Simultaneous Multi-Channel Microwave Photonic Signal Processing

Review Simultaneous Multi-Channel Microwave Photonic Signal Processing

Lawrence R. Chen 1,* ID , Parisa Moslemi 1, Ming Ma 1 and Rhys Adams 2

1 Department of Electrical and Computer Engineering, McGill University, Montreal, QC H3A 0E9, Canada; [email protected] (P.M.); [email protected] (M.M.) 2 Department of Physics, CEGEP Vanier College, St. Laurent, QC H4L 3X9, Canada; [email protected] * Correspondence: [email protected]; Tel.: +1-514-398-1879

Received: 25 October 2017; Accepted: 15 November 2017; Published: 17 November 2017

Abstract: Microwave photonic (MWP) systems exploit the advantages of photonics, especially with regards to ultrabroad bandwidth and adaptability, features that are signiﬁcantly more challenging to obtain in the electronic domain. Thus, MWP systems can be used to realize a number of microwave signal processing functions including, amongst others, waveform generation and radio-frequency spectrum analysis (RFSA). In this paper, we review recent results on ﬁber and integrated approaches for simultaneous generation of multiple chirped microwave waveforms as well as multi-channel RFSA of ultrahigh repetition optical rate pulse trains.

Keywords: microwave photonics; microwave photonic signal processing; photonic generation of chirped microwave signals; ﬁber Bragg gratings; RF spectrum measurement; silicon photonics

1. Introduction Microwave photonics (MWP) unites the disciplines of microwave engineering with optoelectronics, and focuses on the use of photonic techniques and technologies to generate, process, and analyze/characterize microwave signals or to obtain radio-frequency (RF) characteristics of optical signals [1–3]. Photonics provides ultrabroad bandwidth and supports parallelization and adaptiveness (e.g., to achieve reconfiguration and tuning); thus, MWP enables a number of important functions in microwave systems that are either too complex or not possible to implement with conventional electronic approaches. Over the years, applications of MWP have evolved to include, amongst others, communications (e.g., to support the interface of wireless and optical communications, as well as for emerging 5G communications and the Internet of Things), sensing (e.g., to enhance resolution and increase the interrogation speed of conventional fiber optic sensor systems), and instrumentation (e.g., wideband signal characterization). To support these various applications, numerous functions are required, such as photonic generation of arbitrary waveforms, e.g., microwave, millimeter wave, and THz signals [4,5]; photonic processing of microwave signals, e.g., filtering, time delay, and phase shifting [6–8]; and photonic characterization of microwave signals, e.g., spectrum analysis and instantaneous frequency measurement (IFM) [9,10]. Chirped microwave waveforms have been used widely in various applications, especially radar systems [11]. Photonic generation of chirped microwave waveforms offers the possibility to obtain central frequencies of tens to hundreds of GHz as well as significant RF chirp rates, thereby supporting tens of GHz of bandwidth [4,5]. Photonic approaches also provide increased flexibility, especially in terms of tuning the central frequency and/or RF chirp rate of the waveforms. Such features and capabilities are not generally possible or have limitations with electronics. A variety of photonic approaches have been explored for RF arbitrary waveform generation and, in particular,

Photonics 2017, 4, 44; doi:10.3390/photonics4040044 www.mdpi.com/journal/photonics Photonics 2017, 4, 44 2 of 20 chirped microwave waveforms. Most implementations demonstrated to date are capable of only generating a single waveform at a time, i.e., of a specific central frequency or RF chirp rate. On the other hand, the ability to obtain simultaneously multiple chirped microwave waveforms, each having its own characteristics, may enhance flexibility and provide new functionality in instrumentation and imaging applications. In this paper, we describe two fiber-based implementations for simultaneous generation of multiple (at least two) chirped microwave waveforms. The first approach uses superimposed linearly chirped Bragg gratings (BGs) in a Sagnac interferometer while the second incorporates multiple linearly chirped BGs in a multi-channel arrayed waveguide Sagnac interferometer (AWGSI). We show how these structures can be used to synthesize multiple chirped microwave waveforms with the same central frequency and different RF chirp rates, as well as to obtain independent control over the central frequency and RF chirp rates. Electrical spectrum analysis of ultrabroadband photonic RF arbitrary waveforms and ultrahigh repetition rate optical pulse trains is necessary for monitoring the quality of the waveforms. It is performed typically using a photodiode for optical-to-electrical (O/E) conversion and an electrical spectrum analyzer (ESA). However, this approach is limited by the bandwidth of available electronics and, hence, cannot be used to characterize photonic waveforms that have a bandwidth in excess of 100 GHz. While a trade-off between measurement bandwidth and resolution has to be made, photonic implementation of radio-frequency spectrum analysis (RFSA) based on ultrafast nonlinear optics (e.g., Kerr nonlinearity) allows for characterizing signals with a bandwidth well beyond 100 GHz. Photonic RFSA was originally proposed and demonstrated using optical fiber as the nonlinear medium [12]; it has since been reported using integrated technologies in chalcogenide, silicon-on-insulator, and silica material platforms [13–17]. In all demonstrations, however, only a single waveform can be characterized at a time. Simultaneous multi-channel (or multi-signal) RFSA with a single integrated device may be more practical compared to using (and duplicating) multiple nonlinear waveguides for parallel single channel operation. Integrated waveguides can be engineered to support several propagating spatial modes, which we can exploit to perform multi-channel nonlinear optical signal processing, including RFSA. This creates a new degree of freedom for scaling the number of channels that can be characterized simultaneously. In this paper, we describe how to harness nonlinear optics in a mode selective manner using an integrated silicon photonic (SiP) device, ultimately leading to the realization of on-chip multi-channel RFSA.

2. Photonic Generation of Chirped Microwave Waveforms

2.1. General Considerations There are many different techniques that use photonics for arbitrary microwave waveform generation. A relatively straightforward and powerful approach is to perform optical pulse shaping to synthesize the desired optical (temporal) waveform followed by O/E conversion (see Figure1a). The ability to tailor the optical pulses translates into the ability to realize reconfigurable and tunable microwave waveform generation. A number of optical pulse shaping techniques exist, including classical Fourier transform pulse shaping, direct space-to-time pulse shaping, temporal pulse shaping, and optical spectral shaping followed by wavelength-to-time mapping (WTM) [4,18]. In terms of ease of implementation, the latter approach is very attractive: a spectral shaper is used to tailor the amplitude spectrum from a pulsed broadband optical source and the shaped spectrum then propagates through a dispersive medium where the frequency content is distributed in the time domain, i.e., WTM, see Figure1b [4,19]. To generate a uniform microwave waveform, i.e., with constant frequency or that is chirp-free, we require a spectral shaper that has a periodic filter response, i.e., a constant free spectral range (FSR), and a linear WTM. On the other hand, to obtain a chirped microwave waveform, we can follow one of two approaches: (1) use a spectral shaper with a constant FSR and a nonlinear WTM [20,21] or (2) use a spectral shaper with a variable FSR followed by a linear WTM. While both approaches have been Photonics 2017, 4, 44 3 of 20 demonstrated, we consider the second, as it avoids the need for specially designed dispersive media with nonlinearPhotonics delay 2017, 4,characteristics 44 or the limitations of such media, e.g., group delay ripple3 of 20 associated with nonlinearly chirped BGs. Moreover, a simple length of single-mode fiber (SMF) or dispersion group delay ripple associated with nonlinearly chirped BGs. Moreover, a simple length of compensatingsingle-mode fiber (DCF)fiber (SMF) can or implement dispersion compensati linear WTMng fiber over (DCF) a broadcan implement optical linear bandwidth. WTM over It a should be noted thatbroad the principle optical bandwidth. component It should in the be systems noted that for generatingthe principle chirpedcomponent microwave in the systems waveforms for is the spectral shaper:generating it must chirped allow microwave for synthesizing waveforms is thethe spec desiredtral shaper: amplitude it must spectrumallow for synthesizing from the inputthe source, as this willdesired ultimately amplitude correspond spectrum from to the the desiredinput source, waveform as this will after ultimately WTM. correspond to the desired waveform after WTM.

