the elimination of a conventional source inductor can improveoverall LNA performance in subthreshold operation.

4. CONCLUSION

A 5.8 GHz LNA using 130 nm CMOS technology has beenpresented, which operates in a subthreshold region for low powerapplications. The LNA consumes 980 �W from 1.8V powersupply and total chip area is 0.7 mm2. By eliminating a sourcedegeneration inductor, forward gain of the LNA is improved. Atthe operation frequency, forward gain (S21) is 13.4 dB and noisefigure (NF) is 5.2 dB. This circuit has the highest FoM among therecently published subthreshold LNAs.

ACKNOWLEDGMENTS

This work was supported by “Next-generation growth engine”project of the Korea Ministry of Commerce, Industry and Energyand by Inter-University Semiconductor Research Center (ISRC).The authors would like thank Dongbu Hitek and Yeocho Yoon forchip fabrication and helpful discussions.

REFERENCES

1. D.K. Shaeffer and T.H. Lee, A 1.5-V, 1.5-GHz CMOS low noiseamplifier, IEEE J Solid-State Circuits 32 (1997), 745–759.

2. B.G. Perumana, S. Chakraborty, C. Lee, and J. Laskar, A fully mono-lithic 260-�W, 1-GHz subthreshold low noise amplifier, IEEE Micro-wave Wireless Compon Lett 15 (2005), 428–430.

3. L.K. Meng, N.C. Yong, Y.K. Seng, and D.M. Anh, A 2.4 GHz ultra lowpower subthreshold CMOS low-noise amplifier, Microwave Opt Tech-nol Lett 49 (2007), 743–744.

4. H. Lee and S. Mohammadi, A 3GHz subthreshold CMOS low noiseamplifier, Digest of IEEE Radio Frequency Integrated Circuits Sympo-sium, San Francisco, USA, 2006.

5. I. Song, M.S. Koo, H.-S. Jhon, and H. Shin, CMOS low-noise amplifierwith noise suppression technique from gate resistance, Asia-PacificWorkshop on Fundamentals and Applications of Advanced Semicon-ductor Devices, Gyeongju, Republic of Korea, 2007, pp. 25–28.

6. S. Asgaran, M.J. Deen, and C. Chen, A 4-mW monolithic CMOS LNAat 5.7 GHz with the gate resistance used for input matching, IEEEMicrowave Wireless Compon Lett 16 (2006), 188–190.

7. I. Song, M. Koo, H. Jung, H.-S. Jhon, and H. Shin, Optimization ofcascade configuration in CMOS low-noise amplifier, Microwave OptTechnol Lett 50 (2008), 646–649.

© 2008 Wiley Periodicals, Inc.

ALL-OPTICAL CLOCK ENHANCEMENTFOR TRANSMITTED NRZ DATASTREAMS BASED ON CFBG

Ming Chen,1,2 Feng Zhang,1 Shuisheng Jian,1 and D. S. Citrin2

1 Key Laboratory of All Optical Network & AdvancedTelecommunication Network of EMC, Beijing Jiaotong University,Beijing, 100044, China; Corresponding author:05111023@bjtu.edu.cn2 School of Electrical and Computer Engineering, Georgia Institute ofTechnology, Atlanta, GA 30332-0250

Received 9 March 2008

ABSTRACT: A new but simply implemented all-optical clock enhance-ment scheme for nonreturn-to-zero (NRZ) data streams utilizing a semi-conductor optical amplifier (SOA) and a chirped fiber Bragg grating(CFBG) is presented. The clock-to-carrier suppression ratio is highlyimproved by more than 23 dB by the CFBG compared with the valueobtained only including the SOA. In addition, the clock is recoveredbased on stimulated Brillouin scattering (SBS). The clock recovery forthe NRZ signal following various lengths of single-mode fiber (SMF) isnumerical simulated and also demonstrated experimentally. The recov-ered clock degrades as the length of fiber increases. © 2008 Wiley Peri-odicals, Inc. Microwave Opt Technol Lett 50: 2764–2768, 2008;Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.23787

Key words: all-optical clock recovery; non-return-to-zero; semiconduc-tor optical amplifier; chirped fiber Bragg grating; stimulated Brillouinscattering

