752IEICE TRANS. ELECTRON., VOL.E98–C, NO.8 AUGUST 2015

INVITED PAPER Special Section on Microwave Photonics

Generating UWB and Microwave Waveforms Using SiliconPhotonics

Lawrence R. CHEN†a), Nonmember

SUMMARY We provide an overview of techniques for the photonicgeneration of arbitrary RF waveforms, particularly those suitable for im-pulse radio or multi-band ultrawideband (UWB)-over-fiber transmission,and chirped microwave waveforms, with an emphasis on microwave pho-tonic filtering and optical spectral shaping followed by wavelength-to-timemapping. We discuss possibilities for integrating the various device andcomponent technologies with silicon photonics.key words: microwave photonics, silicon photonics, waveform generation

1. Introduction

Techniques for generating arbitrary RF waveforms are im-portant for a broad range of applications from communica-tions to imaging and sensing to instrumentation. For exam-ple, ultrawideband (UWB) has attracted interest for short-range, high-speed wireless communications and sensor net-works. The use of UWB-over-fiber has recently emerged asa viable approach to extend reach and the area covered [1].In this sense, in addition to being primed for optical trans-mission, photonic generation of UWB signals can exploitthe optical components and technologies that are already in-volved. Photonic approaches also provide increased flexi-bility, particularly with regards to reconfigurability and tun-ability. This is extremely valuable for generating waveformsthat are suitable for impulse radio (IR) UWB, e.g., doubletsor triplets, as well as multi-band (MB) UWB where the elec-trical spectrum is separated into multiple channels with cor-respondingly longer waveforms in the time domain. Finally,photonic approaches may enable different modulation for-mats, including pulse polarity modulation, pulse shape mod-ulation, and bi-phase modulation.

As a second example, chirped microwave waveforms(and their subsequent compression) are useful in radar sys-tems for increasing detection distance or resolution [2].While such waveforms can be generated in the electronicdomain, their bandwidths and central frequencies are lim-ited by the sampling rate of digital electronics. On the otherhand, photonic techniques offer the possibility of achievingcentral frequencies of tens to hundreds of GHz as well assignificant chirp rates, thereby supporting tens of GHz ofbandwidth. As with UWB generation, the use of photonicsalso offers the possibility for tuning and reconfiguration, as

Manuscript received January 15, 2015.Manuscript revised March 6, 2015.†The author is with the Department of Electrical and Computer

Engineering, McGill University, Montreal, QC H3A 0E9 Canada.a) E-mail: lawrence.chen@mcgill.ca

DOI: 10.1587/transele.E98.C.752

well as compatibility with fiber optic transmission.A variety of techniques for photonic generation of IR-

UWB, MB-UWB, and chirped microwave waveforms havebeen reported. These include, amongst others, the use ofoptical frequency combs, nonlinear optical effects in fiberor semiconductor optical amplifiers, phase modulation-to-intensity modulation using discrimination filters, opticalspectral shaping followed by wavelength-to-time mapping,direct space-to-time pulse shaping, temporal pulse shaping,and microwave photonic filters (MPFs) [3], [4].

Typically, the system implementations are based ondiscrete components and involve bulky (e.g., fiber-based)and/or benchtop components. In recent years, there hasbeen a focus on integration, particularly to address issuesrelated to compactness, stability, power consumption, andultimately mass production for reduced cost and practicaldeployment [5]. In this paper, we describe the use of siliconphotonics (SiP) for generating UWB and chirped microwavewaveforms. SiP is emerging as the platform of choice overother semiconductor technologies such as InP for photonicintegration. In addition to providing a small footprint, theability to integrate active with passive devices, and the pos-sibility to reduce power consumption, SiP uses the sameprocessing tools as CMOS fabrication. This has resultedin high quality control, increased yield (reliability), as wellas performance of SiP integrated circuits thereby paving thepathway for commercialization [6], [7]. In this paper, weconsider the implementation of MPFs and optical spectralshapers in SiP.

The remainder of this paper is organized as follows.Section 2 describes MPFs for generating RF waveforms,e.g., for IR-UWB and MB-UWB transmission. Section 3reviews optical spectral shaping followed by wavelength-to-time mapping for generating chirped microwave waveforms.Finally, perspectives and conclusions are given in Sect. 4.

2. Generating UWB and RF Waveforms Using Mi-crowave Photonic Filters

In this section, we discuss the use of MPFs to generate UWBand RF waveforms. After illustrating the basic principle ofwaveform generation, we provide a brief review of MPFs.Next, we describe specific examples of generating IR-UWBand MB-UWB waveforms with MPFs. We then presentan approach for generating arbitrary waveforms based onan MPF involving nonlinear mixing in a silicon nanowire(SNW). This is followed by a discussion of implementing

Copyright c© 2015 The Institute of Electronics, Information and Communication Engineers

CHEN: GENERATING UWB AND MICROWAVE WAVEFORMS USING SILICON PHOTONICS753

Fig. 1 (a) Concept of Fourier transform optical pulse shaping with opti-cal filters and (b) RF waveform generation based on MPFs.

MPF building blocks in SiP.