Photonics 2017, 4, 44 3 of 20 output t t waveform group delay ripple opticalassociated with nonlinearly chirped optical-to-BGs. Moreover, a simple length of pulse shaping electrical single-modeinput pulse fiber (SMF) or dispersionshaped compensati optical ng fiber (DCF)conversion can implement linear WTM tover a broad optical bandwidth. It shouldwaveform be noted that the principle component in the systems for

generating chirped microwaveFT pulse shaping waveforms is the spectral shaper: it must allow for synthesizing the desired amplitude spectrumDST pulse shaping from the input source, as this will ultimately correspond to the desired waveform after WTM.temporal pulse shaping optical spectral shaping & wavelength-to-time-mapping (a) output input optical filter amplitude shaped optical t t optical-to- waveform spectrum opticalresponse spectrum pulse shaping electrical input pulse shaped optical conversion t waveform λ λ λ output temporal waveform FT pulse shaping pulsed spectral dispersive DST pulse shaping photodiode source shaper medium temporal pulse shaping t optical spectral shaping & wavelength-to-time-mapping optical domain electrical(a) domain input optical filter amplitude shaped(b optical) spectrum response spectrum Figure 1. Principle of (a) photonic generation of arbitrary microwave waveforms based on optical Figure 1. Principlepulse shaping of and (a) optical-to-electrical photonicλ generationλ (O/E) conversion of arbitraryλ and microwave(b) generationoutput waveformsof chirpedtemporal microwave based on optical waveform pulse shapingwaveforms and optical-to-electricalbased on optical spectral (O/E)shaping conversionand wavelength-to-time and (b) mapping generation (WTM). of chirped microwave pulsed spectral dispersive photodiode source shaper medium waveforms based on optical spectral shaping and wavelength-to-time mappingt (WTM). 2.2. Photonic Generation of Chirped Microwave Waveforms Using Superimposed LCFBGs optical domain electrical domain 2.2. Photonic GenerationSpectral shapers of Chirped in both Microwave fiber and integrated Waveforms(b) forms Using that provide Superimposed an aperiodic LCFBGs response (i.e., variableFigure FSR) 1.have Principle been of considered,(a) photonic generationincluding of a arbitrary serial arraymicrowave of BGs waveforms (sometimes based onreferred optical to as a Spectralspatially shaperspulse discrete shaping in chirped and both optical-to-electrical BG fiber or a andstep-chirped (O/E) integrated conversion BG) [22,23], formsand ( ba) Fabry–Pérotgeneration that provide of chirpedcavity microwave anwith aperiodic distributed response (i.e., variableresonances FSR)waveforms based have basedon been spatially on optical considered, separate spectral shapinor overlapping includingg and wavelength-to-time (either a serial fully array mappingor partially) of (WTM). BGs linearly (sometimes chirped BGs referred to [24,25], a Michelson interferometer incorporating linearly chirped BGs in each arm [26,27], or a as a spatiallySagnac2.2. discrete Photonic interferometer chirpedGeneration incorporating BGof Chirped or a Microwave step-chirped a single Waveforms linear BG)ly chirped Using [22 ,Superimposed23 BG], [28,29]. a Fabry–P LCFBGsThe Sagnacérot cavity configuration, with distributed resonancesillustrated basedSpectral onin spatiallyFigureshapers 2a,in both separateprovides fiber and orthe integrated overlappingsame functionality forms that (either provide as fullythe an Michelsonaperiodic or partially) response interferometer linearly (i.e., chirped BGs [24,25incorporating],variable a Michelson FSR) two have identical interferometer been considered, and oppositely including incorporating chirpe a sedrial BGs. array linearlyUnlike of BGs the chirped(sometimes serial array BGs referred or inFabry-Pérot to each as a arm [26,27], or a Sagnaccavity interferometerspatially with discretedistributed incorporatingchirped resonances, BG or a thestep-chirped a singlespectral linearly reBGsponse) [22,23], chirpedof thea Fabry–Pérot Sagnac BG [interferometer28 cavity,29]. Thewith Sagnacdistributedcan be tuned configuration, readilyresonances by adjusting based on the spatially path mismatchseparate or inoverlapping the loop. (eitherMoreover, fully orthe partially) configuration linearly ischirped simple, BGs as it illustratedrequires in[24,25], Figure only a2 Michelsona, a single provides grating interferomet the and same iser robust incorporating functionality to environmental linearly as thechirped perturbations. Michelson BGs in eachThe interferometer spectralarm [26,27], response or incorporatinga of two identicaltheSagnac Sagnac and oppositely interferometer interferometer chirped incorporating incorporating BGs. a Unlikesingle a linearly linear the chirpedly serial chirped BG array BG is given[28,29]. or Fabry-P by The [4,30]: Sagnacé rot configuration, cavity with distributed resonances, theillustrated spectral in Figure response 2a, provides of the Sagnac the same interferometer functionality as canthe beMichelson tuned readilyinterferometer by adjusting the incorporating two identical and oppositelylinearly chirpe chirpedd BGs. BG Unlike the serial array or Fabry-Pérot path mismatchcavity in with the distributed loop. Moreover, resonances, the the configurationspectral response of is the simple, Sagnac asinterferometer it requires can only be tuned a single grating and is robustreadily to environmental by adjusting the path perturbations. mismatch in the The loop. spectral Moreover, response the configuration of the is Sagnacsimple, as interferometer it incorporatingrequires a linearly only a chirpedsingle grating BG and is givenis robust by to en [4vironmental,30]: perturbations. The spectral response of the Sagnac interferometer incorporating a linearly chirped BG is given by [4,30]: L1 Sagnac loop L2 linearly chirped BG 3 dB coupler

L1 inputSagnac loop output L2 (a) 3 dB coupler

input output (a)

Figure 2. Cont. Photonics 2017, 4, 44 4 of 20

Photonics 2017, 4, 44 4 of 20

(b)

(c)

