JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 1, JANUARY 1, 2013 145

Generation of Versatile Waveforms From CW LightUsing a Dual-Drive Mach-Zehnder Modulator and

Employing Chromatic DispersionBo Dai, Student Member, IEEE, Zhensen Gao, Student Member, IEEE, Xu Wang, Senior Member, IEEE,Hongwei Chen, Member, IEEE, Nobuyuki Kataoka, Member, IEEE, and Naoya Wada, Member, IEEE

Abstract—In this paper, we analyze waveform generation usinga single-stage dual-drive Mach-Zehnder modulator and a disper-sive fiber. We derive a mathematical expression for the waveformgeneration process in the time domain and use this to propose awaveform generation algorithm. Furthermore, versatile wave-forms, such as short pulse, trapezoidal, triangular and sawtoothwaveforms and doublet pulse, are theoretically generated underdifferent combinations of the four variables. The generated wave-forms are analyzed in terms of the gradient and the instantaneousfrequency. Finally, the waveform generation is experimentallydemonstrated at the repetition rate of 10 GHz.

Index Terms—Chromatic dispersion, electro-optic modulator,waveform generation.

I. INTRODUCTION

P HOTONIC waveform generation technique has a signif-icant impact on many fields of science and engineering,

including optical communication, biomedical optical imagingand microwave signal generation. Hence, generating differentprospective waveforms is an active research area [1]–[5].Among numerous photonic waveform generation approaches,the Fourier synthesis approach is a practical method that iswidely used, in which the optical spectral comb is firstly gener-ated from an input signal and then is convolved with the Fouriertransform of a spectral filter to produce prospective waveforms.In the Fourier synthesis approach, the first step is to gen-

erate optical spectral comb. Usually, optical spectral comb canbe generated by using cascaded modulation which consists ofoptical phase modulators and intensity modulators [6]–[8]. An-

Manuscript received February 15, 2012; revised September 06, 2012; ac-cepted October 15, 2012. Date of publication October 19, 2012; date of currentversion December 28, 2012.B. Dai and X. Wang are with the School of Engineering and Physical

Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, U.K. (e-mail:X.Wang@hw.ac.uk).Z. Gao was with the School of Engineering and Physical Sciences, Heriot-

Watt University, Edinburgh, EH14 4AS, U.K. He is now with Bell Laboratories,Alcatel-Lucent, Shanghai, China.H. Chen is with the State Key Laboratory on Integrated Optoelectronics, Ts-

inghua National Laboratory for Information, Science and Technology (TNList),Department of Electronic Engineering, Tsinghua University, Beijing, 100084,China.N. Kataoka and N. Wada are with the Photonic Network System Labora-

tory, Photonic Network Research Institute, National Institute of Information andCommunications Technology (NICT), Tokyo, 184-0015, Japan.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/JLT.2012.2225827

other scheme is to use a dual-drive Mach-Zehnder Modulator(DD-MZM) to generate a flat spectral comb [9]–[11]. Due tothe good stability and high coherence of the generated spectralcomb, the generation of 200 fs (FWHM) ultra-short pulses canbe achieved using this approach. In addition to this, as shown inthis work, the repetition rate may be widely tunable, rangingfrom 5 GHz to 17 GHz. Furthermore, compared to the cas-caded modulations, the single-stage dual-drive modulation cannot only reduce component cost but also simplify the system.The second step of the Fourier synthesis approach is to ma-

nipulate the generated spectral comb. Traditionally, gratings andlenses are applied to the composition of spectral components[12]–[14]. The implementation of liquid crystal modulator ar-rays leads to a new regime for arbitrary waveform generationby means of line-by-line manipulation of the spectral comb[15],[16]. Independent programmable control of more than 100 spec-tral lines at 5 GHz line spacing was obtained by using the free-space platform, which was a significant step for complex wave-form generation. Another alternative waveform generation ap-proach, which relies on a single transverse spatial mode, canintegrate with fiber systems well [17], [18]. The Fourier syn-thesis approach was successfully achieved in the time domainwhen chromatic dispersion for longitudinal spectral decompo-sition was used.In our recent research, we demonstrated generation of ver-