1. INTRODUCTION

All-optical 3-R regenerators (reamplify, reshape, retime) are apromising technology for advanced optical networking to over-come impairments caused by noise, attenuation, fiber dispersion,and nonlinearities. All-optical clock recovery, as one of fundamen-tal technology for all optical reshaping and retiming, has beendemonstrated using Fabry-Perot lasers [1, 2], phase-locked loops[3], multisection laser diodes [4], self-pulsating lasers [5], andstimulated Brillouin scattering (SBS) [6]. Most of the reportedschemes are focused on the return-to-zero (RZ) format data. How-ever, the nonreturn-to-zero (NRZ) format data is well establishedin current lightwave systems because of its relative ease of oper-ation and its high bandwidth efficiency. Owing to the absence of anobvious clock component in the NRZ modulation spectrum, apreliminary processing stage to enhance the clock component forthe NRZ signal is required [7–9].

In this article, a novel all-optical clock enhancement scheme forNRZ data streams using a semiconductor optical amplifier (SOA)and a chirped fiber Bragg grating (CFBG) is presented. The CFBGis introduced to get higher clock-to-carrier ratio (CCR). TheCFBG, in essence which acts as a frequency modulation to am-plitude modulation (FM-to-AM) converter, induces chirp to inten-sify the SPM-induced chirp by the SOA. The CCR of the NRZsignal after the CFBG is highly improved by more than 15 dBcompared with [7]. The enhanced clock is extracted based onstimulated Brillouin scattering (SBS), with the advantage of in-sensitivity to the polarization of the injection signal compared withthe two-section DFB laser. A numerical model is built to analyzethe clock recovery from NRZ data streams transmitted over vari-ous lengths of single-mode fiber (SMF) and also demonstratedexperimentally. The scheme could be extended to multi-channeland rate systems with multi-CFBG’s or array waveguide gratings(AWG).

TABLE 1 Performance Comparison of Subthreshold CMOSLNAs

Gain[dB]

NF[dB]

VDD

[V]ID

[�A]f0

[GHz]FoM

[GHz/mW]

Perumana et al. [2] 13.6 4.6 1 260 1 9.77Meng et al. [3] 9.8 3.6 1 650 2.4 8.84Lee and

Mohammad [4]9.1 4.7 0.6 670 3 10.96

This work 13.4 5.2 1.8 545 5.8 11.98

2764 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 11, November 2008 DOI 10.1002/mop

2. PRINCIPLE AND SIMULATION

The schematic diagram and principle of clock enhancement for theNRZ signal is shown in Figure 1. As the high-power NRZ opticalpulses pass through a SOA, the signal inevitably experiencesself-phase modulation (SPM), which shifts the frequency to the red(blue) at the leading (tailing) edge. Because of gain saturation inthe SOA, an overshoot is generated at the leading edge of eachinput pulse. However, the suppression ratio between the clockcomponent and the carrier is still low, so the CFBG is introducedto work in conjunction with the SOA. The chirp induced by theCFBG and SOA have the same sign, which is beneficial forobtaining highly improved the clock-to-carrier ratio. Furthermore,the CFBG converts the frequency chirp into an amplitude fluctu-ation as the CFBG can be considered as a band-pass filter; thisgenerates overshoots at each leading or tailing edge of the NRZpulses. The overshoots, which have a clock component in thefrequency domain, are clearly visible in the experimental result asshown in Figure 1. As the central wavelength of the NRZ signal isadjusted to the tailing edge of the CFBG reflection spectrum, thepower of the central and red-shifted frequency are attenuated.However, the clock frequency is preserved, thus resulting in anenhanced clock component and further improving the CCR. In thisarticle, CCR is calculated from the difference value of the powerbetween the first-order discrete clock component and carrier com-ponent.

The NRZ signal with enhanced clock component is split intotwo beams propagating in opposite directions: the larger one is thepump; the other beam is additional modulated at the Brillouin shift(10.484 GHz) to be the Stokes wave. The nonlinear interactionbetween the pump and the backward-propagating signal inducedstimulated Brillouin scattering (SBS). When the pump power ishigher than the SBS threshold, the stimulated scattering processtransforms most of the energy of the pump light to the counter-propagating wave, and the comb gain spectrum is generated toamplify the corresponding components of the seed signal, thusfacilitating the extraction of the clock in the optical domain. Owingto the additional modulation, the variation of the pump detuningdue to the signal frequency has been discussed in [10]. With the

extra modulation, control of the frequency of the seed signal can beavoided. The upper bound of data rate for the clock extractionscheme is about 300 Gb/s [10].