2.1 Basic Principle

Figure 1 (a) shows the general schematic for optical pulseshaping based on using an optical filter to tailor the ampli-tude and phase of the spectral content associated with an ul-trashort optical input pulse (also referred to as Fourier trans-form optical pulse shaping) [8]. The transfer function (spec-tral response) of the optical filter, Hopt(ω), must satisfy therelationship

Hopt(ω) = |Hopt(ω)| exp( jφHopt (ω)) =Eopt

out (ω)

Eoptin (ω)

(1)

where Eoptout (ω) and Eopt

in (ω) are the Fourier transforms ofthe output and input electric fields, respectively, of the de-sired optical waveform and input ultrashort optical pulse.Assuming that the synthesized output waveform is longerin duration than the input (which is typical in most opti-cal pulse shaping applications), the spectrum of the outputsignal is given approximately by that of the filter response,Eopt

out (ω) ≈ Hopt(ω), i.e., the filter operates over a relativelyflat (constant) portion of the input spectrum. In an analogousmanner, as depicted in Fig. 1 (b), a microwave filter with fre-quency response HRF(Ω) can be used to process an inputRF impulse represented by its Fourier transform, ERF

in (Ω),according to

ERFout(Ω) = HRF(Ω)ERF

in (Ω) (2)

where ERFout(Ω) is the Fourier transform of the desired out-

put waveform (we have used Ω to denote frequencies in themicrowave range to distinguish them from ω, which repre-sents optical frequencies). Again, if the synthesized outputwaveform is long in duration compared to the input, thenERF

out(Ω) ≈ HRF(Ω). In this paper, we consider the use ofMPFs to realize the desired microwave filter responses.

2.2 Brief Review of Microwave Photonic Filters

The field of MPFs is extremely rich and the design of filters

Fig. 2 General schematic of an MPF.

with reconfiguration and/or tuning capabilities has been thesubject of intense research. Indeed, many filter structureshave been proposed, including those with notch responses,tailored responses involving complex tap coefficients, dis-persive filters or those with specific phase profiles, and sin-gle or multiple passband responses. Excellent review arti-cles on MPFs and microwave photonic signal processing canbe found in [9]–[12]. For completeness, we provide some oftheir salient features.

The typical MPF structure is illustrated in Fig. 2. Theinput microwave signal xin(t) is converted to the opticaldomain via modulation (E/O conversion), e.g., using anelectro-optic modulator (EOM) fed by a single carrier fre-quency or multiple carrier frequencies source. The electricfield of the modulated optical signal, ein(t), which carriesthe information about the input microwave signal, is thenprocessed in the optical domain by a photonic subsystem.The purpose of the subsystem is to take samples of themicrowave signal, which are conveyed by the optical car-rier(s), and weigh, delay, and combine them. The subsys-tem can comprise a variety of components, from passive de-vices such as couplers, variable optical attenuators (VOAs),fiber Bragg gratings (FBGs), and fiber delay lines to activecomponents such as Erbium-doped or semiconductor opti-cal amplifiers. After photonic processing, the power of theoutput optical signal, |eout(t)|2, is detected using an opticalreceiver (O/E conversion) to remove the optical carrier(s)and extract the processed microwave signal xout(t).

Generally speaking, the MPF cannot be viewed as alinear system relating xin(t) and xout(t). However, under cer-tain conditions (see further [10]), we can consider a linearoperation such that the input and output microwave signalsare related by

xout(t) = xin(t) ∗ hRFMPF(t) (3)

where hRFMPF(t) is the MPF impulse response with corre-

sponding frequency response HRFMPF(Ω). Note that the MPF

frequency response does not correspond directly to thetransfer function of the photonic subsystem. However, cer-tain features of the photonic subsystem are correlated to theMPF response. For example, if the photonic subsystem in-volves feedback, the MPF transfer function can take on theform of an infinite impulse response (IIR) filter; on the other

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hand, it will have the form of a finite impulse response (FIR)filter when there is no optical feedback. In the discussionthat follows, we restrict ourselves to FIR MPFs.

Consider an optical source comprising multiple carrierfrequencies that are uniformly spaced, e.g., from a bank oflasers. Assuming incoherent superposition of the carriers(samples or taps), the MPF frequency response is given by

HRFMPF(Ω) ∝

N∑m=1

Pm exp[− j(m − 1)ΩΔτ] (4)

where N is the number of taps, Pm is the amplitude (weight)of the mth tap, Δλ is the wavelength separation between taps,and Δτ = DΔλ is the tap delay with D being the dispersionin [ps/nm] of the medium used to implement the delay. Thetap amplitudes can be controlled to shape (reconfigure) thefilter response while the tap delay can be varied to tune thefrequency response. Note that the MPF frequency responseis periodic with a period 2π/Δτ = 2π/(DΔλ).

2.3 Review of Results Using Fiber-Based Implementa-tions

Figure 3 illustrates several different MPF implementationsand the overall system for generating IR-UWB and MB-UWB waveforms [13]–[16]. The MPFs use multiple car-rier frequencies which are generated either with several dis-crete lasers as in Fig. 3 (a) [13] or by spectral slicing a broad-band source as in Figs. 3 (b) and (c) [14]–[16]. In Fig. 3 (b),an arrayed waveguide grating (AWG) is employed to cre-ate discrete spectral slices; VOAs provide control over theiramplitudes. A number of space switches and a second setof AWGs select and direct the spectral slices to one of twoEOMs where E/O conversion occurs. The EOMs are biasedfor operation on opposite slopes of the modulator transferfunction so as to obtain positive or negative taps. Note thata spectral slice can implement a positive tap or a negativetap, but not both at the same time. The MPF implementa-tion in Fig. 3 (a) is similar except that discrete lasers replacethe broadband source and AWGs to define the taps (the tapamplitudes can be set by adjusting the powers of the lasers).In all cases, a length of single mode fiber (SMF) is used asa dispersive medium to create the necessary tap delays.