Figure 2. (a) Spectral shaper based on a Sagnac interferometer incorporating a single linearly chirped Figure 2. (a) Spectral shaper based on a Sagnac interferometer incorporating a single linearly chirped Bragg grating (BG). Schematic of the system generating two (or multiple) chirped microwave pulses Bragg grating (BG). Schematic of the system generating two (or multiple) chirped microwave pulses simultaneously with (b) multiple Sagnac interferometers each containing a linearly chirped BG and simultaneously with (b) multiple Sagnac interferometers each containing a linearly chirped BG and (c) a single Sagnac interferometer containing superimposed linearly chirped BGs. TLCBG(i) denotes the (c) a singlespectral Sagnac response interferometer of the i-th Sagnac containing interferometer. superimposed linearly chirped BGs. TLCBG(i) denotes the spectral response of the i-th Sagnac interferometer. π 1  4 neff  λ − λ  T()λ = R ()λ 1+ cos λΔL + c  g   2   (1) 1 2 4πλne f f Cλ − λ ( ) = ( ) +  c  + LCBG c T λ Rg λ 1 cos 2 λ ∆L , , (1) 2 λc CLCBG where Rg(λ) is the reflectivity of the grating, neff is the effective index of the waveguide, CLCBG is the where Rg(λ) is the reflectivity of the grating, neff is the effective index of the waveguide, CLCBG is the linear chirp of the grating (in nm/mm or nm/cm), ∆L = L1 − L2 is the path mismatch between the two linear chirp of the grating (in nm/mm or nm/cm), ∆L = L1 − L2 is the path mismatch between the arms in the Sagnac interferometer, and λc is the center wavelength. The spectral response has a two armswavelength in the dependent Sagnac interferometer, FSR defined by and λc is the center wavelength. The spectral response has a wavelength dependent FSR defined by λ2 λ2 FSR()λ = 0 = 0 2n 2 L()λ  ()λ −2λ  λeff0 Δ + λ0 0 (2) FSR(λ) = =2neff  L  , (2)  C (λ−λ ) 2ne f f L(λ) 2n ∆LLCBG+  , 0 e f f CLCBG where L()λ denotes the wavelength dependent, equivalent cavity length. After linear WTM in a where L(λ) denotes the wavelength dependent, equivalent cavity length. After linear WTM in a dispersive medium with a first-order dispersion coefficient.. Φ λ (in units of ps/nm), the dispersiveinstantaneous medium frequency with a first-order of the microwav dispersione waveform coefficient can beΦ approximatedλ (in units of by ps/nm), the instantaneous frequency of the microwave waveform can be approximated by  1  t 1  ΔL  f ()t ∝ 2n  × −  +   RF eff C  λ2Φ 2 λ Φ  λ2Φ (3) 1 LCBG  0 t λ 0 1λ  0 λ ∆ L fRF(t) ∝ 2ne f f  ×  − ..  + ,.. , (3) C .. 2 2 LCBG 2 λ0Φ λ Φ and the corresponding RF chirp rate is λ0Φλ λ 0 λ and the corresponding RF chirp rate is df ()t 2neff 1 RF = dt C λ2Φ 2 (4) LCBG 0 λ . d f (t) 2ne f f 1 RF = . (4) A single linearly chirped BG in adt Sagnac interferometerC .. 2 provides a single aperiodic spectral LCBG λ2Φ response (within the grating bandwidth), which can 0be λused to generate a single chirped Amicrowave single linearly waveform. chirped In order BG to in generate a Sagnac multiple interferometer chirped microwave provides waveforms a single simultaneously, aperiodic spectral we require multiple spectral shapers, e.g., multiple or parallel Sagnac interferometers, each response (within the grating bandwidth), which can be used to generate a single chirped microwave incorporating their own linearly chirped BG as illustrated in Figure 2b. As shown in Figure 2c, we waveform. In order to generate multiple chirped microwave waveforms simultaneously, we require can replace the multiple Sagnac interferometers and multiple linearly chirped BGs by a single multipleSagnac spectral interferometer shapers, incorporating e.g., multiple superimpos or paralleled linearly Sagnac chirped interferometers, BGs to achieve each incorporatingthe same their own linearly chirped BG as illustrated in Figure2b. As shown in Figure2c, we can replace the multiple Sagnac interferometers and multiple linearly chirped BGs by a single Sagnac interferometer incorporating superimposed linearly chirped BGs to achieve the same functionality [31]. Photonics 2017, 4, 44 5 of 20

