated by writing the impedance in terms of the current densityand the dyadic Green function of the probe exciting thewaveguide structure [4], [10]

(2)

where is the surface of the probe inside the waveguide. As-suming a y-directed uniform angular current density

. The tunneling is observedwhen the input impedancein the above equation contains no imaginary part.The latter type tunneling phenomenon offers more flexibility

to achieve tunable resonant cavities without geometrical andstructural modifications of the device itself [4]. Another dis-tinctive feature of the wire-based tunneling structure is veryhigh concentration of the electric field around the wire tips atthe entrance and exit points of the tunneling wave. The con-centrated fields are produced because of the tunneling channelin this case only comprises of a thin wire whose width can bediminishing small. Exploiting the wire-tunneling, a dielectricsensing set-up has been fabricated and reported earlier [11]. Itimplements rectangular waveguide, an array of wires, and largedielectric samples that cover the entire wire dimensions. Intu-itively, one would expect more sensitivity to an external pertur-bation if the array of wires is replaced by a single wire fed by awave-guiding channel comparable to its diameter. This is pos-sible because in such a case, the same amount of energy wouldtunnel through a single wire, resulting in stronger field concen-trations within a small volume around the wire tip. Therefore, asshown in this work, such a single-wire tunneling probe woulddetermine the presence and dielectric properties of very smallperturbations comparable to the size of the wire tip. Note that

1536-1225 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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2 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 0, 2015

Fig. 1. (a) 3-D view of proposed energy tunneling based air-suspended mi-crostrip wire-loaded structure. (b) 2-D back view of the microstrip structure andposition of the dielectric sample.

Fig. 2. (a) E-field distribution of the upper side of wire without dielectricsample (b) E-field distribution with mm FR4 dielectric sample.

in the other contemporary cavity-perturbation techniques [12],[13], the waveguide natural modes are excited and perturbed.Hence the required sample sizes are comparable to the wave-guide dimensions.

II. SIMULATION RESULTS

To demonstrate the intuitions presented in Section I, a tun-neling structure comprising of two short-circuited air-filled mi-crostrip transmission lines sharing a common ground plane issimulated in full-wave simulation softwareAgilent’s HFSS. Thesimulation set-up, as presented in Fig. 1, consists of a single wireconnecting the two cavities through a hole which is drilled closeto the conducting back plane. The structure is dimensioned suchthat the tunneling takes place around 7GHz. The simulated elec-tric field plot, depicted in Fig. 2(a), shows that indeed the highestfields are concentrated around the wire tips. The strong fields arethen perturbed by placing a mm FR4 sample be-tween the trace and the wire tip. As shown in Fig. 3, a significantfrequency shift of 60 MHz is detected between the location ofthe perturbed and unperturbed resonance peaks.The resulting electric field plot (Fig. 2) also shows that the

FR4 sample channels the dominant electric fields, thus causingthe effective wire length to increase. Consequently, the tun-neling frequency shifts to a lower value. As seen from theplot, the full energy transmission is not achieved because ofthe considerable radiation loss from the half-wavelength wirepresent in an air cavity. The radiated fields can be minimizedby using dielectric filled in the gap between the signal trace andthe ground.With the use of dielectric, the gap between the signaltrace and the ground can be reduced for the same line impedanceso that the electric fields stay confined. Nonetheless, in this ap-plication, the electric field concentration at a specific frequency

Fig. 3. Simulated and response of the microstrip structure with19.3 mm wire with and without dielectric sample.

Fig. 4. Photograph of manufactured air suspended microstrip structure ma-chined out of a single aluminum block. The tunneling wire, dielectric sample,and measurement setup is shown in inset.

is more important than the energy transfer so that the shift in theresonance peak in the frequency response can be detected.

III. THE PHYSICAL ENERGY TUNNELING MICROSTRIP SENSOR

The fabricated microstrip based structure along with the mea-surement setup is shown in Fig. 4. The top and bottom mi-crostrip is 60 mm long and 4.2 mm wide and suspended inair at 10 mm height from the ground plane. The characteristicimpedance of themicrostrip is close to 160 at 7 GHz. The highcharacteristic impedance was chosen instead of 50 , as the dif-ference between the microstrip width and diameter of SMA be-comes very large (40 and 0.5 mm, respectively) at 7 GHz whichwould make it very difficult to launch energy. Moreover, sincethe microstrip is shorted at far end; matching at the tunnelingfrequency is naturally achieved and the mismatch at other fre-quencies does not affect the results at tunneling frequency.A copper strand of 0.5-mm diameter and 19.3-mm length is

used to load the microstrip cavity as shown in Fig. 1(b). A tinypiece of adhesive insulation paper tape is placed on the bottomof the microstrip in order to avoid the accentual short betweenthe wire and the microstrip. A small plastic jacket is placed inthe middle of the wire so as to fit the 1.5 mm ground hole for

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RAMZAN et al.: MICROSTRIP PROBE BASED ON EM ENERGY TUNNELING FOR DIELECTRIC SAMPLES 3

Fig. 5. Measured S11 and S21 response of the microstrip structure with19.3 mm wire with and without dielectric sample.

mechanical support without an electric connection. All the sidewalls are 3-mm thickness and the thickness of the ground planeis 2.4mm. Further thickness reduction is recommended, but wasnot possible due to the limited capability of the available millingmachine.