A numerical model was also implemented to analyze the clockrecovery from the NRZ data streams transmitted over differentdistances. The split-segment model is used to analyze the pulsepropagation in the SOA [11], assuming the slowly varying enve-lope approximation. The length of the SOA in the simulations isset to 500 �m. The width and the thickness of the active region inSOA are set to be 2 �m and 0.15 �m, respectively. The CFBG istreated by coupled-mode theory [12, 13]. Figure 2 gives thesimulation results of the initial NRZ waveform, following theSOA, and after the CFBG. The overshoot at each leading edge ofthe NRZ signal is clearly visible after passing through the SOA.The data also experiences negative frequency chirp induced by theSOA and the CFBG, and then the strong amplitude fluctuations canbe depicted as overshoots at both leading and trailing edges. Theclock component can be enhanced greatly.

Figure 3 shows the variation of CCR after SOA and CCRafter CFBG with the injection current of the SOA. As the SOAcurrent increases, the clock component can be enhanced due tothe increased SOA gain and the shortened carrier lifetime, andthus the CCR increases accordingly. However, the SOA comesto gain saturation quickly with the high-injection current, andthe NRZ signal passing though the SOA undergoes slightchange on the gain. Moreover, the gain spectrum of the SOA asthe function of the wavelength becomes unsymmetrical and the

Figure 1 Schematic diagram and principle of the clock enhancement forNRZ data. [Color figure can be viewed in the online issue, which isavailable at www.interscience.wiley.com]

Figure 2 Simulated NRZ waveform of the initial signal, the NRZ signal after the SOA and after the CFBG. [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com]

Figure 3 CCR after SOA, CCR after CFBG vs. the injection current ofthe SOA

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 11, November 2008 2765

peak shift to short wavelength if the current go on increasing,which resulting in the reduction of the gain of the clock com-ponent. According to the simulation result, the optimal value ofthe SOA current is approximately 200 mA, whereas the valueneeds to be adjusted in the practical application. The variationof the CCR after the SOA induces the durative impact for NRZsignal passing through the CFBG, and the CCR is highlyimproved by utilizing the CFBG.

Figure 4 shows the effect of the frequency deviation betweenthe NRZ data and the CFBG on the CCR after CFBG, whichillustrates a good explanation of adjusting the central wavelengthof the NRZ signal to the tailing edge of the CFBG reflectionspectrum. The 3-dB CFBG bandwidth is set to be 50 GHz insimulation. The CCR slightly increases while both the clock andcarrier components are within the 3-dB bandwidth, unless thecentral wavelength of the NRZ signal is adjusted to the longwavelength edge to obtain the blue-shifted frequency components.However, the power of clock component also maybe sharplyfalling off once the wavelength of NRZ signal overstep the boundsof the tailing edge.

Under steady-state conditions (CW or quasi-CW pump),SBS can also be calculated by coupled-mode theory. The nu-merical method to solve the resulting coupled equations isdiscussed in [14]. The acoustic-phonon lifetime and Brillouin-gain coefficient at line center are taken to be 4 � 10�9 s and4 � 10�11 m/W, respectively. We calculate the optimum value

of the length of the DSF (7.6 km) and the ratio of the pump tothe Stokes wave (95:5). The value obtained is subsequentlyemployed in the experiment.

3. EXPERIMENTAL SETUP

The experiment setup is sketched in Figure 5. The 9.953 Gb/sNRZ data stream is generated by modulating the continuouswave (CW) output of a distributed feedback fiber laser with aLiNbO3 Mach-Zehnder modulator (MZM) driven by patterngenerator (Agilent N4901B) with 223�1 bits length. The centralwavelength of the NRZ data is set to 1555.203 nm. The SOAused is a COVEGA SOA1117 with Steinhart constants a �1.129241 � 10�3, b � 2.341077 � 10�4, and c � 8.775468 �10�8. The performance of the setup is investigated by a digitalsampling oscilloscope (Agilent 86100B) and an optical spec-trum analyzer (ANDO AQ6317C). The input power of the SMFis 0 dBm. The input power of the SOA is maintained at �4dBm. The bias current of the SOA is adjusted to 283 mA to getthe best performance. A CFBG with reflection spectrum centralwavelength 1554.94 nm is used as the filter and the linear-chirpelement. The CFBG used in this experiment is successfullyfabricated to solve the temperature excursion, PolarizationMode Dispersion (PMD) and group delay ripple. The reflectionspectrum and time delay of the CFBG is shown in Figure 6,which is tested by EG&G CD400 Laser Chromatic DispersionMeasurement System. The clockwise propagating signal ismodulated by the Brillouin shift of dispersion shift fiber (DSF)