The superimposedPhotonics 2017, 4, 44 gratings operate over different spectral bands and hence, operate independently.5 of 20 As such, the structure can be considered equivalent to multiple Sagnac interferometers operating functionality [31]. The superimposed gratings operate over different spectral bands and hence, in parallel whereby each one generates a single chirped microwave waveform. A drawback of this operate independently. As such, the structure can be considered equivalent to multiple Sagnac configuration, though, is that the superimposed gratings all have the same path mismatch. interferometers operating in parallel whereby each one generates a single chirped microwave Equationswaveform. A (1 drawback)–(4) are alsoof this valid configuration, for the case though, of superimposed is that the superimposed gratings. gratings The spectral all have response the T(λ)sameeffectively path mismatch. comprises multiple spectral bands, each associated with the response of one of the gratings inEquations the superimposed (1)–(4) are also structure. valid for Moreover, the case theof superimposed characteristics gratings. of each The spectral spectral band, response and hence the propertiesT()λ effectively of the comprises chirped multiple microwave spectral waveform bands, ea thatch associated can be generated, with the response are determined of one of the by the correspondinggratings in gratingthe superimposed in the superimposed structure. Moreover structure., the As characteristics shown by Equations of each spectral (3) and band, (4), for and a fixed WTM,hence the centralthe properties frequency of the of chirped each chirped microwave microwave waveform waveform, that can be givengenerated, by f RFare( 0determined), depends by on the the corresponding grating in the superimposed structure.= As shown by Equations (3) and (4), for a path mismatch ∆L (r the corresponding delay time ∆t ne f f ∆L /c0, where c0 is the() speed of light fixed WTM, the central frequency of each chirped microwave waveform, given by fRF 0 , depends in vacuum) while the RF chirp rate depends only on the grating chirp (CLCBG). As all of the gratings Δ = ( Δ ) experienceon the thepath same mismatch path mismatch,∆L (r the corresponding all of the generated delay time chirped t n microwaveeff L c0 , where waveforms c0 is the have speed the of same centrallight frequency. in vacuum) Moreover, while the ifRF the chirp superimposed rate depends gratings only on havethe grating the same chirp chirp, (CLCBG then). As theall of generated the microwavegratings waveforms experience willthe same also havepath mismatch, the same RFall chirpof the rate.generated On the chirped other hand,microwave if the waveforms superimposed have the same central frequency. Moreover, if the superimposed gratings have the same chirp, then gratings have different chirps, then we can obtain chirped microwave waveforms having the same the generated microwave waveforms will also have the same RF chirp rate. On the other hand, if central frequency, but with different values of RF chirp rate. the superimposed gratings have different chirps, then we can obtain chirped microwave waveforms Tohaving demonstrate the same central the principle, frequency, we but generate with different simultaneously values of RF two chirp chirped rate. microwave waveforms using a fiber-basedTo demonstrate Sagnac the principle, interferometer we generate incorporating simultaneously two two superimposed chirped microwave linearly waveforms chirped BGs. Figureusing3 depicts a fiber-based the experimental Sagnac interferometer setup. We incorporating use a femtosecond two superimposed mode-locked linearly laser chirped operating BGs. at a repetitionFigure rate3 depicts of 20 the MHz experimental (corresponding setup. We to aus periode a femtosecond of 50 ns) mode-locke as the broadbandd laser operating source. at WTM a is .. repetition rate of 20 MHz (corresponding to a period of 50 ns) as the broadband source. WTM is achieved using a length of DCF with a dispersion of Φλ = −1719 ps/nm. The two superimposed Φ gratingsachieved have using the same a length reflectivity of DCF with of ~80%; a dispersion the central of wavelengthsλ = −1719 ps/nm. are The 1545.4 two nmsuperimposed and 1551.1 nm (the spectralgratings separationhave the same is ~5.7 reflectivity nm), the of corresponding ~80%; the central 3 dB wavelengths bandwidths are are 1545.4 4.4 nmnm andand 4.91551.1 nm, nm and the dispersions(the spectral are C separationLCBG1 = 53.3 is ~5.7 ps/nm nm), and the CcorrespondingLCBG2 = 47.8 ps/nm.3 dB bandwidths Erbium dopedare 4.4 fibernm and amplifiers 4.9 nm, and (EDFAs) are usedthe dispersions to compensate are C forLCBG1losses. = 53.3 ps/nm The average and CLCBG power2 = 47.8 of ps/nm. the broadband Erbium doped pulses fiber launched amplifiers into the Sagnac(EDFAs) interferometer are used to is compensate ~3 dBm. Wefor uselosses. polarization The average controllers power of the (PCs) broadband to adjust pulses and launched optimize the into the Sagnac interferometer is ~3 dBm. We use polarization controllers (PCs) to adjust and interference pattern of the Sagnac response and one tunable optical delay line (ODL) to adjust the delay optimize the interference pattern of the Sagnac response and one tunable optical delay line (ODL) timeto or adjust path mismatch the delay betweentime or path the twomismatch arms. betw By adjustingeen the two the arms. ODL, By we adjusting can readily the obtainODL, we waveforms can at differentreadily obtain central waveforms frequencies at different (as described central byfrequencies Equation (as (3 described)) in real by time. Equation Prior (3)) to O/E in real conversion, time. we removePrior to amplifiedO/E conversion, spontaneous we remove emission amplified (ASE) spontaneous noise from emission the EDFAs (ASE) usingnoise from an optical the EDFAs bandpass filterusing (OBF). an We optical measure bandpass the spectral filter (OBF). responses We ofmeas theure generated the spectral waveforms responses using of anthe optical generated complex spectrumwaveforms analyzer using (OCSA) an optical having complex a resolution spectrum of analyzer 0.16 pm (OCSA) and record having the a resolution temporal waveformsof 0.16 pm and using a highrecord bandwidth the temporal photodiode waveforms (PD) for using O/E a conversionhigh bandwidth connected photodiode to a 33 (PD) GHz for real-time O/E conversion oscilloscope (RTO)connected operating to ata 33 80 GHz GS/s. real-time After O/E oscilloscope conversion, (RTO) we operating also obtain at 80 the GS/s. RF After spectra O/E using conversion, a 40 GHz we ESA withalso a resolution obtain the bandwidth RF spectra of using 20 kHz a 40 (we GHz use ESA optical with filters a resolution to separate bandwidth spectrally of 20 the kHz two (we waveforms use optical filters to separate spectrally the two waveforms prior to measuring their RF spectra). Note prior to measuring their RF spectra). Note that, since the system for generating the waveforms is linear, that, since the system for generating the waveforms is linear, the order in which the two the orderoperations—spectral in which the two shaping operations—spectral and WTM—are performe shapingd anddoes WTM—are not matter; performedin our experiments, does not we matter; in ourperform experiments, WTM prior we performto spectral WTM shaping. prior to spectral shaping.

OCSA

FigureFigure 3. Experimental 3. Experimental setup setup for simultaneous for simultaneous generation generation of multiple of multiple chirped chirped microwave microwave waveforms waveforms using a Sagnac interferometer incorporating superimposed linearly chirped BGs. using a Sagnac interferometer incorporating superimposed linearly chirped BGs.

Photonics 2017, 4, 44 6 of 20

TheThe characteristics characteristics of theof the generated generated waveforms waveforms are are summarized summarized in Figuresin Figures4–6 4–6.. Figure Figure4 shows 4 shows the opticalthe spectraoptical spectra and temporal and temporal waveforms waveforms for a delay for a time delay in thetime Sagnac in the interferometerSagnac interferometer of ∆t = −of100 ∆t ps,= 0 ps,−100 and ps, +100 0 ps, ps (theand difference+100 ps (the in powerdifference between in po thewer two between spectral the bands two spectral and hence bands the twoand waveformshence the is duetwo in waveforms part to the is spectrum due in part of the to pulsed the spectrum source andof the the pulsed setting source of the EDFAand the used setting prior of to the detection). EDFA Theused two waveformsprior to detection). are separated The two temporally waveforms by are 9.8 ns;sepa thisrated separation temporally is determined by 9.8 ns; this by theseparation product is of thedetermined difference between by the product the central of the wavelengths difference ofbetween the two the spectral central bandswavelengths (5.7 nm) of and the thetwo amount spectral of dispersionbands (5.7 (− 1719nm) ps/nm).and the amount Since we of use dispersion a negative (−1719 dispersion ps/nm). element Since we in ouruse experiments,a negative dispersion the WTM is reversed:element in while our experiments, the spectra show the WTM the FSR is reversed varying: while in one the direction, spectra show the temporal the FSR tracesvarying show in one the reverse.direction, Moreover, the temporal the first traces (temporal) show the waveform reverse. Mo (onreover, the left)the first corresponds (temporal) to waveform longer wavelengths, (on the left) whereascorresponds the second to longer waveform wavelengths, (on the right) whereas is associated the second with waveform shorter wavelengths.(on the right) is Figure associated5 shows with the calculatedshorter spectrogramswavelengths. forFigure these 5 waveforms, shows the whichcalculated confirm spectrograms simultaneous for generationthese waveforms, of two differentwhich chirpedconfirm microwave simultaneous waveforms. generation By tuning of two the differen delay, wet chirped can change microwave the sign waveforms. of the RF chirp By tuning rate as the well as thedelay, central we can frequency change (asthe explained sign of the previously, RF chirp ra bothte as waveforms well as the have central the frequency same central (as frequency).explained Sincepreviously, the grating both chirps waveforms are different, have the both same waveforms central fr exhibitequency). different Since the RF grating chirp rates. chirps Finally, are different, Figure6 both waveforms exhibit different RF chirp rates. Finally, Figure 6 shows the RF spectra for the two shows the RF spectra for the two waveforms. The waveforms occupy a frequency span of up to 26 GHz waveforms. The waveforms occupy a frequency span of up to 26 GHz for delay times of ±100 ps for delay times of ±100 ps and up to 19 GHz for a delay time of 0; these results are consistent with those and up to 19 GHz for a delay time of 0; these results are consistent with those shown in the shown in the spectrogram distributions. The full-width at half-maximum (FWHM) durations for the spectrogram distributions. The full-width at half-maximum (FWHM) durations for the first and first and second waveforms are ~8.4 ns and ~7.0 ns, respectively; the corresponding time bandwidth second waveforms are ~8.4 ns and ~7.0 ns, respectively; the corresponding time bandwidth productsproducts (TBWPs) (TBWPs) are are as largeas large as as 274 274 and and 224. 224.