satile waveforms using a single-stage DD-MZM followed by asingle mode fiber (SMF) [19]. In this paper, we concentrate onthe further study of dual-drive modulation with induced chro-matic dispersion for the formation of waveforms. We build atheoretical model of the waveform generation process. There arefour variables that are related to the waveform generation. Byadjusting these four variables, we predict the generation of ver-satile waveforms. Furthermore, we analyze the generated wave-forms and compare them with experimental measurements. Thepaper is organized as follows. In Section II, the theoretical anal-ysis for the proposed scheme is explored and the operation prin-ciple is investigated. In Sections III and IV, the algorithm on theprediction of waveform generation and the experimental setupare discussed. Several examples of the versatile waveform gen-eration are then described in Section V, before concluding inSection VI.

II. THEORETICAL ANALYSIS OF THE PROPOSED SCHEME

Fig. 1(a) shows the schematic diagram for the proposedwave-form generation scheme. A continuous-wave (CW) laser is used

0733-8724/$31.00 © 2012 IEEE

146 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 1, JANUARY 1, 2013

Fig. 1. (a) Schematic diagram of waveform generation scheme and (b) gener-ated spectral comb.

as the light source. The CW light is directed into the LiNbODD-MZM. RF sinusoidal signal is generated from a RF syn-thesizer, divided into two paths (RF-a and RF-b) by a hybridcoupler and amplified by two microwave amplifiers to drivethe DD-MZM. The relative amplitudes ( and ) and thephase difference of the two RF signals can be adjusted by twoRF attenuators and a tunable delay line. After undergoing theelectro-optic modulation, an optical spectral combwithmultiplesidebands on both sides of the fundamental component is gen-erated from the CW light, as shown in Fig. 1(b).The output electrical field from the DD-MZM is given as [20]

(1)

where is the amplitude of CW light electrical field; isoptical carrier frequency; is switching voltage; isswitching bias voltage; and are the DC bias volt-ages applied to the two arms; and and are the RFmodulating electrical voltage. and can be expressedas two sinusoidal functions: and

, where and are the amplitudes of the twoRF signals; is the frequency of the modulating RF signal; andis the phase shift according to the delay between the two RF

signals. In our theoretical analysis, the linewidth of CW light isassumed to be much narrower than the modulation frequency.After Jacobi Anger expansion, the output electrical field can

be written as follows

(2)

From (2), it can be seen that the number and the magnitude ofgenerated comb lines are determined by the amplitudes of thetwo RF signals. After the generation of spectral comb, a spanof SMF is used to induce the chromatic dispersion for the for-mation of waveform. The chromatic dispersion results from thederivative of the group delay with respect to each spectral combline [21]. The attenuation and nonlinear effects of SMF are ne-glected and only the first order chromatic dispersion is consid-ered in this paper. Due to the presence of chromatic dispersion,the electrical field with induced chromatic dispersion after SMFcan be expressed as:

(3)

where is the dispersion phase angle and is related to both thelength ( in kilometer) and the dispersion characteristic ( inps/nm km) of SMF, whose expression is

(4)

where is velocity of light in a vacuum. The induced chro-matic dispersion recomposes the spectral comb, operating thewaveform formation. It is worth noting that since the forma-tion of waveforms is based on the chromatic dispersion, it re-quires a zero-dispersion for a further propagation of the gener-ated waveforms.

DAI et al.: GENERATION OF VERSATILE WAVEFORMS USING A MACH-ZEHNDER MODULATOR 147

(5)

For detection, a photodiode (PD) is employed for O/E con-version. The output intensity of the signal is expressed in (5),where is responsivity of the photodetector. From (5), we cansee that each harmonic is resolved and can be analyzedindividually. It is the amplitudes of the modulating RF signals( and ), the phase difference between the two RF signals, the difference of the two bias voltages

and the chromatic dispersion of the SMF that determine thewaveform formation. In the generation of the spectral comb, theamplitudes of the two RF signals determine the number of spec-tral components, which is also mentioned in [11]. Nevertheless,this term is limited by the gain and saturation power of the RFamplifiers and the maximum RF input power of the modulator.