The input to the MPF is a broadband RF signal, i.e., ashort electrical pulse. The MPF response is then configuredto shape the input RF spectrum to obtain the desired out-put temporal waveform as described by Eq. (2). Note thatwe can also interpret the system operation as generating aspecific temporal waveform whose electrical spectrum sat-isfies a given requirement, e.g., for IR-UWB or MB-UWBtransmission.

Figure 4 highlights examples of the different wave-forms that can be generated. For example, pulse doubletsobtained using the MPFs in Figs. 3 (a) and (b) are shown inFigs. 4 (a) and (b), respectively. In both cases, 3 taps areemployed with a weight distribution of [0.5,−1, 0.5]. InFig. 4 (a), the taps are based on 3 discrete lasers with a wave-

Fig. 3 General schematic of MPFs and systems for generating IR-UWBand MB-UWB waveforms. The MPFs are implemented with (a) discretelasers (after [13]), (b) spectral slicing with AWGs (after [14], [15]), and (c)spectral slicing with a periodic optical filter and balanced detection (after[16]). BBS: broadband source, PC: polarization controller, ODL: opticaldelay line (all schematics are courtesy of and adapted from J. Mora).

length separation of 0.74 nm (centered at 1550.12 nm) and5.43 km of SMF is used to provide a tap delay of ∼68 ps. InFig. 4 (b), the taps are based on 3 adjacent channels froman AWG with a 3 dB channel bandwidth of 0.4 nm andchannel spacing of 0.8 nm (centered near 1547.72 nm);again 5.43 km of SMF is used to provide the tap delay(∼74 ps). Note that the characteristics of the waveforms—intime and in electrical spectrum—are very similar regardlessof whether discrete lasers or a spectrally sliced broadbandsource is used (the wavelength separation between taps andtap delay are approximately the same). By increasing thenumber of taps and controlling their amplitudes to create anapodized profile, a Gaussian-like waveform can be gener-ated, giving rise to a signal that is suitable for MB-UWBcommunications. The results obtained using the MPF inFig. 3 (b) with a broadband source having a Gaussian-likespectrum and 3 dB bandwidth of 8 nm centered at ∼1546 nmand 23 taps are depicted in Fig. 4 (c) [the AWG has the samecharacteristics as described above and 5 km of SMF is usedto provide the tap delay].

The MPF shown in Fig. 3 (c) differs from those inFigs. 3 (a) and (b) in two regards. First, a periodic optical fil-

CHEN: GENERATING UWB AND MICROWAVE WAVEFORMS USING SILICON PHOTONICS755

Fig. 4 Pulse doublet generated using (a) the MPF from Fig. 3 (a) (after[13]) and (b) the MPF from Fig. 3 (b) (after [14]). (c) A Gaussian-likewaveform suitable for MB-UWB transmission generated using the MPFfrom Fig. 3 (b) (after [15]). The corresponding electrical spectra are alsoshown (all results are courtesy of and adapted from J. Mora).

ter, here based on a Mach-Zehnder delay line interferometer(MZ-DLI), is used for spectral slicing. In this case, the re-sulting sinusoidal and continuous tap distribution producesa single bandpass MPF [17]. Second, a balanced photodiode(BPD) is used for O/E conversion. This allows both positiveand negative portions in the generated electrical temporalwaveform and differential detection removes the DC com-ponent of the signal. To control the weight of the sinusoidaland continuous taps, the spectrum of the broadband sourceis first shaped with an optical filter. By tuning the delay inthe MZ-DLI, the free spectral range (FSR) of the periodicoptical filter can be tuned. For a fixed length of SMF, thiscauses the tap delay to vary, which in turn tunes the pass-band frequency of the MPF response. Figure 5 (a) shows thegeneration of Gaussian-like waveforms with different peri-ods; sample electrical spectra demonstrating tuning appearin Fig. 5 (b). These results were obtained using a broadbandsource with a Gaussian-spectrum and a 3 dB bandwidth of16 nm centered at 1546.9 nm and using 5 km of SMF to setthe tap delay; the delay in the MZ-DLI was tuned between

Fig. 5 (a) Gaussian-like temporal waveforms with different periods gen-erated using the MPF in Fig. 3 (c). (b) Sample electrical spectra (after [16]).(All results are courtesy of and adapted from J. Mora).

2.9 ps and 7.2 ps.We now describe an alternate implementation of a

reconfigurable MPF for generating arbitrary RF wave-forms [18]. Figure 6 (a) illustrates a schematic of the pro-posed approach. As with the systems described previously,it is based on a FIR MPF. Partially degenerated four wavemixing (FWM) in a nonlinear medium is used to increase thenumber of optical carriers/taps [18]–[20]. In particular, atleast N = 2M taps can be obtained starting from M sources.The tap weights are adjusted using a spectral shaper in orderto control the MPF amplitude response and correspondingly,the generated RF waveform. As mentioned previously, ad-justing the tap delay Δτ allows for tuning the central fre-quency of the MPF passband response. The taps are thensplit by a 3 dB coupler and the two copies are delayed rel-ative to each other by an additional amount of Δτ/2 beforebeing detected with a BPD.