(a) (b)

(e) (f)

Figure 4. Spectral and temporal results for delay times of −100 ps (a,b); 0 ps (c,d); and 100 ps (e,f). Figure 4. Spectral and temporal results for delay times of −100 ps (a,b); 0 ps (c,d); and 100 ps (e,f).

Photonics 2017, 4, 44 7 of 20 Photonics 2017, 4, 44 7 of 20 Photonics 2017, 4, 44 7 of 20

(a)(a)

(b)(b)

(c)(c) Figure 5. Spectrogram distributions for the waveforms shown in Figure 4: delay times of (a) −100 ps; FigureFigure 5. Spectrogram 5. Spectrogram distributions distributions for for the the waveforms waveform showns shown in in Figure Figure4 :4: delay delay times times of of ( (aa)) −100100 ps; ps; (b) 0 ps; and (c) 100 ps. (b) 0(b ps;) 0 andps; and (c) 100(c) 100 ps. ps.

Figure 6. Radio-frequency (RF) spectra for the two generated waveforms at longer wavelengths (left) Figure 6. Radio-frequency (RF) spectra for the two generated waveforms at longer wavelengths (left) Figureand shorter 6. Radio-frequency wavelengths (right (RF))spectra for different for the delay two times. generated waveforms at longer wavelengths (left) and shorter wavelengths (right) for different delay times. and shorter wavelengths (right) for different delay times. 2.3.2.3. Photonic Photonic Generation Generation of Chirpedof Chirped Microwave Microwave Waveforms Waveforms Using Using an anArrayed Arrayed Waveguide Waveguide Grating Grating 2.3.SagnacSagnac Photonic Interferometer Interferometer Generation of Chirped Microwave Waveforms Using an Arrayed Waveguide Grating Sagnac Interferometer TheThe use use of ofsuperimposed superimposed gratings gratings in ina Sagnaca Sagnac interferometer interferometer allows allows for for the the simultaneous simultaneous generationgenerationThe use of of ofmultiple superimposedmultiple chirped chirped gratingsmicrowave microwave in awaveforms Sagnacwaveforms interferometer using using a simplea simple allows structure structure for thewith with simultaneous real-time real-time generationtunability/reconfigurability.tunability/reconfigurability. of multiple chirped However, However, microwave one one main waveformsmain limitation limitation using of ofthe athe simpleapproach approach structure is isthe the fact with fact that real-timethat the the tunability/reconﬁgurability.generatedgenerated waveforms waveforms have have the However, the same same central one central main frequenc frequenc limitationy. Thus,y. ofThus, the while approachwhile the the Sagnac isSagnac the interferometer fact interferometer that the generated with with waveformssuperimposedsuperimposed have thegratings gratings same centralhas has the frequency.the same same functional Thus,functional whileityity as the asmultiple Sagnac multiple interferometerSagnac Sagnac interferometers interferometers with superimposed with with gratingsindividualindividual has gratings, the gratings, same it cannot functionalityit cannot achieve achieve asthe multiplethe same same capability capability Sagnac for interferometers for independent independent tuning with tuning individualof ofthe the waveform waveform gratings, itcharacteristics. cannotcharacteristics. achieve the same capability for independent tuning of the waveform characteristics.

Photonics 2017, 4, 44 8 of 20

CapmanyPhotonics 2017, et 4, 44 al. demonstrated that it is possible to create a multi-channel (or multi-wavelength/8 of 20 multiple spectral bands) Sagnac interferometer using arrayed waveguide gratings (AWGs), Capmany et al. demonstrated that it is possible to create a multi-channel (or i.e., an AWGSI (see Figure7a) [ 32]. The AWGSI can also achieve the same functionality as multiple multi-wavelength/multiple spectral bands) Sagnac interferometer using arrayed waveguide gratings Sagnac(AWGs), interferometers, i.e., an AWGSI especially (see Figure if 7a) we [32]. consider The AWGSI that eachcan also Sagnac achieve interferometer the same functionality operates as over a speciﬁcmultiple spectral Sagnac band.interferometers, In each especially branch of if we the consider AWGSI that (i.e., each in Sagnac each spectralinterferometer band operates or channel), we canover incorporate a specific spectral a linearly band. chirpedIn each branch BG as of wellthe AWGSI as a tunable (i.e., in each ODL spectral (see Figure band or7 b).channel), In so we doing, we nowcan haveincorporate a Sagnac a linearly interferometer chirped BG operating as well asover a tunable multiple ODL spectral(see Figure bands 7b). where,In so doing, in each, we now we have controlhave over a Sagnac the characteristics interferometer by operating tuning theover different multiple ODLs spectral [33 bands]. Thus, where, each in channel each, we of have the control AWGSI can be usedover to the generate characteristics a single by chirped tuning the microwave different OD waveformLs [33]. Thus, where each the channel characteristics of the AWGSI of the can waveform, be suchused as the to signgenerate and a magnitudesingle chirped of microwave the RF chirp wave rateform and where the centralthe characteristics frequency, of arethe determinedwaveform, by such as the sign and magnitude of the RF chirp rate and the central frequency, are determined by the the characteristics of the linearly chirped BG and the delay time. In other words, we can generate characteristics of the linearly chirped BG and the delay time. In other words, we can generate simultaneously multiple chirped microwave waveforms where we can adjust the central frequency simultaneously multiple chirped microwave waveforms where we can adjust the central frequency and RFand chirp RF chirp rate rate of eachof each waveform waveform independently independently and in in real real time. time.