III. ALGORITHM OF DETERMINING VARIABLES

According to the theoretical analysis, there are four variablesthat affact the waveform formation, based on which we use themulti-variable control method to search the values of the fourvariables for the generation of an optimumwaveform. The flow-chart of the algorithm is depicted in Fig. 2. Firstly, a target wave-form is proposed and the properties of the target waveforms(such as waveform linearity, optical spectrum and power spec-trum) are calculated. These properties are the conditions of thewaveform generation. Besides, tolerant values are introducedinto the conditions to relax conditions. Secondly, initial valuesare assigned to the four variables and the searching ranges ofthese four variables are also given. By substituting these initialvalues into (5), a waveform is generated. Thirdly, the propertiesof the generated waveform are calculated and compared with thetarget waveform. If they are unmatched, the values of the vari-ables are changed one by one for another round of waveformgeneration and condition matching. However, once the compar-ison is matched, the values of the variables are recorded. Mean-while, the searching ranges of the variable are narrowed and thetolerant values are reduced to tighten up the restrictions. A newset of initial values within narrowed searching ranges are givento generate waveform. Then, the variable searching procedurecontinues until all combinations of the four variables within thesearching ranges are tested. Finally, after the variable searchingfinishes, the recording of the four variables is checked. If thereis no recording, it indicates that the proposed scheme can notgenerate the target waveform. Otherwise, the recorded variablesare used for waveform generation and the generated waveformis the optimum one for the target waveform.According to (5), the output signal is manipulated as a whole

by adjusting the four variables and it is not straightforward togenerate any arbitrary waveforms by controlling the limitedvariables individually. However, it is a very simple scheme toset up and control for the generation of versatile meaningfulwaveforms with acceptable tolerances.

Fig. 2. Flowchart of the waveform generation algorithm.

IV. EXPERIMENTAL SETUP

The experimental setup to verify the proposed scheme isshown in Fig. 1(a). The four variables are controlled by dif-ferent components. The amplitudes of the two RF signals (and ) are adjusted by two RF attenuators. The control of thephase difference between the two RF signals is realized byinserting some delay on one branch. The two RF signals areamplified by two RF amplifiers. The gains of the amplifiersare dB and the saturation powers are dBm. Thedifference of the two bias voltages is adjustedby the DC voltage controllers and the chromatic dispersion ofthe SMF depends on the length of the SMF. The DD-MZMhas the optical bandwidth of GHz. The switching voltages

for both electrodes are about 6.5 V, which are measuredat 1 GHz with the use of one electrode only. The PD used inthe experiment has the bandwidth of 40 GHz, which cuts offthe high-order harmonics.

V. WAVEFORM GENERATION

A. Short Pulse

In [9], the authors has demonstrated the generation of shortpulses by using a single-stage DD-MZMunder the flat-spectrumcondition, which is

(6)

(7)

Firstly, we use (5) to calculate the signal based on the flat-spectrum condition to examine the feasibility of the derivedequation. In our calculation, both switching voltage, , andswitching bias voltage, , are 4 V. According to the flatspectrum condition, we set V, V,V and V. There is no delay between the two RFsignals, i.e., . The chromatic dispersion, , is 17 ps/nmkm and the length of the SMF is 1.1 km. Besides, it is worthnoting that the maximum value of the parameter in (5) de-pends on the bandwidth of the PD. The calculated short pulsesare illustrated in Fig. 3(a). We also carry out a proof-to-prin-ciple experiment. In the experiment, a 10 GHz sinusoidal signalis used as the modulating RF signal. Under the flat-spectrum

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Fig. 3. (a) Calculated and (b) measured short pulses under the flat spectrumconditions. (c) Calculated normalized gradient and instantaneous frequency cor-responding to short pulse intensity profile.

condition, 4 ps (FWHM) pulses are generated at the repetitionrate of 10 GHz, as shown in Fig. 3(b).The optical spectrum is shown in Fig. 1(b), which is a flat

spectral comb. The detailed waveform for only one pulse is il-lustrated in Fig. 3(c). Since the frequency comb has a rectan-gular shape, the resultant temporal waveform presents afunction and there are pedestals around the main lobes. Thedetailed discussion on this phenomenon can be found in [10].The normalized gradient and the instantaneous frequency arealso plotted to show the properties of the waveform. The gra-dient tells the intensity change and the linearity of the gener-ated waveform, while the instantaneous frequency indicates thephase information and chirp of the waveform. Equation (5) onlyprovides the intensity synthesis. To show the phase oscillationin the generated pulse, the instantaneous frequency is calculatedby (3). The successful generation of pulses indicates that the de-rived equation, (5), is workable and can be used to predict morewaveform generations.To analyze the tolerance of the system during the operation,

