19. W.H. Theunissen, Reconfigurable contour beam synthesis using amechanical FEM surface description of dual offset reflector antennasurfaces, Ph.D. thesis, University of Pretoria, South Africa, 1999.

© 2002 Wiley Periodicals, Inc.

NUMERICAL INVESTIGATION OFDISPERSION-MANAGED SYSTEM WITHCONCATENATED CHIRPED FIBERBRAGG GRATING

Lin Zhu, Guozhong Wang, Li Xia, and Shizhong XieDepartment of Electronics Engineering of Tsinghua UniversityBeijing 100084

Received 20 October 2001

ABSTRACT: Concatenated chirped fiber Bragg grating (CBG) hasbeen used to compensate for the dispersion in an optical-fiber communi-cation system. Dispersion compensation fiber (DCF) is replaced withCBG in normalized sections of a 10-Gbit/s dispersion-managed systemover 800 km. The performance of this system was improved by addingan optical filter behind the CBG in each normalized section. © 2002Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 163–165, 2002;Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.10264

Key words: dispersion compensation; system simulation; chirped fiberBragg grating

Fiber Bragg grating (FBG) may be an effective solution for dis-persion compensation in dense, high-bit-rate wavelength-divisionmultiplexing (WDM) systems because of the low insertion loss,the absence of nonlinear effects and the capability in high-orderdispersion compensation [1]. It has been suggested that the designof future optical transparent networks could be facilitated by theuse of so-called normalized sections [2, 3]. In this Letter dispersioncompensation fiber (DCF) is replaced with chirped fiber Bragggrating (CBG) in each normalized section of a 10-Gbit/s disper-sion-managed system. It will be demonstrated that the linearity ofCBG’s time-delay spectrum is crucial to this kind of systemthrough numerical modeling. The system performance was alsoimproved by the addition of an optical filter behind CBG in eachnormalized section. The result will be very helpful for the practicaldesign of dispersion-managed systems with concatenated CBG.

1. INTRODUCTION

The grating period of the CBG we used can be expressed by

�� z� � �0�1 � Cg1z�. (1)

Cg1 is a linear chirp coefficient, which can determine the disper-sion of the chirped grating. �0 is the period length in the middle ofthe grating. Other structure parameters include average refractiveindex n, modulation depth �n and grating length l. The apodiza-tion shading function used is raised cosine. Given these parame-ters, the CBG’s reflection and time-delay spectrum can be deter-mined through numerical simulation. The often-preferredpiecewise-uniform approach to modeling nonuniform gratings isbased on identifying 2 � 2 matrices for each uniform section of thegrating, and then multiplying all of these together to obtain a single2 � 2 matrix that describes the whole grating [4]. The reflectionand time-delay spectrum of the CBG used are shown in Figure 1.

2. SYSTEM TRANSMISSION MODEL

The dispersion-managed system model is described in Figure 2.The DFB laser frequency is chosen at 1550.0 nm. The outputpower of the DFB is 1 mW. Continuous-wave (CW) light isexternally modulated at 10 Gbits/s with an NRZ pseudorandombinary sequence in a chirpless Mach–Zehnder modulator having a30-dB extinction ratio. The signal is launched into a link consistingof dispersion compensation normalized sections with chirpedBragg grating. There are eight normalized sections in the system.CBG is used in each section to compensate for the section disper-sion. The fiber loss in each section is compensated by an erbium-doped optical-fiber amplifier (EDFA). The calculation of the prop-agation in the optical fibers is performed with the use of a standardsplit-step algorithm with adaptive step size [5]. The EDFA ismodeled by wavelength-independent gain. In order to concentrateon the influence of dispersion and nonlinear effects in the trans-mission system and highlight the effect of optical filter, the noiseis ignored. The fiber parameters are listed in Table 1. The fiberlength in each section is 100 km. The EDFA gain is 20 dB, toexactly compensate for fiber loss. In Figure 2(b) the filter is afourth-order low-pass Bessel filter with a 3-dB bandwidth of 20GHz.