Figure 6 (b) depicts the experimental setup where anSNW serves as the nonlinear medium. The SNW is 20 mmin length and has a cross-section of W × H = 500 nm ×220 nm with a top oxide cladding. It is designed to have asmall amount of anomalous dispersion near 1550 nm with adispersion slope ∼0 ps/(nm2·km) for broadband FWM [20].Vertical grating couplers (VGCs) are used for input and out-put coupling and to ensure operation with TE-polarized lightin the SNW. The total fiber-to-fiber coupling loss is ∼22 dBand each VGC introduces ∼10 dB insertion loss (recent de-signs can reduce this loss further to ∼4 dB per coupler [21]).

To demonstrate the principle, we use M = 2 opticalsources (at 1547 nm and 1550 nm). An electric impulsegenerator drives the EOM for O/E conversion (the modu-lated optical pulses have a FWHM duration of ∼100 ps); thecorresponding spectrum of the electric impulses is shown inthe inset of Fig. 6 (b). The modulated optical taps are ampli-fied to an average power of ∼14 dBm before being coupledinto the SNW. After FWM in the SNW, the 4 output taps are

756IEICE TRANS. ELECTRON., VOL.E98–C, NO.8 AUGUST 2015

Fig. 6 (a) Schematic of the proposed RF arbitrary waveform generatorbased on an N-tap FIR MPF. (b) Corresponding experimental setup. Theinset shows the RF spectrum of the electrical pulses. CW: continuous wave,Disp: dispersive medium, TLS: tunable laser source, DFB: distributed feed-back laser, CSA: communications signal analyzer, RF-SA: radio-frequencyspectrum analyzer.

amplified and their amplitudes are controlled using a bench-top spectral shaper (Finisar Waveshaper 1000-S, WS). Theyare amplified again before propagating through ∼5 km ofSMF to provide a tap delay of Δτ = 250 ps. The taps aresplit equally into 2 copies with a 3 dB coupler and their rel-ative delay is set to Δτ/2 = 125 ps using a pair of tunableoptical delay lines (ODLs). The two copies are detected us-ing a 45 GHz BPD.

Figures 7 (a)–(c) show the optical spectrum at the out-put of the EOM (before the SNW), after FWM in theSNW to increase the number of taps, and after the spectralshaper set to provide equal weight taps. The correspond-ing temporal waveform and electrical spectrum are shown inFigs. 7 (d) and (e). The RF spectrum, centered at 3.98 GHz,has a shape that is expected for an MPF comprising uniformtaps and for a waveform with a constant envelope.

Figure 8 illustrates the capability of the approach togenerate different waveforms and to tune the central fre-quency. For example, Fig. 8 shows the waveforms and cor-responding electrical spectra when the spectral shaper con-trols the tap weights to obtain sawtooth and apodized pro-files. For the apodized waveform, there is a clear reduction

Fig. 7 Results for a uniform waveform with 4 taps. Optical spectrum at(a) the output of the EOM (before the SNW), (b) after FWM in the SNW,(c) after the spectral shaper; (d) corresponding temporal waveform, and (e)electrical spectrum. Measurements (dotted, black) and simulations (solid,red).

Fig. 8 Results for a sawtooth waveform with 4 taps: (a) temporal wave-form and (b) RF spectrum. Results for an apodized waveform with 4 taps:(c, e) temporal waveforms and (d, f) RF spectra. Δτ = 250 ps (c, d) andΔτ = 180 ps (e, f). Measurements (dotted, black) and simulations (solid,red).

in the sidelobe level as compared with Fig. 7 (e). By reduc-ing the tap delay to Δτ = 180 ps, we can tune the centralfrequency of the MPF passband, see Fig. 8 (e) [note that theODLs need to be re-adjusted to provide a relative delay ofΔτ/2 = 90 ps between the two copies]. While the temporalwaveform exhibits a ‘skew’ due to the fact that the pulsescorresponding to the taps overlap slightly in time, i.e., theseparation between a positive and negative pulse is 90 pswhereas the duration of each pulse is 100 ps, the RF spec-trum shifts to 5.49 GHz and exhibits a similar shape to thatin Fig. 8 (d). Tuning of the apodized waveforms can be use-ful for MB-UWB communications.

In all of the results shown above, shorter electricalpulses at the input to the system (equivalently with a broaderinput spectrum) will allow for a greater range of waveformsto be synthesized (including at higher frequencies). More-over, increasing the number of taps will provide greater con-trol over the MPF filter response, and hence the generatedwaveforms. The results also correspond to MPFs that havea linear phase response. MPFs can be designed with non-

CHEN: GENERATING UWB AND MICROWAVE WAVEFORMS USING SILICON PHOTONICS757

linear phase responses [22]–[24]; in this case, we can cre-ate chirped waveforms or perform pulse compression. Thisprovides yet another degree of freedom for waveform gen-eration.

2.4 Towards an Integrated Solution

While the MPFs described in Sect. 2.3 involve discrete fiberand/or benchtop components, a number of these buildingblocks or their functionalities have been realized in SiP.First, in-line SNW VOAs with a dynamic range of 30 dBand capable of operating at speeds of up to 1 GHz [25] aswell as SiP space switches integrated with CMOS drivershave been demonstrated [26]. Next, a 512×512 AWG routerwith 25 GHz channel spacing was recently reported [27].O/E and E/O conversion with SiP technologies can be read-ily achieved: a number of high-performance SiP modulatorsexist [28], including those capable of advanced modulationformats [29], as well as PDs and BPDs [30], [31].