the influences of RF phase noise and DC bias drift over the per-formance of waveform generation are investigated theoretically.Root-mean-square errors (RMSE) are calculated to evaluate thequality of the waveforms with the induced noises. According tothe calculation, the system suffers from the RF phase noise se-riously (blue solid line in Fig. 4), if the two RF signals from twoindependent synthesizers are employed without phase locking.In our experiment, the RF phase noise is avoided by using thetwo RF signals from a single synthesizer. Futhermore, using asingle synthesizer can also reduce the complexity of the system.

Fig. 4. Influence of RF phase noise and bias drift.

The DC bias drift is an unavoidable issue in this system. Ac-cording to our analysis, the generated waveforms have less than3.8% errors compared to the optimum one even when the biasdrift is up to 5% (brown dashed line), which indicates that thesystem has a high tolerance to the bias drift. Furthermore, in theexperiment, the waveform generation is very stable.

B. Trapezoidal Waveform

Trapezoidal waveforms can deliver the same energy as withless dissipation as compared to pulses and were suggested tobe used in the liquid Crystal Displays (LCDs) [22]. We can alsogenerate trapezoidal waveform using the proposed scheme. Thefirst step is to calculate the properties of the target waveform. Atrapezoidal waveform have a flat top, i.e., a section of zero-gra-dient, and the intensity in this section is larger than those in theother sections. The target waveform and normalized gradientare plotted using dashed lines in Fig. 5(a). In the calculation,we firstly assume that % ripple is allowed in the flat-top sec-tion. Then, we use the algorithm discribed in Section III to de-termine the optimum values of the four variables. The variablesare obtained when the ripple in the flat-top section converges to

%. V, V, V andV. There is no delay between the two RF signals and the lengthof SMF is 1.1 km.The calculated waveform is plotted in Fig. 5(b) and a misfit

curve comparing the target and calculated waveform is depictedin the subplot of Fig. 5(a). Besides, RMSE, calculated to mea-sure the difference beween the target and calculated waveforms,is 5.61%. The normalized gradient of the calculated waveformhas a zero-level gradient, as shown in Fig. 5(a), indicating theflatness of the flat top. An up-chirp occurs within the flat-top sec-tion, while on the leading and tailing edges, the instantaneousfrequency decreases, i.e., down-chirp. In the experiment, wetry to generate the trapezoidal waveform that is consistent withthe calculated waveform. The measured waveform is shown inFig. 5(c), which is symmetric and have a flat top (20 ps) andsmooth leading and tailing edges (40 ps each). Compared withthe target waveform, the measured waveform has the RMSE of5.96%. The optical spectrum is shown in Fig. 5(d).

C. Triangular Waveform

When V and other variables remain the same,the formation of triangular waveforms is achieved, as depictedin Fig. 6(b). The calculated waveform is compared with thetarget waveform in Fig. 6(a). The normalized misfit curve is

DAI et al.: GENERATION OF VERSATILE WAVEFORMS USING A MACH-ZEHNDER MODULATOR 149

Fig. 5. (a) The target trapezoidal waveform and the gradient and instantaneousfrequency of the calculated waveform. (b) Calculated and (c) measured trape-zoidal waveforms. (d) Measured optical spectrum.

bounded within , which indicates that the difference be-tween the target and calculated waveforms is very slight. TheRMSE of the calculated result is 6.42%. Two horizontal sec-tions in the gradient shows the linearity in the leading and tailingsides. The instantaneous frequency is also plotted in Fig. 6(a).Two spikes of the instantaneous frequency on the two sidesindicate steep changes in the phase. It is clear that the gener-ated triangular waveform is chirped. The experimentally mea-sured waveform and optical spectrum of the generated trian-gular waveform are shown in Fig. 6(c) and (d), respectively.The width is about 15 ps (FWHM). The RMSE of the mea-sured waveform is 7.03%. Two spectral lines in the frequencycomb (highlighted with arrows in Fig. 6(d)) are suppressed bythe modulation.