IV. MEASUREMENT RESULTS

The transmission and reflection coefficients are measured byusing a Rohde & Schwarz, ZVL13 Vector Network Analyzer.Two dielectric samples FR4 ( ) and Rogers Duroid 6006( ) are inserted into the cavity and carefully at the wiretip. The resulting transmission and reflection coefficients are de-picted in Fig. 5. As in simulation, a 60MHz shift in the tunnelingfrequency is observed for the FR4 sample. When the structure isperturbed by a higher permittivity Duroid sample, an increase inthe wire’s effective length causes a further 20 MHz shift in thetunneling frequency. Considering the size of the sample whichis only mm , the frequency shift is large enoughand can be easily detected by any sensitive commercial demod-ulator.The 3 dB difference between the measurement and simula-

tion transmission coefficients is mainly due to the conductorlosses present in the 2-mm-thick walled fabricated structure.The HFSS setup, on the other hand, implements perfect elec-trical and magnetic boundaries to decrease the simulation times.The difference in the measured resonant frequency is due to theeffective reduction in the wire length due to the presence of thethick ground plane. As shown in Fig. 4, the open structure witha large air gap between trace and ground bears resemblance toan antenna system in which a half dipole is fed by a microstriptransmission line. The structure, therefore, is prone to high ra-diation losses which is evident from a 9-dB transmission loss at

the resonance. To verify this assumption, the structure was cov-ered by an adhesive copper tape from all sides. The measuredtransmission loss in this case was reduced to only dB.

V. SUMMARY AND CONCLUSIONS

This work presents a sensitive microstrip probe, which is ableto detect minimal changes in the dielectric composition of ma-terials. The sensitivity is obtained by exploiting the energy tun-neling phenomenon in which strong concentrated electric fieldsare created at the tip of a wire fed by a high impedanceguiding channel. When mm samples of FR4 andRogers Duroid materials were placed at the probe tip, respectiveshifts of 60- and 80-MHz shift were detected from the centerfrequency of 7.6 GHz. The structure, size can be easily scaledby changing the center frequency and the feeding mechanismto make it suitable to the desired application. Considering theresolution offered by the proposed probing technique, it can bepotentially used in biomedical and crime scene forensic anal-ysis.

REFERENCES[1] A. Alu and N. Engheta, “Light squeezing through arbitraily shaped

plasmonic channels and sharp bends,” Phys. Rev. B, vol. 78, pp.035440–035445, Jul. 2008.

[2] A. Alu, M. Silveirinha, and N. Engheta, “Transmission-line analysisof epsilon-near-zero (ENZ)-filled narrow channels,” Phys. Rev. E, vol.78, Jul. 23, 2008, Art. ID. 016604.

[3] M. G. Silveirinha and N. Engheta, “Theory of supercoupling,squeezing wave energy, and field confinement in narrow channels andtight bends using near-zero metamaterials,” Phys. Rev. B., vol. 76,no. 24, Dec. 2007, Art. ID. 245109.

[4] [Please provide issue number.]O. Siddiqui, M.Kashanianfard, and O. Ramahi, “Frequency-selective energy tunnelingin wire-loaded narrow waveguide channels,” Progr. Electromagn. Res.Lett., vol. 15, pp. 153–161, 2010.

[5] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Lowfrequency plasmons in thin-wire structures,” J. Physics: CondensedMatter, vol. 10, no. 22, pp. 4785–4809, Jun. 1998.

[6] J. Witzens, M. Loncar, and A. Scherer A, “Self-collimation in planarphotonic crystals,” IEEE J. Sel. Topics Quantum Electron., vol. 8, no.6, pp. 1246–1257, Nov.–Dec. 2002.

[7] O. F. Siddiqui and G. V. Eleftheriades, “Resonant modes in continuousmetallic grids over ground and related spatial-filtering applications,” J.Appl. Phys., vol. 99, pp. 083102–083110, May 2006.

[8] P. Belov, C. Simovski, and P. Ikonen, “Canalization of subwavelengthimages by electromagnetic crystals,” Phys. Rev. B, vol. 7, no. 19, pp.193105–193108, May 2005.

[9] P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwaveimaging using an array of parallel conducting wires as a lens,” Phys.Rev. B, vol. 73, pp. 033108–033111, Jan. 2006.

[10] R. Collins, Field Theory of Guided Waves, 2nd ed. New York, NY,USA: Wiley–IEEE, 1991, pp. 471–483.

[11] O. F. Siddiqui and O. Ramahi, “A novel dielectric detection systembased on wire-loaded waveguides,” IEEE Microw. Wireless Compon.Lett., vol. 21, no. 2, pp. 113–115, Feb. 2011.

[12] M. Santra and K. Limaye, “Estimation of complex permittivity of arbi-trary shape and size dielectric samples using cavity measurement tech-nique at microwave frequencies,” IEEE Trans. Microw. Theory Techn.,vol. 53, no. 2, pp. 718–722, Feb. 2005.

[13] J. Sheen, “Measurements of microwave dielectric properties by anamended cavity perturbation technique,” Measurement, vol. 42, no. 1,pp. 57–61, Jan. 2009.