Various forms of optical delays in silicon have alsobeen demonstrated. These include delay lines based on pho-tonic crystals, coupled ring resonators, and various Bragg-grating structures such as serial grating arrays, step-chirpedgratings, continuously chirped gratings, and cascaded grat-ings. With grating structures, delays up to several hundredsof ps spanning a few nm or tens of ps spanning broaderwavelength ranges are readily accessible [19], [32]–[34].

In addition to realizing discrete building blocks in SiP,there have been significant efforts at integrating various de-vices to increase processing capability and functionality.For example, AWG routers, modulators, and photodiodeshave been integrated to implement an 8×8 SiP optical switchfor high performance computing and data center applica-tions [35]. The ability to integrate various building blockswill allow for the realization of compact, high performanceMPFs for generating arbitrary RF waveforms for a variety ofapplications. Indeed, there have been recent demonstrationsof integrated MPFs in various material platforms [5], [36]–[39].

3. Generating Chirped Microwave Waveforms Basedon Optical Spectral Shaping and Wavelength-to-Time Mapping

In this section, we describe the generation of chirped mi-crowave waveforms based on optical spectra shaping fol-lowed by wavelength-to-time mapping [4], [40]–[42]. Webegin with a brief review of the relevant theory, followed byan overview of recently demonstrated results based on fiberimplementations. We then discuss progress in developingintegrated spectral shapers in SiP.

3.1 Principle of Operation

A schematic of the principle of operation is shown in Fig. 9.The system comprises a broadband source, e.g., from amode-locked fiber laser, an optical pulse/spectral shaper,

Fig. 9 General system for generating chirped microwave waveformsbased on optical spectral shaping followed by wavelength-to-time mapping.

and a dispersive medium. The spectral shaper is used tomodify the spectrum of the pulsed source, typically in am-plitude only. The shaped spectrum then propagates throughthe dispersive medium where a wavelength-to-time mappingprocess takes place, i.e., the shape of the spectrum is mappedto the time domain. The resulting temporal signal corre-sponds to the microwave waveform which is detected by aPD. Note that the linearity of the system allows for the or-der of spectral shaping and wavelength-to-time mapping tobe interchanged. The key component in the system is thespectral shaper: it must be capable of generating the desiredamplitude spectrum which ultimately corresponds to the de-sired microwave waveform.

Wavelength-to-time mapping is based on real-timeFourier transformation of an input signal in a dispersivemedium [43]. For example, consider a dispersive mediumwhere the relative delay and frequency are related linearlyby t = Φω where Φ is the first-order dispersion coefficient(Φ = d2Φ/dω2 with Φ being the phase of the dispersivemedium). Let a(t) be an input signal with pulse duration Δt0to the dispersive medium. The output signal b(t) is given by[43]:

b(t) ∝ A(ω)ω=t/Φ (5)

where A(ω) is the Fourier transform of a(t) whenΔt2

0

2Φ� π

(the input signal must be confined within a time window thatsatisfies this condition). The main point of Eq. (5) is thatthe envelope of the output signal b(t) in time correspondsto the spectrum of the input signal a(t). The linear relation-ship t = Φω sets a linear wavelength-to-time mapping. Itis also possible to consider a nonlinear wavelength-to-timemapping, e.g., with a higher-order dispersive medium. Inparticular, if the relative delay can be represented as

t = Φω +12

...Φω

2 (6)

where...Φ (= d3Φ/dω3) is the second-order dispersion coeffi-

cient, we obtain the following nonlinear wavelength-to-timemapping [44]:

ω =−Φ ±

√Φ2 + 2

...Φt

...Φ

(7)

To generate a uniform (sinusoidal-like) microwavewaveform, we require a spectral shaper with a sinu-soidal/periodic filter response, i.e., with uniform (constant)FSR, followed by a linear wavelength-to-time mapping. To

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generate a chirped microwave waveform, there are two ap-proaches: the first uses a spectral shaper with a periodicresponse followed by a nonlinear wavelength-to-time map-ping [44], [45] while the second uses a spectral shaper withan aperiodic response followed by a linear wavelength-to-time mapping [46], [47]. Generally speaking, by control-ling the FSR (or variation in FSR), as well as the first-orderand/or second-order dispersion coefficients, we can tailorthe central frequency and chirp rate of the generated mi-crowave waveforms.

3.2 Review of Results Using Fiber-Based Implementa-tions

It is relatively simple to realize (all-fiber) sinusoidal/periodicoptical filters. For example, we can use a fiber-based MZ-DLI or incorporate a short length of polarization maintain-ing fiber (PMF) in a Sagnac loop. In these cases, the FSRof the filters are determined by the delay in the MZ-DLI orlength of PMF in the Sagnac loop.

To obtain a nonlinear wavelength-to-time mapping, anonlinearly chirped FBG can be used as the dispersivemedium. A number of well-established approaches exist toproduce FBGs with tailored dispersive properties (in largepart due to the development of FBG-based dispersion com-pensating modules for fiber optic communications): a non-linear chirped phase mask can be employed or a linear strainor temperature gradient can be applied to a linearly chirpedFBG. The latter approach was exploited in [44] to realizea tunable nonlinearly chirped FBG spanning a bandwidthof ∼12 nm (e.g., with first- and second-order dispersion co-efficients of Φ = 295.1 ps2 and

...Φ = 20.9 ps3). By us-

ing a spectral shaper based on a length of PMF in a Sagnacloop (to generate a uniform comb of slices from broadbandpulses with a 3 dB bandwidth of 8 nm), chirped microwavewaveforms 243 ps in duration with an instantaneous fre-quency varying from 25 GHz to 43 GHz, corresponding to achirp rate of 0.074 GHz/ps, were obtained [44] (see Fig. 10).While the overall system is simple to implement, the useof FBGs to implement a nonlinear wavelength-to-time map-ping causes several issues. First, long gratings, e.g., severalcm’s to 1 m, are required to have both broad bandwidth andlarge dispersion. Moreover, the group delay ripple needs tobe minimized to avoid degradation in the chirped microwave

Fig. 10 Pulse profile and instantaneous frequency vs. time for chirpedmicrowave waveforms generated using a periodic spectral filter and a non-linearly chirped FBG (adapted from and courtesy of J. Yao).

waveforms, especially if they are to be compressed subse-quently.