λ 1 … λ 2 λ AWG N AWG 1×N 1×N

… coupler λ λ λ 1 2 N in out (a)

(b)

Figure 7. (a) Schematic of an arrayed waveguide Sagnac interferometer (AWGSI) (adapted from [32]) Figure 7. (a) Schematic of an arrayed waveguide Sagnac interferometer (AWGSI) (adapted from [32]) and (b) its use for simultaneously generating multiple chirped microwave waveforms. and (b) its use for simultaneously generating multiple chirped microwave waveforms. As a proof-of-principle demonstration, we generate simultaneously two chirped microwave Aswaveforms a proof-of-principle using a fiber-based demonstration, two-channel we AWGSI generate incorporating simultaneously linearly two chirped chirped BGs. microwave The waveformsexperimental using setup a is ﬁber-based shown in Figure two-channel 8 and is nominally AWGSI the incorporatingsame as that shown linearly in Figure chirped 3, with BGs. The experimentalthe exception of setup the AWGSI is shown replacing in Figure the8 Sagnac and is interferometer nominally the with same superimposed as that shown gratings. in Figure To 3, implement the two-channel AWGSI, we use 3 dB couplers and a pair of matched OBFs in each with the exception of the AWGSI replacing the Sagnac interferometer with superimposed gratings. branch. The spectral widths of the two channels (set by the OBFs) are 1 nm and 0.7 nm. Each branch To implementincorporates the a two-channel linearly chirped AWGSI, BG having we use a 3reflectivity dB couplers ~80%, and center a pair wavelength of matched = OBFs 1540 innm, each 3 dB branch. The spectralbandwidth widths ~10 ofnm, the and two dispersion channels of (set ~140 by theps/nm OBFs) (i.e., are gratings 1 nm andwith 0.7 the nm. same Each characteristics branch incorporates are a linearlyused). chirped The OBFs BG havingin each abranch reﬂectivity are adjusted ~80%, center to occupy wavelength different = 1540spectral nm, bands 3 dB bandwidthof the grating ~10 nm, and dispersionresponse; in of this ~140 case, ps/nm the bottom (i.e., gratings branch is with set to the cover same shorter characteristics wavelengths are while used). the The top OBFs branch in each branchcovers are adjustedlonger wavelengths. to occupy different Each branch spectral also bands has ofits theown grating tunable response; ODL to in control this case, the the path bottom branchmismatch/delay is set to cover time shorter to allow wavelengths for independent while tuning the topof the branch central covers frequency longer and wavelengths. sign of the RF Each branchchirp also rate. has its own tunable ODL to control the path mismatch/delay time to allow for independent tuning of the central frequency and sign of the RF chirp rate. Photonics 2017, 4, 44 9 of 20

Photonics 2017, 4, 44 9 of 20

OCSA

FigureFigure 8. Schematic 8. Schematic of of experimental experimentalsetup setup forfor simultaneoussimultaneous generation generation of two of two chirped chirped microwave microwave waveforms using AWGSI incorporating linearly chirped BGs. waveforms using AWGSI incorporating linearly chirped BGs. Figure 8. Schematic of experimental setup for simultaneous generation of two chirped microwave Thewaveforms characteristics using AWGSI of theincorporating generated linearly waveform chirpeds areBGs. summarized in Figures 9–11. In these experiments,The characteristics we fix the path of themismatch/delay generated time waveforms in the bottom are branch summarized (at shorter wavelengths) in Figures to9– 11. In these∆t = −The experiments,70 ps characteristics and vary the we delayof ﬁx the the in generated the path top mismatch/delaybranch waveform (at longers are wavelengths). summarized time in the Figurein bottom Figures 9 shows branch9–11. the In optical (at these shorter wavelengths)spectraexperiments, and to temporal ∆wet = fix− the70 waveforms. pspath and mismatch/delay vary Again, the due delay timeto inth ein the use the topof bottom a branchnegative branch (at dispersion longer (at shorter wavelengths). element, wavelengths) the WTM Figure to 9 showsis∆t the=reversed. −70 optical ps and The spectra vary corresponding the and delay temporal in the calculated top waveforms. branch spec (at trogramslonger Again, wavelengths). dueappear to thein Figure useFigure of 9 a shows10. negative Clearly, the optical dispersion the element,characteristicsspectra the and WTM temporal of is the reversed. first waveforms. waveform The corresponding Again, (on the due left to an th calculatedde associateduse of a spectrogramsnegative with longer dispersion wavelengths) appear element, in Figure vary the 10WTMwhile. Clearly, those of the second waveform (on the right and associated with shorter wavelengths) are held the characteristicsis reversed. The of the corresponding ﬁrst waveform calculated (on the left spec andtrograms associated appear with in longer Figure wavelengths) 10. Clearly, vary the while constant.characteristics This ofshows the first the waveformability of (onthe theAWGSI left an tod associatedprovide independent with longer tuningwavelengths) of the varygenerated while those of the second waveform (on the right and associated with shorter wavelengths) are held constant. waveforms,those of the a secondcapability waveform not possi (onble withthe right superimposed and associated gratings. with shorter wavelengths) are held This shows the ability of the AWGSI to provide independent tuning of the generated waveforms, constant. This shows the ability of the AWGSI to provide independent tuning of the generated a capabilitywaveforms, not possiblea capability with not superimposedpossible with superimposed gratings. gratings.

(a) (b)

(e) (f)

Figure 9. Spectral and temporal results. The delay time in the bottom branch at shorter wavelengths is fixed at −70 ps while that( ein) the top branch at longer wavelengths is varied:(f) −70 ps (a,b); 0 ps (c,d); andFigure +70 9. ps Spectral (e,f). and temporal results. The delay time in the bottom branch at shorter wavelengths Figure 9. Spectral and temporal results. The delay time in the bottom branch at shorter wavelengths is is fixed at −70 ps while that in the top branch at longer wavelengths is varied: −70 ps (a,b); 0 ps (c,d); − − ﬁxedand at +7070 ps ps (e while,f). that in the top branch at longer wavelengths is varied: 70 ps (a,b); 0 ps (c,d); and +70 ps (e,f).

Photonics 2017, 4, 44 10 of 20 Photonics 2017, 4, 44 10 of 20 Photonics 2017, 4, 44 10 of 20

(a) (a)

(b) (b)

(c) Figure 10. Spectrogram distributions for the waveform(c) s shown in Figure 9: delay times of (a) −70 ps; Figure 10. Spectrogram distributions for the waveforms shown in Figure9: delay times of ( a) −70 ps; Figure(b) 0 ps; 10. and Spectrogram (c) 70 ps. distributions for the waveforms shown in Figure 9: delay times of (a) −70 ps; (b) 0 ps; and (c) 70 ps. (b) 0 ps; and (c) 70 ps.