The parameters of CBG in the normalized section are carefullychosen to exactly compensate for the dispersion of the 100-km-long fiber used. Those parameters are listed in Table 2, and are thesame as those listed in Figure 1.

Figure 1 n � 1.458, 1 � 7.0 cm, �n � 2e-4, Cg1 � �6.2e-4/m. (a) Reflection spectrum of CBG. (b) Time-delay spectrum of CBG

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 33, No. 3, May 5 2002 163

3. SYSTEM SIMULATION RESULT

Figure 3 is the result of the simulation. Figure 3(a) is the eyediagram of the signal from the first normalized section, from whichit can be seen that the fiber dispersion is compensated for on thewhole. Figure 3(b) is the eye diagram of the signal from the last

normalized section. The eye diagram is very bad; its deteriorationis more than 3 dB. Given apodization shading function, it is foundthat the system performance cannot be improved by changing onlythe value of Cg1. This means that the deterioration of systemperformance is not due to residual dispersion. The numerical-simulation result shows that the time-delay spectrum of the CBGused is not linear enough to be used in a concatenated system.Otherwise the concatenated deterioration effect from nonlineartime-delay spectrum of the CBG will seriously worsen the system

Figure 2 (a) Postcompensation system model (a) without and (b) withoptical filter

TABLE 1 Fiber Parameters

Dispersion (ps/nm/km) 17.0Dispersion slope (ps/nm2/km) 0.050Nonlinear coefficient (mW/km) 0.0012Loss coefficient (dB/km) 0.20

TABLE 2 CBG Parameters

Length (cm) 7.0Cg1 (1/m) �6.2e-4�n 2e-4Central wavelength (nm) 1550.0

Figure 3 The result of system simulation. Eye diagrams of the signals from (a) the first section, (b) the last section, (c) the last section with long CBG,and (d) the last section with long CBG and optical filter

164 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 33, No. 3, May 5 2002

performance. If the grating length of 7 cm is changed to 12 cm ineach normalized section, the result of Figure 3(c) can be obtained.The system performance is improved. Comparison of the CBGwith different lengths above shows that the long CBG’s time-delayspectrum is more linear. Obviously, the linearity of the CBG’stime-delay spectrum is crucial to this kind of system. But in thatsituation, the shape of the signal from CBG will be somewhatcompressed at the front and back edges, which makes the uppereyelids very thick. This will be disadvantageous to the systemperformance. In order to get better system performance, we use thesystem model in Figure 2(b). Because the optical filter’s bandwidthis much smaller than the CBG’s, the filter in each normalizedsection can eliminate some unnecessary high-frequency compo-nents due to CBG. Compared with Figure 3(c), the result of Figure3(d) demonstrates that this method could improve the systemperformance. The effects of optical filters in this system are not assame as those used behind EDFA [6]. Because no noise is con-sidered in the system, the system performance improvement is notdue to the ASE noise filter.

4. CONCLUSIONS

Concatenated chirped fiber Bragg grating (CBG) has been used tocompensate for the dispersion in a 10-Gbit/s dispersion-managedsystem over 800 km. It was demonstrated that the linearity of theCBG’s time-delay spectrum is crucial to this kind of systemthrough numerical modeling. System performance was improvedby the addition of an optical filter behind the CBG in eachnormalized section.

REFERENCES

1. C.R. Giles, Lightwave applications of fiber Bragg grattings, J Light-wave Technol 15 (1997), 1391–1404.

2. E.J. Bachus, M. Eiselt, K. Habel, K.D. Langer, E.U. Scheuing, and F.C.Tischer, Photonic network design based on reference circuits. In OpticalNetwork Design and Modeling ONDM’97, Vienna, Austria, pp. 56–69.

3. N. Hanik, A. Gladisch, and G. Lehr, An effective method to designtransparent optical WDM-networks. In Technology and InfrastructureNOC’98, Manchester, U.K., pp. 190–197.

4. T. Erdogan, Fiber grating spectra, J Lightwave Technol 15 (1997),1277–1294.

5. G.P. Agrawal, Nonlinear fiber optics. San Diego, CA: Academic, 1995.6. V.K. Mezentsev, S.K. Turitsyn, and N.J. Doran, System optimization of

80 Gbit/s single channel transmission over 1000 km of standard fiber,Electron Lett 36 (2000), 1949–1950.

© 2002 Wiley Periodicals, Inc.