D. Doublet Pulse

In the generation of doublet pulses, the amplitudes of the RFsignals and the DC bias voltages become V, V,

V and V. A 18 ps delay to RF-b is alsoadded, which results in a phase shift between the two RF mod-ulating signals. Fig. 7(a) and (b) show the calculated and mea-sured waveforms. The doublet pulses are symmetric and havedeep dips in the middle. The peak separation is about 15 ps.In the frequency comb, three spectral lines, including the cen-tral spectral line, are suppressed by 20 dB after the modulation,

Fig. 6. (a) The target triangular waveform and the gradient and instantaneousfrequency of the calculated waveform. (b) Calculated and (c) measured trian-gular waveforms. (d) Measured optical spectrum.

as marked in Fig. 7(c). In the calculation, we also generate 1Gbit/s doublet pulses and investigate the power spectrum. Togenerate 1 Gbit/s doublet pulses, 1 GHz RF modulating signalis used. The amplitudes of the RF signals and the DC bias areunchanged. The delay of RF-b becomes 175 ps and the length ofSMF is shortened to 0.2 km. The calculated power spectrum isillustrated in Fig. 7(d). The U.S. Federal Communication Com-mission (FCC) specified ultra-wideband (UWB) indoor emis-sion mask is also plotted for comparison [23]. The power spec-trum of the doublet pulses is centered around 6.5 GHz and has a10 dB bandwidth of about 6 GHz, which fits well the FCC-spec-ified spectral mask.

E. Sawtooth Waveform

It has been demonstrated that the use of sawtooth (asym-metric triangular) waveform can provide three-fold improve-ment relative to the use of Gaussian pulses for wavelength con-version due to the asymmetric spectral intensity evolution ofsawtooth waveform [13]. Sawtooth waveforms can also be gen-erated by means of the proposed scheme, as shown in Fig. 8(b)and (c). Both RF modulating signals are kept at 5 V. 97 ps delayis added to RF-b. The difference of the DC bias voltages is ad-justed to 2.7 V. The length of SMF is extended to 1.47 km for

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Fig. 7. (a) Calculated and (b) measured doublet pulses. (c) Measured opticalspectrum. (d) Calculated power spectrum of the 1 Gbit/s doublet pulses. Reddashed line: FCC spectral mask for indoor applications. Inset diagram: thewaveform of the generated 1 Gbit/s doublet pulse.

larger chromatic dispersion. In Fig. 8(a), a negative stationarysection of the normalized gradient states that the waveform hasa linear tailing side. The instantaneous frequency behaves in anonlinear fashion and decreases on the tailing edge of the gener-ated sawtooth waveform. A misfit curve is depicted in the sub-plot to and the difference in the tailing side is within . TheRMSE of the calculated waveform is 9.51%. In the experiment,we also generate the sawtooth waveform as expected. They havesharp leading side and slow downward ramp, whose width isabout 30 ps (FWHW). The measured waveform has the RMSEof 11.38%. The frequency comb is asymmetric and the spectrallines on the right side of the center are suppressed gradually, asshown in Fig. 8(d).

VI. CONCLUSION

We have built the waveform generation model based on asingle-stage DD-MZM and a SMF employing direct detection,and derived the mathematical expression for the system. Themodel can help with the prediction of the waveform generation.In this system, there are four variables affecting the waveformformation. Under the different combinations of these four vari-ables, versatile waveforms, short pulse, trapezoidal, triangularand sawtooth waveforms and doublet pulse have been obtained.The characteristics of these waveforms have been evaluatedby investigating the gradient and the instantaneous frequency.Also, the generation of these waveforms has been demonstratedat the repetition rate of 10 GHz in the experiment. In addition,

Fig. 8. (a) The target sawtooth waveform and the gradient and instantaneousfrequency of the calculated waveform. (b) Calculated and (c) measured saw-tooth waveforms. (d) Measured optical spectrum.

the scheme has two potential features, tunable repetition rateand tunable center wavelength, due to the adjustable RF signaland CW light source. This scheme is particularly attractive as awaveform generation source for photonic network applications.