The use of a spectral shaper with an aperiodic responsefollowed by a linear wavelength-to-time mapping, e.g., ina length of SMF or dispersion compensating fiber, avoidsthe problems associated with nonlinearly chirped FBGs (al-beit at the expense of compactness). Although more com-plex in design, aperiodic optical filters can nonetheless beimplemented readily using FBGs or ring resonators in SiP.A simple all-fiber distributed Fabry-Perot (FP) filter can beformed by superimposing two spatially offset and linearlychirped FBGs as shown in Fig. 11 [48]. If the FBGs havedifferent chirp rates, the FSR becomes wavelength depen-dent [46]:

FS R(λ) =λ2

0

2neff

(L + C1−C2

C1C2(λ − λ0)

) (8)

where neff is the effective index of the fiber, C1 and C2 arethe chirp rates, L is the spatial offset between the gratings,and λ0 is the starting wavelength. To simplify fabrication, itis possible to use two identical linearly chirped FBGs withopposite orientation (C1 = −C2).

To demonstrate the principle, two 1 cm long linearlychirped FBGs were employed to realize a spectral shaperspanning a wavelength range of ∼1.5 nm with variableFSR. The spectral shaper was used to shape the spectrumof broadband pulses from a mode-locked fiber laser (3 dBbandwidth of 8 nm); with 58 km of SMF as the dispersivemedium, chirped microwave waveforms 1,250 ps in dura-tion with a central frequency of 15 GHz and a chirp rate of0.022 GHz/ps were synthesized [46]. The results are sum-marized in Fig. 12.

Once the grating parameters are set, it is not possibleto vary the FSR of the spectral shaper and as such, it isnot possible to tune the chirped microwave waveform. Toovercome this limitation, a spectral shaper based on incor-porating a linearly chirped FBG within a Sagnac loop wasproposed [47], see Fig. 13.

The transfer function (response) of a Sagnac loop in-corporating an FBG can be written as [49]:

T =|Eout |2|Ein|2 = Rg(λ) cos

(2πneff

λΔL +

φ(λ) − φ′(λ)2

)(9)

Fig. 11 Schematic of an all-fiber distributed FP resonator with varyingFSR based on two superimposed and spatially offset linearly chirped FBGs.

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Fig. 12 (a) Spectral response of all-fiber distributed FP resonator withincreasing FSR. (b) Pulse profile and instantaneous frequency of the gener-ated microwave waveform with negative chirp (courtesy of J. Yao).

Fig. 13 An all-fiber spectral shaper based on a Sagnac loop incorporatinga linearly chirped FBG. PC: polarization controller.

where Rg(λ) is the reflectivity of the grating, φ(λ) and φ′(λ)are the phase delays in reflection for light entering clock-wise and counter-clockwise, respectively, and ΔL = L1 − L2

is the path mismatch in the loop. For a uniform FBG,φ(λ) = φ′(λ) and for equal path lengths, ΔL = 0 such thatthe transfer function corresponds to the FBG reflection re-sponse: T = Rg(λ). For a uniform grating with ΔL � 0,the grating response is modulated sinusoidally, yielding aperiodic or comb-like filter. When the grating is nonuni-form, φ(λ) � φ′(λ). For a linearly chirped FBG with a linearchirp rate C (nm/cm), we can re-write the transfer functionin Eq. (9) as:

T =12

Rg(λ)

{1 + cos

[4πneff

λ2cλ

(ΔL +

Δλ

C

)]}(10)

where Δλ represents the wavelength detuning from the cen-ter wavelength λc. For ΔL = 0, the spectral response issymmetric about λc and the FSR decreases with increasedwavelength detuning (from λc). For ΔL � 0 (the value ofmismatch must be sufficiently large), the spectral responseis no longer symmetric about λc and we can control the vari-ation in FSR, i.e., with a monotonic increase or decrease inFSR over the grating bandwidth, by tuning ΔL (the sign ofΔL determines whether there is a monotonic increase or de-

Fig. 14 Generating chirped microwave waveforms using a spectralshaper based on a Sagnac loop incorporating a linearly chirped FBG: (a,d) response of spectral shaper with decreasing/increasing FSR, (b, e) corre-sponding waveforms (without averaging) with positive/negative chirp, and(c, f) instantaneous frequency vs. time (courtesy of J. Yao).

crease in FSR).To verify the principle, a Sagnac loop incorporating a

tunable delay to control the value ΔL and a 1 cm long lin-early chirped FBG with a chirp rate of 2 nm/cm was con-structed. The spectral shaper was used to filter the spectrumof a broadband pulsed source (3 dB bandwidth of 8 nm);in particular, the path mismatch ΔL was tuned to createa monotonic increase or decrease in FSR (correspondingto a negative or positive chirp rate in the generated wave-form). Chirped microwave waveforms 1,150 ps in dura-tion with a central frequency and chirp rate of 20.2 GHzand 0.02 GHz/ps or 24.5 GHz and −0.022 GHz/ps weregenerated after linear wavelength-to-mapping in 30.8 km ofSMF [47]. The results are shown in Fig. 14. The instanta-neous frequency vs. time shows that the chirp is quite linear.These chirped waveforms can be compressed by a factor of∼55 and the compressed pulses exhibit relatively low side-lobes (see [47] for further details).

