result for � the quality factors of both resonators become equal.And when the angle increases further, Q of QDR without CEPbecomes even lower than of the resonator with CEP, which arguesabout sharp growth of radiation loss in the resonator without CEPat large �. Evidently, the further increase of � makes no sensebecause Q decreases to a not-well measured level already at �� 77.2�.

As Q of dielectric resonator depends considerably on fre-quency, i.e. azimuthal index n, a frequency dependence of Q forthe same polarization for two values of � � 67�and �� 77.2� was measured (Fig. 4). In the same figure for com-parison an analogous dependence is given for the resonator in aform of cylindrical disk of 2.6 mm height. As can been seenfrom Figure 4, Q-factor increases with growth of frequency forall of the resonators. And at the same time, Q of the cylindricaldisk resonator without CEP is equal to or higher than Q of thecone resonator without CEP as well. The frequency dependenceof cone resonator at � � 65� lies higher as against thedependence at � � 77.2�. One cannot see a tendency towards

concurrence of the curves obtained at � � 65� and �� 77.2� when frequency grows. And what is more, a maximalvalue of Q for large values of � does not exceed Q values of thecylindrical disk. In other words, we do not register increase ofQ in the cone WGM resonator at great values of �.

In summary, we studied eigen frequencies and quality factorvalues as functions of generatrix angle in millimeter-wave coneWGM resonators made of Teflon. We did not observe a ten-dency towards increase of quality factor at large tilting ofgeneratrix about a cone base. Nevertheless, the cone WGMresonators made of high-quality single crystal dielectrics suchas sapphire are of considerable interest for impedance studies ofhigh-Tc superconducting films in a broad wavelength range,from microwaves to millimeter and, perhaps, sub-millimeterwaves.

REFERENCES

1. A.B. Matsko, A.A. Savchenkov, D. Strekalov, V.S. Ilchenko, and L.Maleki, Review of applications whispering-gallery mode resonators inphotonics and nonlinear optics, IPN Progress Report 42–162, Jet Pro-pulsion Laboratory, California Institute of Technology, 2005.

2. N. Cherpak, A. Barannik,Yu. Filipov, Yu. Prokopenko, and S. Vitusev-ich, Accurate microwave technique of surface resistance measurementof large-area HTS films using sapphire quasi-optical resonator, IEEETrans Appl Supercond 13 (2003), 3570–3573.

3. D.K. Armani, T.J. Kippenberg, S.M. Spillane, and K.J. Vahala, Ultra-high-Q toroid microcavity on a chip, Nature 421 (2003), 925–928.

4. T.J. Kippenberg, S.M. Spillane, D.K. Armani, and K.J. Vahala, Fabri-cation and coupling to planar high-Q silica disk microcavities, ApplPhys Lett 83 (2003), 797–799.

5. A.A. Barannik, S.A. Bunyaev, and N.T. Cherpak, Conical quasiopticaldielectric resonator, Tech Phys Lett 31 (2005), 811–812.

© 2007 Wiley Periodicals, Inc.

A NOVEL VIA-FREE COMPOSITERIGHT- AND LEFT-HANDEDTRANSMISSION LINE USINGDEFECTED GROUND STRUCTURE

Jae-Hyun Park,1 Young-Ho Ryu,2 Jae-Gon Lee,1 andJeong-Hae Lee1

1 Department of Electronic and Electrical Engineering, HongikUniversity, Seoul 121–791, Korea2 School of Electrical Engineering and Computer Science, KyungpookNational University, Korea

Received 29 December 2006

ABSTRACT: In this letter, a novel via-free composite right- and left-handed transmission line (CRLH TL) is proposed using defected groundstructure (DGS). The required shunt inductance and series capacitancefor left-handed transmission line are provided by the mender-line ofDGS and inter-digital gap in signal line, respectively. The dispersionrelations are analyzed using the derived equivalent circuit and Bloch-Flo-quet theory. The measured results of dispersion curves of CRLH TLshave good agreements with those of simulation and theory. A pro-posed via-free CRLH TL has broad LH bandwidth of 88.7% below 1GHz. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett49: 1989 –1993, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22624

Key words: composite right- and left-handed transmission line (CRLHTL); defected ground structure (DGS); metamaterials

Figure 3 Plots of the experimental quality factor Q versus generatrixslope angle relative to the axis for a conical quasi-optical dielectric reso-nator without and with a conducting endplate in the base plane. Dashed lineshows the Q value of a hemispherical resonator with a conducting endplatein the base plane