A BROADBAND FOLDED PLANARMONOPOLE ANTENNA FORMOBILE PHONES

Gwo-Yun Lee, Shih-Huang Yeh, and Kin-Lu WongDepartment of Electrical EngineeringNational Sun Yat-Sen UniversityKaohsiung 804, Taiwan

Received 16 October 2001

ABSTRACT: This article presents a broadband folded planar mono-pole antenna suitable for DCS (1710–1880 MHz), PCS (1850–1990MHz), UMTS (1920–2170 MHz), and WLAN (2400–2484 MHz) opera-tions for mobile phones. In addition to the broadband operation, theproposed folded monopole has compact dimensions of 10 mm height, 5mm width, and 17.5 mm length. Experimental results of the constructed

prototype are presented and discussed. © 2002 Wiley Periodicals, Inc.Microwave Opt Technol Lett 33: 165–167, 2002; Published online inWiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10265

Key words: planar monopole antennas; mobile phone antennas; broad-band monopole antennas

1. INTRODUCTION

Broadband planar monopole antennas with compact dimensions[1–3] have potential applications for multiband mobile phones.The related designs include short-circuiting the planar monopole tothe ground [1], fabricating the planar monopole on a dielectricsubstrate of very high relative permittivity (about 80) [2], using astacked planar monopole comprising a top-loaded element and aparasitic square element [3], and so on. These designs, however,still show a relatively larger antenna height above the ground plane(greater than 10% of the wavelength of the lowest operatingfrequency), which makes them less attractive for use in mobilephones.

In this article, a novel broadband folded planar monopoleantenna for applications in mobile phones is proposed. By foldinga planar monopole of a rectangular shape, the antenna length canbe greatly reduced, and in addition, a wide operating bandwidth isobtained. The proposed folded planar monopole has compact di-mensions of 10 � 17.5 � 5 mm3, and shows a very wide operatingbandwidth of about 900 MHz, from about 1.7 to 2.6 GHz. Forapplications to a mobile phone, the total antenna height from theground plane is only 13 mm (less than 8% of the wavelength at 1.7GHz), and the operating bandwidth covers the DCS (digital com-munication system, 1710–1880 MHz), PCS (personal communi-cation system, 1850–1990 MHz), UMTS (universal mobile tele-communication system, 1920–2170 MHz), and WLAN (wirelesslocal area network, 2400–2484 MHz) bands. Details of the an-tenna design and the obtained experimental results are presentedand discussed.

2. ANTENNA DESIGN

Figure 1 shows the proposed broadband folded monopole antennafor a mobile phone to cover the DCS/PCS/UMTS/WLAN bands.The folded monopole is mounted on top of a grounded FR4substrate (thickness 0.4 mm, relative permittivity 4.4, and size35 � 100 mm2), which can be considered to be the circuit boardof a practical mobile phone. Notice that, in the figure, the dimen-sions are not to scale, and some dimensions are exaggerated forclarity. The folded monopole has two opposite sections of dimen-sions 10 � 17.5 mm2, which are parallel to each other, and a sidesection of dimensions 10 � 5 mm2. The design dimensions of theproposed antenna are obtained with the aid of the IE3D simulationsoftware.

At one end of the folded monopole, a conducting wire, whichis also used to support the monopole, connects a 50-� microstripline printed on the grounded substrate to the monopole. To excitethe monopole in the experiment, a coax feed through a 50-� SMAconnector placed on the ground-plane side of the substrate is used.In practical applications, the 50-� microstrip line can be directlyconnected to the transmitter/receiver of the mobile phone.

There is a gap of 3 mm between the folded planar monopoleand the ground plane. This gap is usually required for a planarmonopole placed above a ground plane in order to achieve goodimpedance matching over a wide bandwidth. As for the width (5mm in this design) of the monopole’s side section, when it isincreased, the length (17.5 mm in this design) of the monopole

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 33, No. 3, May 5 2002 165