3.3 Towards Integration in SiP

The results shown in Sect. 3.2 demonstrate the capabilitiesof optical spectral shaping followed by wavelength-to-timemapping for generating chirped microwave waveforms. Wenow discuss recent progress on developing integrated spec-tral shapers.

We have fabricated Sagnac loops incorporating uni-form and linearly chirped Bragg gratings in SiP, see Fig. 15.The devices were fabricated using electron beam lithogra-

760IEICE TRANS. ELECTRON., VOL.E98–C, NO.8 AUGUST 2015

Fig. 15 Schematic of optical spectral shaper based on a Sagnac loop in-corporating a uniform or chirped Bragg grating integrated in SiP. The wave-guide cross-section and parameters for the sidewall Bragg gratings are alsoillustrated.

phy and a full etch. The Si waveguides have a thickness of220 nm on top of a 3 μm buried oxide (BOX) layer on a Sisubstrate. The Bragg gratings are based on sidewall corru-gations [50] with a depth ΔW = W1 − W2. For the uniformBragg grating, we use a period Λ = 320 nm, a waveguidewidth W1 = 500 nm, a corrugation depth ΔW = 10 nm, and3,000 periods. The chirped Bragg grating is based on taper-ing the waveguide width [32]. We also use Λ = 320 nm,ΔW = 10 nm, and 10,000 periods; the waveguide widthW1 varies linearly from 500 nm to 510 nm from one end ofthe grating to the other (corresponding to a grating chirp ofC ∼ 0.26 nm/mm). A 10 μm long taper is used to bring thewaveguide width from 510 nm at one end of the grating backto 500 nm. The multimode interference (MMI) coupler is6 μm wide and 127 μm long and the input or output waveg-uides (each 500 nm in width) are separated by 3 μm. Allwaveguides and gratings are covered by an index-matched2 μm top oxide cladding layer. VGCs, which couple lightinto and out of the chip, also ensure TE mode operation.

Figure 16 (a) shows the measured response in which auniform Bragg grating is located symmetrically within theSagnac loop. The passband has a bandwidth of 3.2 nm andexhibits an out-of-band rejection (OBRR) of ∼15 dB. Theresponse is shown normalized to that of the VGCs, whichare obtained via separate measurements on a test structurecomprising the VGCs and a short length of waveguide only;the fiber-to-fiber insertion loss is 25 dB so that the insertionloss of the passband is estimated to be 2 dB. Apodization canbe used to reduce the sidelobes in the grating response [51].Figure 16 (b) shows the measured response when a chirpedBragg grating is located nearly in the center of the Sagnacloop (ΔL = 100 μm only). The response is nearly symmetricabout the center wavelength with an FSR that decreases withincreasing wavelength detuning from λc (the response willbecome more asymmetric, i.e., with a monotonic increaseor decrease in FSR over the entire bandwidth, if the pathmismatch is made much larger). Note that the visibility ofthe fringes is quite high (typically ∼20 dB).

Fig. 16 Measured response of Sagnac loop incorporating a uniformBragg grating (a) and chirped Bragg grating (b). The red arrows in (b)highlight the decrease in FSR with increasing detuning from the centerwavelength.

We then used the device to spectrally shape the outputpulses from a passively mode-locked fiber laser. The pulseshave a Gaussian-like spectrum with a 3 dB bandwidth of1.5 nm which we tune to different locations to capture in-creasing or decreasing FSR. For example, using 24 km ofSMF as the dispersive medium, we generated a chirped mi-crowave waveform with a total duration of ∼1,000 ps andchirp rates of ∼ ± 0.02 GHz/ps. The results are summarizedin Fig. 17.

We have also implemented a distributed FP filter in SiPbased on two spatially offset Bragg gratings with oppositechirp, see. Figure 18. As before, the Si waveguides have athickness of 220 nm on top of a 3 μm BOX layer on a Sisubstrate and are covered by an index-matched 2 μm top ox-ide cladding. Each chirped Bragg grating has Λ = 315 nm,ΔW = 10 nm, and 500 periods; the waveguide width Wvaries linearly from 500 nm to 520 nm from one end ofthe grating to the other (corresponding to a grating chirp of|C1| = |C2| = 12.2 nm/mm). The two gratings are separatedby a length L = 457.5 μm. We use the reflection response,which is extracted via a Y-splitter. Again, VGCs are used tocouple light into and out of the chip.

Figure 19 shows the measured response of the dis-tributed FP filter in SiP; the FSR clearly increases with in-creasing wavelength. We then implemented the filter inthe waveform generation system. Pulses from a passivelymode-locked fiber laser are filtered so that we operate overa wavelength range of ∼16 nm of the distributed FP filterresponse. We used 5 km of SMF as the dispersive mediumfor wavelength-to-time mapping. This results in a chirpedmicrowave waveform with a total duration of ∼1,100 ps anda chirp rate of 0.012 GHz/ps, see Fig. 19.