Figure 4 CCR after CFBG vs. the frequency deviation between the NRZdata and the CFBG

Figure 5 Schematic of experiment setup. SMF: single mode fiber, ISO: isolator, PC: polarization controller, DSF: dispersion shift fiber, MZM: M-Zmodulator, OC: optical circulator

Figure 6 The reflectivity and time delay for the CFBG. [Color figure canbe viewed in the online issue, which is available at www.interscience.wi-ley.com]

2766 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 11, November 2008 DOI 10.1002/mop

using the Mach-Zehnder modulator (MZM). The anticlockwisesignal with 95% of the total power functions as the pump. Thepolarization controllers maintained the same polarization statefor the pump and Stokes waves.

Figure 7 shows the spectrum of the initial NRZ signal, the NRZafter SOA, the NRZ after CFBG, and the recovered clock. Thereis almost no clock component in the input NRZ data. After passingthrough the SOA, it is not difficult to see the clock componentfrom the figure, and the clock-to-data suppression ratio of the NRZsignal is improved to �25.3 dB, owing to the self-phase modula-tion of SOA. However, other frequency components are still ratherstrong, and the CCR is not high enough to implement the clockrecovery based on SBS. Whereas, the CCR is further increased to�2.1 dB after passing through the CFBG. The CFBG is employedafter the SOA to enhance the frequency shift, and also to convertthe frequency chirp into an amplitude fluctuation. To the best ofour knowledge, this is a promising efficient technology to obtainhigh improvement of the clock-to-carrier ratio. The NRZ datastream with higher CCR is injected the clock recovery structure.As both of the power of clock and carrier component power arehigher than the SBS threshold, the clock can be extracted. Thespectrum of the recovered clock is shown in Figure 7, and thefrequency shift compared the spectrum of NRZ signal after theCFBG is owing to additional modulated at the Brillouin shift(10.484 GHz).

4. CLOCK RECOVERY FOR TRANSMITTED NRZ DATASTREAMS

The NRZ signal is transmitted over various lengths of SMFwithout any dispersion compensation. As the SMF length isincreased, the signal-to-noise ratio (SNR) and eye diagram ofthe NRZ signal are degraded due to attenuation, dispersion, andnonlinearity of the SMF. The power of the clock component inspectrum declined further relative to the total signal power,subsequently, the efficiency of clock enhancement due to theSOA � CFBG combination falls off as the distance increases.The clock-to-carrier ratio of the NRZ signal passed throughboth the SOA and the CFBG is reduced with increased SMFlength as shown in Figure 8. The ratio is found to be �29.8 dB(after the SOA) and �8.2 dB (after the CFBG), respectively, asthe length of the SMF is 47 km. The clock still can be recoveredas shown in Figures 9(b) and 9(e). Figure 9 shows the theoret-

ical and experimental results for the recovered clock. Theamplitude of the clock recovered falls off sharply with theincreasing SMF length. As the degradation of the SNR pro-gressed, the amplification efficiency of the high-gain EDFA wasalso degraded, and thus the amplitude of the clock componentextracted was reduced.

Furthermore, a high-gain EDFA is used to increase thepower of the signal above 100 mW to exceed the SBS threshold.The degraded NRZ signal is amplified, thus introducing moreadditional noise, which in practice also affects the quality ofclock recovery. In addition, the amplification efficiency of theEDFA decreases with low SNR, and the amplitude of therecovered clock may be reduced. As the SBS occurred in theDSF, the Brillouin gain saturates at different times for thecarrier and clock component of the seed signal because of thepower difference between them. Since the power of the seeddata is much higher than the clock, the carrier component in thespectrum of the seed light undergoes more Brillouin gain. Whenthe power of clock component of the pump signal is lower thanthe Brillouin threshold, the comb optical filter for the corre-sponding frequency in the seed could not be shaped by SBS.When the distance transmitted in the SMF is 67 km, the ratio ofthe signal after the SOA is �30.3 dB, and after the CFBG is�10.1 dB, which is degraded by about 10 dB compared with thecase of 0 km length. It is difficult to extract the clock compo-nent based on SBS when the clock-to-carrier ratio is lower than�10 dB. In this case, the clock can not be recovered as seen inFigures 9(c) and 9(f).