Figure 4 Unloaded quality factor f as a function of resonant frequencyf for Teflon resonators in a form of: (1) cone without CEP for � � 65° (2)cone with CEP for � � 65°; (3) cone without CEP for � � 77.2°; (4) conewith CEP for � � 77.2°; (5) cylinder of 2.6 mm thickness without CEP

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 8, August 2007 1989

1. INTRODUCTION

There has been a growing research for various metamaterials withsimultaneously negative values of effective permittivity and per-meability. In particular, because planar type of one-dimensionalcomposite right- and left-handed transmission line (CRLH TL) canbe simply fabricated and has a wide application, RF-devices suchas band stop/pass filters, couplers, backward antennas, and reso-nators are developed and their characteristics are analyzed [1–3].There are several types of CRLH TL such as series gap and shuntstub CRLH TL [4], mushroom CRLH TL [5], and split-ringresonator (SRR) CRLH TL [6]. They have via structure to giveshunt inductance, and thus, are not easy to be fabricated. Recently,via-free CRLH TLs such as virtual ground patch CRLH TL andcomplementary split-ring resonator (CSRR) CRLH TL have beenreported [7, 8]. However, the virtual ground patch CRLH TL hasrelatively narrow bandwidth for LH region below 1 GHz fre-quency range. Also, the CSRR CRLH TL is difficult to control theparameter values of capacitance and inductance due to restrictionof structure. In this letter, a novel via-free microstrip CRLH TLwith inter-digital capacitor and defected ground structure (DGS) consisting of grounded rectangular patch and meander-line is

proposed. The proposed CRLH TL provided the shunt inductanceby a meander line in DGS. It is easy to increase the shuntinductance, and possible to obtain relatively broad LH bandwidthwithout increasing the dimension of structure. To analyze theproposed structure, equivalent circuit of previously publishedCSRR [8] is applied to our structure. It is found that this equivalentcircuit of CSRR is not suitable for our structure because theanalyzed results do not agree with simulated results. Thus, newequivalent circuit, which includes the effects of DGS [9], is pro-posed and good results are obtained from our model. To confirmthe characteristics of CRLH TL, the dispersion curves of theproposed CRLH TLs are measured. The good agreement betweentheory and experimental results will be presented.

2. STRUCTURE AND EQUIVALENT CIRCUIT OF PROPOSEDCRLH TL

Figure 1 shows the proposed CRLH TL structure and its equivalentcircuit of unit cell. The unit cell consists of a series inter-digitalcapacitor and DGS having the rectangular patch with meander-lineinductor. This structure has property of effective negative permit-tivity due to the electrical coupling among the host transmissionline, patch, and ground [8]. Due to coupling, potential differencebetween the ground and patch exist. Thus, a current flows on themeander-line. Then, the magnetic fields are induced by the current.Therefore, the shunt inductance of the proposed structure can bedominant in specific frequency band. The effective negative per-meability, which is part of LH TL, is implemented by a seriesinter-digital capacitor in signal line as shown in Figure 1(a).Consequently, the CRLH TL has effective �� and �� due toseries capacitance (Cgap) of inter-digital capacitor on signal lineand shunt inductance (Lres) of meander line, respectively. Theresulting equivalent circuit is expressed as shown in Figure 1(c).Since the structure is located on ground plane, the equivalentcircuit must partly include DGS effects [9]. In an equivalent circuitof the unit cell, Cdgs and Ldgs express capacitance and inductanceof DGS, respectively. Ctr and Ltr express capacitance and induc-tance of RH TL, respectively. Also, Lres and Cres are inductance ofmeander line and capacitance between the rectangular patch andground, respectively. Finally, Cgap is capacitance of inter-digitalcapacitor.

3. ANALYSIS AND DISCUSSION

In Figure 1(c), this modeling is represented in �-network withrespect to Cgap and Ctr/2. To obtain dispersion curve of the peri-

Figure 1 Proposed CRLH TL. (a) Top view. (b) Bottom view. (c)Equivalent circuit of the unit cell

Figure 2 Modified equivalent circuit

1990 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 8, August 2007 DOI 10.1002/mop

odic structure, the �-network is changed to T-network becauseT-network is easy to analyze for periodic structures. Figure 2shows the modified T-equivalent circuit, which represents an ef-fective double negative property in the specific frequency range,i.e., Z acts as a capacitance and Y acts as an inductance in thespecific frequency band. The parameters of modified circuit forFigure 1(c) can be simply calculated as