ACKNOWLEDGMENT

This work was partially supported by the Royal Society in-ternational joint projects and the Royal Society of Edinburgh(RSE)—National Natural Science Foundation of China (NSFC)Joint Project scheme. The authors very appreciate Dr. BenjaminJ. Puttnam of NICT for his constructive comments. The authorswould also like to thank Mr. H. Sumimoto of NICT for his tech-nique support.

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Bo Dai (S’10) received the B.Eng. (Hon. I) degree in electronic engineeringfrom City University of Hong Kong in 2009. He is currently pursuing the Ph.D.degree in the School of Engineering and Physical Sciences, Heriot-Watt Uni-versity, Edinburgh, U.K.

Zhensen Gao (S’10) received the B.S. and M.S. degrees in the Department ofPhysics from Harbin Institute of Technology, Harbin, China, in 2006 and 2008,respectively, and the Ph.D. degree in electrical engineering from Heriot-WattUniversity, Edinburgh, U.K.He joined Alcatel-Lucent, Shanghai Bell, China as a Research Scientist in op-

tical communication. His research interests include optical code division mul-tiple access, micro-ring resonator and radio-over-fiber technologies.

Xu Wang (S’91–M’98–SM’06) received the B.S. degree in physics from Zhe-jiang University, Hangzhou, China, in 1989, the M.S. degree in electronics en-gineering from the University of Electronics Science and Technology of China(UESTC), Chengdu, China, in 1992, and the Ph.D. degree in electronics engi-neering from the Chinese University of Hong Kong (CUHK) in 2001.From 1992 to 1997, he was a Lecturer with the National Key Laboratory of

Fiber Optic Broadband Transmission and Communication Networks of UESTC.In 2001–2002, he was a Postdoctoral Research Fellow with the Department ofElectronic Engineering, CUHK. From 2002 to 2004, he was with the Depart-ment of Electronic and Information Systems, OsakaUniversity, Osaka, Japan, asa TAO Research Fellow. From 2004 to 2007, he was an Expert Researcher withthe Photonic Network Group, National Institute of Information and Communi-cations Technology (NICT), Tokyo, Japan. He joined the School of Engineeringand Physical Sciences, Heriot-Watt University, Edinburgh, U.K., as a SeniorLecturer in July 2007. His research interests include fiber optic communicationnetworks, optical code-division multiplexing, optical packet switching, appli-cation of fiber gratings, microwave photonics, and fiber optic signal processing.He has held five patents and delivered over 40 invited talks in the internationalconferences. He has published more than 180 technical papers.

Hongwei Chen (M’07) was born in Inner Mongolia, China, in 1979. He re-ceived the B.E. and Ph.D. degrees in electronic engineering from Tsinghua Uni-versity, Beijing, China, in 2001 and 2006, respectively.He is currently with the faculty of the Department of Electronic Engi-

neering, Tsinghua University. His current areas of interest are radio-over-fibertechniques, high-speed optical communications and optical packet switchingnetworks.Dr. Chen received the Best Student Paper Award of Asia-Pacific Optical

Communications (APOC) 2004 and was a subcommittee member of APOC2005, 2007, and 2008 and CLEO-PR 2007.

Nobuyuki Kataoka (S’03–M’06) received the B.E., M.E. and Dr. Eng. degreesfrom Osaka University, Osaka, Japan, in 2001, 2003, and 2006, respectively.In 2006, he joined the National Institute of Information and Communications

Technology (NICT), Tokyo, Japan. His research interests are in the area of pho-tonic networks such as optical packet switching and optical code division mul-tiple access.Dr. Kataoka is amember of the Institute of Electronics, Information and Com-

munication Engineers (IEICE) of Japan.

Naoya Wada (M’97) received the B.E., M.E., and Dr. Eng. degrees in elec-tronics from Hokkaido University, Sapporo, Japan, in 1991, 1993, and 1996,respectively.

In 1996, he joined the Communications Research Laboratory (CRL),Ministry of Posts and Telecommunications, Tokyo, Japan. Since April 2009,he has been a leader of the Photonic Network Group (now Photonic NetworkSystem Laboratory) in NICT. His current research interests are in the area ofphotonic networks and optical communication technologies, such as opticalswitching network, energy-efficient network, optical access system, opticalprocessing system, burst-mode optical communication technologies, and hugecapacity transmission based on spatial division multiplexing.