5. CONCLUSIONS

A SOA and a CFBG are combined as a novel scheme to enhancethe clock component before clock recovery based on SBS forNRZ data streams. The clock-to-carrier ratio of the NRZ datastreams is highly improved 23 dB approximately by the CFBGcompared with its value simply after the SOA in the absence ofpropagation through SMF. All-optical clock enhancement andrecovery for NRZ data transmitted in various length of SMF isdemonstrated experimentally and understood theoretically. Asthe SNR of the NRZ signal gets worse, the clock-to-carrier ratiofalls, and the amplitude of clock signal likewise becomes lower.

Figure 7 Spectrum of the initial NRZ signal, the NRZ transmitted afterSOA, after CFBG, and the recovered clock

Figure 8 The experimental result of variation of clock enhancementafter SOA and CFBG with distance of fiber transmission

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 11, November 2008 2767

The all-optical clock enhancement and recovery scheme can beextended to other types of modulation format, high speed andparallel all-optical processing of multiple channels.

ACKNOWLEDGMENTS

This work was supported in part by the National Nature ScienceFoundation (60437010).

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5. P. Barnsley, H. Wickes, G. Wickens, and D. Spirit, All-optical clockrecovery from 5 Gbit/s RZ data using a self-pulsating 1.56-m laserdiode, IEEE Photon Technol Lett 3 (1991), 942–945.

6. D.L. Butler, J.S. Wey, M.W. Chbat, and et al., Optical clock recoveryfrom a data stream of an arbitrary bit rate by use of stimulatedBrillouin scattering, Opt Lett 20 (1995) 560–562.

7. W. Mao, Y. Li, M. Al-Mumin, and G. Li, All-optical clock recoveryfor both RZ and NRZ data, IEEE Photon Technol Lett 14 (2002),873–875.

8. L. Huo, Y. Dong, C. Lou, and Y. Gao, Clock extraction using anoptoelectronic oscillator from high-speed NRZ signal and NRZ-to-RZ format transformation, IEEE Photon Technol Lett 15 (2003),981–983.

9. J. Slovak, C. Bornholdt, J. Kreissl, and et al., Bit rate and wavelengthtransparent all-optical clock recovery scheme for NRZ-coded PRBSsignals, IEEE Photon Technol Lett 18 (2006), 844–846.

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© 2008 Wiley Periodicals, Inc.

A NEW FORMULATION AND SOLUTIONMETHOD OF ELECTROMAGNETICSCATTERING FROM ARBITRARYSHAPED DIELECTRIC OBJECTS

Necmi Serkan TezelDepartment Electronics and Communication Engineering, IstanbulTechnical University, 34469 Maslak, Istanbul, Turkey; Correspondingauthor: tezeln@itu.edu.tr

Received 14 March 2008

ABSTRACT: In this study, a new and computational effective methodrelated to electromagnetic scattering from arbitrary shaped dielectricobjects is proposed. This method is based on Taylor series expansion offields with unknown coefficients on the circles that are inside and out-side of object. By using the boundary condition, series equations areobtained. These series of equations can be solved by using orthogonalityproperties of Fourier expansion functions. This transformation makesthe problem with simple formulation which can be solved computationaleffectively. Results and computational times obtained by transformmethod and those obtained by Method of Moments (MoM) techniqueare compared. Good agreements are observed in results. It is alsoobserved that transform method needs less computational time thanMoM method. © 2008 Wiley Periodicals, Inc. Microwave OptTechnol Lett 50: 2768 –2772, 2008; Published online in Wiley Inter-Science (www.interscience.wiley.com). DOI 10.1002/mop.23786

Key words: electromagnetic scattering, dielectric objects, numericalmethods

Figure 9 The simulated results (a–c) and measured eye-diagram (d–f) for recovered clock. (a,d) for 0 km fiber; (b),(e) for 47 km; (c,f) for 67 km. (d–f):Scale: 319 �W/div; Time: 100.0 ps/div. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com]

2768 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 11, November 2008 DOI 10.1002/mop