Cse � Cgap �Ctr

4, Csh � Ctr �

Ctr2

4 � Cgap(1a)

if � �� 1/�LdgsCdgs, Lse � Ltr � Ldgs (1b)

where Cse and Csh are series and shunt capacitance, respectively.When a frequency is much lower than the resonance frequency ofDGS, the series inductance (Lse) can represent Eq. (1b). By ap-plying the periodic boundary conditions related with Bloch-Flo-quet theorem to the unit cell, the dispersion relation is obtained as

��� �1

dcos�1�1 � ZY� (2)

where is propagation constant for Bloch waves and d is theperiod of the structure. The series impedance and shunt admittancecan also be obtained as

Z��� �1

2 � j�Lse �1

j�Cse� (3a)

Y��� �j�Csh��

2CresLres 1�

�2Lres�Csh � Cres� 1(3b)

In Figure 3, the �(��1, ��2) and X points (�X1, �X2) aredefined as the frequencies at which d is to be 0 and �, respec-tively [5]. The frequencies of the � and X points are calculated byapplying the Eqs. (2), (3), and the condition d � 0 and � asfollowing:

if �se � �sh0, ���1 � �se

��2 � �sh0

if �se � �sh0, ���1 � �sh0

��2 � �se(4a)

��X12

�X22� �

�se2 � �sh0

2

2�

2�sh02 � �p

2

�sh12

���se2 � �sh0

2

2�

2�sh02 � �p

2

�sh12 �2

�se2 �sh0

2 4�sh02 �p

2�1/ 2

(4b)

where � �se2 �

1

LseCse, �p

2 �1

LseCsh

�sh02 �

1

LresCres, �sh1

2 �1

Lres�Csh�Cres�

When � � �se, the series impedance has negative imaginaryvalue. The frequency range of effective negative permeability ofthe proposed CRLH TL moves to lower frequency than that ofpreviously reported CRLH TL [4] whose effective negative fre-quency range is given by � � 1/(LtrCgap)1/2 because of Lse Ltr andCse Cgap. Therefore, the proposed CRLH TL has an advantage ofbroad LH band in the low frequency range. Similarly, when �sh1

� �sh0, the shunt admittance has negative imaginary value(effective negative permittivity). If the ratio of Csh/Cres increases,the ENG (� negative) bandwidth increases. The LH band(��1�X1) can be obtained by the Eq. (4). From this equation, theLH band increases as the ratio of Csh/Cres increases, the ENG (�negative) bandwidth increases. It is also noted that the broad LHband has been obtained at the balanced condition (LseCse � Lre-

sCres). Figure 3 shows dispersion relations that are analyticallyderived using equivalent circuit and Eqs. (2) and (3). The disper-sion relations show that LH passband is changed by parametervalues of Csh, Cres, and Lres, which determine the value of Y inFigure 2. The values of Csh, Cres, and Lres can be easily controlledby adjusting inter-digital gap, the gap of the rectangular patch, andthe length of meander-line, respectively.

4. SIMULATION AND MEASUREMENT

The proposed structure has been designed and analyzed by theequivalent circuit shown in Figure 2. To obtain the broadest LHband below 1 GHz, the dimensions of unit cell element have been

Figure 3 Dispersion characteristics: (a) Cse � 5 pF, Lse � 4 nH, Cres �2 pF, Lres � 15 nH; (b) Cse � 5 pF, Lse � 4 nH, Csh � 10 pF, Cres � 2 pF

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 8, August 2007 1991

selected by Eq. (4). In the modeling, each parameter is extractedfrom full wave simulated results of unit cell. The extracted circuitparameters are Cse � 6.77 pF, Lse � 5.12 nH, Csh � 9.95 pF, Cres

� 1.85 pF, and Lres � 17.40 nH. These values of inductance and

capacitance can be easily controlled by adjusting the rectangularpatch, meander-line, and inter-digital capacitor. In detail, if heightof substrate and rectangular patch size decreases, the CRLH TLhas LH region in high frequency range because the value of Csh

decreases. However, the proposed structure has one disadvantagethat it is difficult to obtain the broad LH band CRLH TL above 1GHz because the rate of Csh/Cres decreases. The photograph anddetailed dimension of the fabricated five-stage CRLH TL areshown in Figure 4. The input and output ports are fabricated using50-� coaxial connector. There needs no tapering to the feed linebecause total impedance of the structure is about 50 � even thoughwidth of input signal line is corresponding to impedance of 9.2 �.A mismatch would occur between the feed and CRLH TL if thetaper existed.