Figure 11. RF spectra for the first generated waveform (left) and the second generated waveform Figure(right) for11. differentRF spectra values for theof delay first generated(the same delaywaveform is applied (left) toand both the branches). second generated waveform Figure(right 11.) RFfor different spectra forvalues the of first delay generated (the same waveformdelay is applied (left to) andboth thebranches). second generated waveform (rightNote) for differentthat the valuesmagnitude of delay of (thethe RF same chirp delay rate is appliedfor both to waveforms both branches). is the same, as the two gratingsNote have that nominally the magnitude the same of thecharacteristics. RF chirp rate It isfor possible both waveforms to have different is the valuessame, ofas RFthe chirp two rate if gratings with different chirp are used. Figure 11 illustrates the RF spectra for the two Notegratings that have the nominally magnitude the of same the RF characteristics. chirp rate for It bothis possible waveforms to haveis different the same, values as the of RF two chirp gratings waveforms. The frequency spans a range of up to 24 GHz for delay times of ±70 ps and up to 16 GHz haverate nominally if gratings the with same different characteristics. chirp are It used. is possible Figure to11 haveillustrates different the RF values spectra of RFfor chirpthe two rate if waveforms.for a delay time The offrequency 0 ps. Given spans the a difference range of up in thtoe 24 spectral GHz for widths delay of times the twoof ±70 channels, ps and upthe todurations 16 GHz gratings with different chirp are used. Figure 11 illustrates the RF spectra for the two waveforms. forof the a delay waveforms time of are0 ps. not Given the same: the difference here, the infirst th ewaveform spectral widths has a FWHMof the two of ~1.7channels, ns while the thatdurations of the ± The frequencyofsecond the waveforms waveform spans aare is range ~1.2not the ns. of same: upThe to waveforms here, 24 GHz the first for are delaywaveform separated times has temporally of a FWHM70 ps andbyof ~1.7~3.4 up nsns, to while 16which GHz that again forof thea is delay timesecond ofdetermined 0 ps. waveform Given by the the separationis ~1.2 difference ns. Theof the in waveforms spectral the spectral bands are widthsseparatedand the ofdispersion. temporally the two For channels, by a delay~3.4 ns, time the which durationsof −70 again ps, the is of the waveformsdeterminedTBWPs are of the not by first the separationand same: second here, of waveforms the spectral first waveform are bands 29.5 and has 14.4,the a dispersion. FWHM respectively. of For ~1.7 a delay ns while time that of −70 of ps, the the second waveformTBWPs is of ~1.2 the ns.first The and waveformssecond waveforms are separated are 29.5 and temporally 14.4, respectively. by ~3.4 ns, which again is determined by the2.4. separation Discussion of the spectral bands and the dispersion. For a delay time of −70 ps, the TBWPs of the first2.4. andDiscussionWe secondhave demonstrated waveforms are simultaneous 29.5 and 14.4, generati respectively.on of multiple (two) chirped microwave waveformsWe have with demonstrated using an optical simultaneous spectral shaper generati basedon on (1)of superimposedmultiple (two) linearly chirped chirped microwave BGs in 2.4. Discussionwaveformsa Sagnac interferometer with using an and optical (2) an spectral AWGSI shaper incorpor basedating on linearly(1) superimposed chirped BGs linearly in each chirped branch. BGs Both in approaches can be scaled to generate a greater number of waveforms: for example, the Wea Sagnac have demonstratedinterferometer and simultaneous (2) an AWGSI generation incorporating of multiple linearly (two) chirped chirped BGs in microwave each branch. waveforms Both approachessuperposition can of atbe leastscaled nine to fiber generate BGs was a greademonstratedter number [34] of and waveforms: AWGs operating for example, over many the with using an optical spectral shaper based on (1) superimposed linearly chirped BGs in a Sagnac superpositionwavelengths areof at readily least nine available. fiber BGs While was demonstratedthe use of superimposed[34] and AWGs gratings operating in overa Sagnac many interferometerwavelengths and are (2) anreadily AWGSI available. incorporating While linearlythe use chirpedof superimposed BGs in each gratings branch. in Both a approachesSagnac can be scaled to generate a greater number of waveforms: for example, the superposition of at least nine fiber BGs was demonstrated [34] and AWGs operating over many wavelengths are readily available. While the use of superimposed gratings in a Sagnac interferometer offers greater simplicity Photonics 2017, 4, 44 11 of 20 in terms of implementation, it cannot provide the same capability as the AWGSI, especially in terms of generatingPhotonics waveforms2017, 4, 44 with very different central frequencies. Moreover, by using tunable11 of chirped 20 BGs,interferometer e.g., through pumpoffers tuninggreater [simplicity35], the AWGSI in term offerss of implementation, the possibility toit generatecannot provide multiple the waveforms, same withcapability independent as the tuning AWGSI, of theespecially central in frequency terms of generating and RF chirp waveforms rate. with very different central Severalfrequencies. factors Moreover, will limitby using the tunable number chirped of waveforms BGs, e.g., through that can pump be tuning generated [35], simultaneously.the AWGSI For example,offers the in possibility fiber, the numberto generate of gratings multiple that wave canforms, be superimposed with independent depends tuning onthe of photosensitivitythe central of thefrequency fiber and and the RF strength chirp rate. of each grating (which is set by corresponding peak refractive index change).Several Another factors factor will is associatedlimit the number with theof wavefo following.rms that The can repetition be generated rate simultaneously. (R) of the mode-locked For laserexample, (or pulsed in fiber, broadband the number source) of gratings used in that the ca systemn be superimposed gives a period depends (or temporalon the photosensitivity window) of 1/R of the fiber and the strength of each grating (which is set by corresponding peak refractive index into which the generated waveforms can be fit without interleaving. To first order, assuming that the change). Another factor is associated with the following. The repetition rate (R) of the mode-locked generated waveforms have the same duration, the total number of waveforms is obtained by dividing laser (or pulsed broadband source) used in the system gives a period (or temporal window) of 1/R the temporalinto which window the generated by the waveforms duration ofcan a be waveform. fit without The interleaving. duration To of first each or waveformder, assuming depends that the on the opticalgenerated spectral waveforms bandwidth have and thethe amountsame duration, of dispersion the total used number for WTM. of waveforms These values is obtained are typically by set by thedividing need to the have temporal very largewindow TBWP by the (e.g., duration to support of a awaveform. high compression The duration ratio). of each As such,waveform while the numberdepends of spectral on the bandsoptical can spectral be high, bandwidth the number and th ofe waveformsamount of dispersion might be less.used for WTM. These Perhapsvalues are the typically greatest set advantage by the need of to the have AWGSI very approachlarge TBWP is (e.g., the potential to support for a integration,high compression e.g., in SiP. In particular,ratio). As such, high while performance the number AWGs of spectral in SiPbands [36 can]have be high, been the number realized of andwaveforms BGs are might now be routinelyless. producedPerhaps [37,38]. the By greatest introducing advantage a pn ofjunction the AWGSI to the approa siliconch waveguideis the potential and for applying integration, a bias e.g., voltage, in SiP. In particular, high performance AWGs in SiP [36] have been realized and BGs are now routinely reconfiguration can be enabled through the plasma dispersion effect. In particular, if the junction is produced [37,38]. By introducing a pn junction to the silicon waveguide and applying a bias voltage, introduced along the rib waveguide BG, the grating chirp, and hence RF chirp rate, can be tuned [27]. reconfiguration can be enabled through the plasma dispersion effect. In particular, if the junction is On theintroduced other hand, along using the rib a pnwaveguidejunction BG, for the a silicon grating waveguide chirp, and hence that is RF part chirp of rate, an interferometer can be tuned [27]. branch will allowOn the for other tuning hand, the using path mismatch,a pn junction and, forhence, a silicon control waveguide over the that central is part frequency. of an interferometer Such advances will resultbranch in will the allow implementation for tuning the of path a fully mismatch, programmable and, hence, and control integrated over the multiple central frequency. chirped microwave Such waveformadvances generator. will result in the implementation of a fully programmable and integrated multiple chirped microwave waveform generator. 3. Photonic Radio-Frequency Spectrum Analysis 3. Photonic Radio-Frequency Spectrum Analysis 3.1. Context 3.1. Context The RF spectrum of an optical signal under test, denoted Es(t), is given by the Fourier transform The RF spectrum2 of an optical signal under test, denoted Es(t), is given by the Fourier transform of its intensity |Es(t)| . In fact, an ESA that is connected to a photodiode that detects Es(t) will display ()2 2 of its intensity Es t . In fact, an ESA that is connected to a photodiode n that detects2o Es(t) will the squared magnitude of the Fourier transform of its intensity, i.e., = |Es(t)| . The principle 2 ℑ{}()2 for photonicdisplay the RFSA squared is illustrated magnitude in of Figurethe Fourier 12 and transform described of its in intensity, detail in i.e., [12 ]. Briefly,Es t the. The signal under test (referred to as the ‘pump’) will phase modulate a continuous wave (CW) ‘probe’ via principle for photonic RFSA is illustrated in Figure 12 and described in detail in [12]. Briefly, the cross-phasesignal under modulation test (referred (XPM) to inas athe nonlinear ‘pump’) waveguide.will phase modulate For certain a continuous conditions, wave it can (CW) be ‘probe’ shown that the XPM-inducedvia cross-phase sidebands modulation on (XPM) the probe, in a nonlinear i.e., from waveguide. phase modulation, For certain are conditions, determined it can by be the shown intensity of thethat signal the underXPM-induced test. Thus, sidebands measuring on the the probe, power i.e., spectral from phase density modulation, around are the determined probe using by an the optical spectrumintensity analyzer of the (OSA)signal under (which test. gives Thus, the measur squareding magnitudethe power spectral of the Fourierdensity transformaround the ofprobe the field of theusing signal an being optical measured) spectrum willanalyzer correspond (OSA) (whi effectivelych gives to the the squared RF spectrum magnitude of the of signal the Fourier under test, transform of the field of the signal nbeing measured)2o 2 will correspond effectively to the RF spectrum of i.e., the OSA measurement gives = |Es(t)| . 2 ℑ{}()2 the signal under test, i.e., the OSA measurement gives Es t . XPM-induced spectral ∝ 2 signal CW broadening |Es(t)| under test probe XPM in a (pump) nonlinear medium