Integrated spectral shapers based on ring resonatorshave also been proposed and realized. For example, Fig. 20

CHEN: GENERATING UWB AND MICROWAVE WAVEFORMS USING SILICON PHOTONICS761

Fig. 17 Generating chirped microwave waveforms with an integratedspectral shaper based on a Sagnac loop incorporating a chirped Bragg grat-ing. Response of the spectral shaper showing input optical pulses tunedto capture (a) increasing and (b) decreasing FSR. Corresponding tempo-ral waveforms after linear wavelength-to-time mapping and instantaneousfrequency vs. time.

Fig. 18 Schematic of distributed FP filter in SiP.

Fig. 19 Spectral response (in reflection) of distributed FP filter in SiP.Corresponding temporal waveform after wavelength-to-time mapping andinstantaneous frequency vs. time.

Fig. 20 Schematic of tunable integrated spectral shaper in SiP based oncascaded microring resonators with additional MZ structures (courtesy ofM. Qi).

Fig. 21 Schematic of integrated spectral shaper in SiP based on cascadedmicroring resonators embedded within an MZI (courtesy of J. Yao).

illustrates a spectral shaper based on 8 cascaded micror-ing resonators [52]. The spectral separation between the re-sponse of consecutive rings is ∼1.3 nm and each ring hasan FSR of ∼16 nm. By tuning the resonant wavelengthsand coupling strengths of each microring resonator (usingmicroheaters placed above each ring for independent con-trol of the resonant wavelength and incorporating an MZstructure with microheaters at the through port of each ringto control the depth of the resonance), full reconfigurationof the spectral shaper is possible (at the through port, thewavelengths and amplitudes of the ‘slices’ from each ringcan be controlled). Using this integrated device to shapethe broadband pulses from a passively mode-locked laser,chirped microwave waveforms centered about 8 GHz with achirp of 0.008 GHz/ps were synthesized [52].

Recently, a different version of an integrated spectralshaper using cascaded microring resonators was reported in[53]. In this case, the microring resonators are embeddedin an MZI. Moreover, the microring radii differ substan-tially in order to provide a larger variation in the spectralseparation between rings (see Fig. 21). The device operatesin reflection mode so that the input and output can share acommon VGC and the MZI configuration increases stabil-ity. As a proof-of-principle demonstration, devices based on4 or 5 rings were fabricated and tested. Chirped microwavewaveforms with bandwidths of 8.5 GHz and 15.5 GHzwith chirp rates of 0.012 GHz/ps and 0.017s GHz/ps wereachieved after linear wavelength-to-time mapping in a dis-persive medium with −948 ps/nm dispersion. These chirprates are ten times greater than those obtained in [52]. Whilethis prototype device was static, it can be readily adapted toallow for reconfigurable operation using thermal tuning asin [52]. Note that in both approaches, the number of cyclesin the waveforms is constrained to the number of cascadedmicrorings. In many practical applications, a larger numberof cycles is necessary which in turn, requires the addition of

762IEICE TRANS. ELECTRON., VOL.E98–C, NO.8 AUGUST 2015

microrings.In Sect. 2, we described some recent developments for

implementing tunable delays in SiP; these can be readilycombined with the spectral shapers described here to realizea fully integrated chirped microwave waveform generationsystem. However, the main challenge resides in obtainingthe necessary dispersion and/or bandwidth for appropriatewavelength-to-time mapping.

4. Summary and Perspectives

We have described the generation of UWB and RF wave-forms based on microwave photonic filtering as well aschirped microwave waveforms using optical spectral shap-ing followed by wavelength-to-time mapping. It should benoted that many of the MPF structures described in the re-view articles [9]–[12] can be employed for waveform gen-eration; we have presented only results in which the filterswere used explicitly for such a purpose. We have also de-scribed briefly the implementation in SiP of a number ofcritical building to realize MPFs or spectral shapers. Whileseveral challenges still remain, e.g., the development of de-lay lines with larger bandwidth-delay products or filters thatcan process a larger number of taps, integrated microwavephotonics is still an emerging field. SiP holds significantpromise to realize a number of component technologies andintegrated systems for demonstrating enhanced capability orfunctionality which, in turn, will pave the way for new ap-plications that will make the technology further commer-cially viable. Combined with recent advances in graphenemicrowave photonics [54], an exciting future undoubtedlylies ahead.

Acknowledgments

This research was supported in part by the Natural Sciencesand Engineering Research Council (Canada), the CanadianMicroelectronics Corporation, and the Fonds de recherche-Nature et technologies (Quebec). I thank Rhys Adams(CEGEP Vanier College); Dr. Reza Ashrafi, Junjia Wang,Ming Ma, Mohammad Rezagholipour Dizaji, and Prof.Martin Rochette (McGill University); and Mina Spasojevicand Jia Li (Ciena) for their contributions to this work.The SiP devices presented in this paper were fabricated byRichard Bojko at the University of Washington Nanofabri-cation Facility, a member of the NSF National Nanotechnol-ogy Infrastructure Network.

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Lawrence R. Chen received the BEng inElectrical Engineering and Mathematics fromMcGill University in 1995 and the MASc andPhD degrees in Electrical and Computer Engi-neering from the University of Toronto in 1997and 2000, respectively. He returned to McGillUniversity in 2000, where he is a Professor inthe Department of Electrical and Computer En-gineering. His research interests are in opticaland microwave signal processing, silicon pho-tonics, and teaching pedagogy. He is currently

Editor-in-Chief of the IEEE Photonics Society Newsletter and an Editor ofOptics Communications. He is a Fellow of the Optical Society of America.