To measure the dispersion curve, two-, three-, and five-stageCRLH TL have been fabricated. The phase of S21 of each stageCRLH TL at the same frequency has been measured. Then, thepropagation constant of is extracted from the measured phase ofS21. The dispersion curves obtained from theory using Eqs. (2) and(3), from full wave simulation assuming the infinite periodicstructure, and from measurement have been compared in Figure 5.As shown in Figure 5, the results of theory, full wave simulation,and measurement show good agreements. The theoretical, simu-lated, and measured LH frequency bands are from 0.39 to 0.86GHz (75.2%), from 0.38 to 0.87 GHz (78.4%), and from 0.37 to0.96 GHz (88.7%), respectively.

Figure 6 shows measured S-parameters for five-stages CRLHTL. In Figure 6, the phase shift per unit cell of the measured CRLHTL at f0 is zero. Therefore, the LH and RH region are divided byf0 of 0.96 GHz. The measured 3 dB fractional bandwidth of LHregion is about 88.7% from 0.37 to 0.96 GHz. Thus, it may beconcluded that the proposed structure can be successfully appliedto various RF-devices such as coupler, resonator, band-stop, andband-pass filter at desired frequency band.

5. CONCLUSION

In this letter, a novel planar CRLH TL using grounded rectangularpatch with meander-line is proposed. Considering DGS effects, itsequivalent circuit is obtained. In this model, each element value isextracted from full wave simulation. Using the equivalent circuitmodeling and Bloch-Floquet theory, the dispersion relations arederived and have good agreements with those of full-wave simu-

Figure 4 (a) Fabricated five-stage CRLH TL. (b) Top and bottom viewof unit cell (w � 10 mm, g � 0.1 mm, l � 7.8 mm, Number of fingerpairs � 10, d1 � 12 mm, d2 � 14.8 mm, dg � 1 mm, mw � mg � 0.2 mm,Total length of meander-line � 3.8 mm). [Color figure can be viewed in theonline issue, which is available at www.interscience.wiley.com]

Figure 5 Dispersion curves

Figure 6 Measured S-parameters

1992 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 8, August 2007 DOI 10.1002/mop

lation and measured results. The fabricated CRLH TL has afractional bandwidth of 88.7% from 0.37 to 0.96 GHz for LHregion. The proposed CRLH TL that has broad LH bandwidth canbe easily designed below 1 GHz.

ACKNOWLEDGMENTS

This work was supported by grant no. R01–2004-000–10158–0from the Basic Research Program of the Korea Science and En-gineering Foundation.

REFERENCES

1. A. Lai, T. Itoh, and C. Caloz, Composite right/left-handed transmissionline metamaterials, IEEE Microwave Mag 5 (2004), 34–50.

2. M.A. Antoniades and G.V. Eleftheriades, A broadband series powerdivider using zero-degree metamaterial phase-shifting lines, IEEE Mi-crowave Wireless Compon Lett 15 (2005), 808–810.

3. J.G. Lee and J.H. Lee, Backward-wave directional coupler with com-plete coupling and broadband using conventional microstrip and 1Dmushroom structure, Microwave Opt Technol Lett 48 (2006), 1293–1296.

4. C. Caloz and T. Itoh, Transmission line approach of left-handed (LH)materials and microstrip implementation of an artificial LH transmis-sion line, IEEE Trans Antennas Propag 52 (2004), 1159–1166.

5. A. Sanada, C. Caloz, and T. Itoh, Planar distributed structures withnegative refractive index, IEEE Trans Microwave Theory Tech 52(2004), 1252–1263.

6. G.V. Eleftheriades, O. Siddiqui, and A.K. Iyer, Transmission line mod-els for negative refractive index media and associated implementationswithout excess resonators, IEEE Microwave Wireless Compon Lett 13(2003), 51–53.

7. A. Sanada, K. Murakami, S. Aso, H. Kubo, and I. Awai, A via-freemicrostrip left-handed transmission line, 2004 IEEE MTT-S Int Micro-wave Symp Dig 1 (2004), 301–304.

8. J.D. Baena, J. Bonache, F. Martin, R.M. Sillero, F. Falcone, T. Lope-tegi, M.A.G. Laso, J. Garcia-Garcia, I. Gil, M.F. Portillo, and M.Sorolla, Equivalent-circuit models for split-ring resonators and comple-mentary split-ring resonators coupled to planar transmission lines, IEEETrans Microwave Theory Tech 53 (2005), 1451–1461.

9. C.S. Kim, J.S. Park, D. Ahn, and J.B. Lim, A novel 1-D periodicdefected ground structure for planar circuits, IEEE Microwave GuidedWave Lett IEEE 10 (2000), 131–133.

© 2007 Wiley Periodicals, Inc.

DYNAMIC DISPERSING TECHNIQUEFOR PR COATING PROCESS INPLANAR LIGHTWAVE CIRCUITFABRICATION

Pua Chang Hong,1 Sulaiman Wadi Harun,2 Chong Wu Yi,1

Kanesh Kumar Jayapalan,1 and Harith Ahmad1

1 Photonics Laboratory, Department of Physics, University of Malaya,50603 Kuala Lumpur, Malaysia2 Department of Electrical Engineering, Faculty of Engineering,University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 9 January 2007

ABSTRACT: A new dynamic dispersing technique (DDT) is proposedand demonstrated to improve the photoresist (PR) coating process inplanar lightwave circuit (PLC) fabrication. In this technique, the PR isdispensed during the wafer’s spin cycle on the spin coater instead of theconventional static dispensing before spinning. In comparison to theconventional static dispersing technique (SDT), DDT has significantlyimproved several properties of the PR layer including its thinning be-havior, coating uniformity, and PR amount. Using DDT, the PR thick-

ness averagely reduces by 0.2 �m. The radial uniformity of the PRfrom the centre is also improved from the average difference of 0.28 �min SDT to 0.14 �m in DDT. Furthermore, the PR amount required forthe coating process is reduced from 3.00 ml (SDT) to 0.25 ml (DDT). Twodifferent DDTs are also compared in this paper including the application ofPR during the spin coater’s acceleration step (1st DDT) and the applicationof PR during the spin coater’s constant speed (2nd DDT). © 2007 WileyPeriodicals, Inc. Microwave Opt Technol Lett 49: 1993–1995, 2007;Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.22609

Key words: spin coating; planar lightwave circuit (PLC); photoresist(PR) coating; dynamic dispensing; static dispensing

1. INTRODUCTION

Photolithography in combination with flame hydrolysis deposition(FHD) and reactive ion etching (RIE) is one of the most attractivetechniques for fabrication of planar lightwave circuit (PLC) de-vices. The methodology used in photolithography and its processesdetermines the size, weight, cost, reliability, and capability of thefabricated device [1]. These variations are mainly based on thetechnique of application of a photoresist (PR) coating on thedevice wafer. A typical method of application is spin coating thatallows for dispensing of uniform, adherent, and defect-free poly-meric films at micron level thickness. The spin coating method iswidely used in fabrication of integrated electronic circuits andPLCs today.

The PR coating is usually applied by dispersing the chemical ina nonuniform stream onto a substrate wafer. Dispersing the PR onthe wafer is done using a pipette. The substrate is next, rotated athigh speeds using a spin coater. When the wafer starts to centrif-ugally accelerate, it creates a force that spreads the PR toward itsedge. This phenomenon subsequently applies a thin layer of PRwith uniform thickness on the wafer [2-4]. In the photolithographyprocess, it is crucial to obtain a thin and uniform PR coating.Variations and inconsistency of the PR thickness will reduce theaccuracy of the mask copy process created by UV radiation pat-terning. This inaccuracy will cause undesirable differences of thedevice channel width between the wafer and the mask pattern, andwill significantly increases transmission losses in the device. Vari-ations in PR thickness will also have a direct impact on the depthof focus (DOF) of the radiation patterning [5]. DOF largely influ-ences the variability of the interconnect lines, and hence, theperformance of the resulting device [4].

The PR type and its usage and wastage amounts are importantcriteria to address in the photolithography process. To achieve athinner layer of PR, one can either use more expensive chemicalcoatings or improve on application technique using typical PR. Inan effort to economize device fabrication, research on thinnercoating application using typical PR is important. The typicalmethod used in dispensing PR onto a substrate is the staticdispersing technique (SDT) in which the PR is dispensed on thewafer surface before its spin cycle. The technique however, wastesover 90% of the chemicals used by the completion of the processcycle [6,7].

In this article, a new dynamic dispersing technique (DDT) isdemonstrated to reduce the PR usage for the coating process. Inthis technique, the PR is dispensed while the wafer is spinning.Reduction of PR waste and usage can significantly reduce produc-tion cost of PLC devices (especially since PR is the most expen-sive chemical used in the photolithography process). The improve-ments of this new dispersing technique on PR film thickness anduniformity is also investigated.

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 8, August 2007 1993