intensity λ intensity λ λ λ λ λ s p s p ℑ 2 ℑ 2 2 OSA measures | {Es}| OSA measures | {|Es| }| Figure 12. Principle for photonic radio-frequency spectrum analysis (RFSA) (adapted from [13]). Figure 12. Principle for photonic radio-frequency spectrum analysis (RFSA) (adapted from [13]).

Photonics 2017, 4, 44 12 of 20

ThePhotonics bandwidth 2017, 4, 44 for photonic RFSA can exceed several THz. The use of bidirectional12 of 20 propagation [39] and orthogonal polarizations [40] in a polarization maintaining highly nonlinear fiber can increaseThe the bandwidth number offor optical photonic signals RFSA that cancan beexceed characterized several THz. using The a single use nonlinearof bidirectional waveguide mediumpropagation to four. [39] However, and orthogonal no further polarizations scaling in [40] the in number a polarization of signals maintaining that can highly be characterized nonlinear is possible.fiber Multi-channelcan increase the simultaneous number of optical RFSA signals operation that can in abe single characterized integrated using device a single will nonlinear be beneficial as it canwaveguide reduce medium footprint to when four. comparedHowever, no to thefurther duplication scaling in of the single number mode of nonlinearsignals that waveguides. can be characterized is possible. Multi-channel simultaneous RFSA operation in a single integrated device Moreover, such a multi-channel approach can still seek to exploit bidirectional propagation and will be beneficial as it can reduce footprint when compared to the duplication of single mode orthogonal polarizations to gain a factor of four in terms of the number of signals (channels) that can nonlinear waveguides. Moreover, such a multi-channel approach can still seek to exploit be processed.bidirectional Integrated propagation waveguides and orthogonal can be engineeredpolarizations to to support gain a severalfactor of propagating four in terms spatial of the modes. Eachnumber of the modes of signals can then(channels) be used that to can process be processe a differentd. Integrated signal; as waveguides such, a single can multimode be engineered waveguide to can supportsupport parallelseveral (simultaneous)propagating spatial multi-channel modes. Each operation, of the modes i.e., spatial can then modes be areused utilized to process rather a than a dedicateddifferent nonlinear signal; as waveguide such, a single per processedmultimode signal. waveguide For example,can support by harnessingparallel (simultaneous) nonlinear optics basedmulti-channel on mode selectivity, operation, Ding i.e., etspatial al. demonstrated modes are simultaneousutilized rather fourthan wavea dedicated mixing (FWM)-basednonlinear wavelengthwaveguide conversion per processed of two wavelengthsignal. For example, channels by [41 harnessing] while we nonlinear achieved optics simultaneous based on regenerative mode wavelengthselectivity, conversion Ding et al. of twodemonstrated wavelength simultaneous channels usingfour wave XPM mixing [42]. Since (FWM)-based photonic implementationwavelength conversion of two wavelength channels [41] while we achieved simultaneous regenerative of RFSA is based on XPM, we consider exploiting mode selective nonlinear optics to characterize wavelength conversion of two wavelength channels using XPM [42]. Since photonic implementation simultaneously multiple ultrahigh repetition rate optical signals [43]. of RFSA is based on XPM, we consider exploiting mode selective nonlinear optics to characterize simultaneously multiple ultrahigh repetition rate optical signals [43]. 3.2. Integrated Mode-Selective Nonlinear Device To3.2. demonstrate Integrated Mode-Selective the principle Nonlinear of operation, Device we designed and fabricated an integrated (two channel) mode selectiveTo demonstrate nonlinear the device principle (MSND) of operation, in SiP aswe depicted designed in and Figure fabricated 13. The an MSNDintegrated uses (two silicon waveguideschannel) that mode have selective a thickness nonlinearH =device 220 nm (MSND) and sit in onSiP top as depicted of a 3 µm in buriedFigure 13. oxide The (BOX) MSND layer uses with a 2 µmsilicon thick waveguides index-matched that have top a oxide thickness cladding H = 220 (the nm waveguide and sit on top cross of sectiona 3 µm buried appears oxide inFigure (BOX) 13c). It compriseslayer with the a following:2 µm thick index-matched vertical grating top couplers oxide cladding (VGCs) (the for waveguide input and cross output section coupling appears to opticalin fiber,Figure a multimode 13c). It (herecomprises two modes)the following: nonlinear vertical waveguide grating (mm-NLWG),couplers (VGCs) and for a modeinput multiplexerand output and coupling to optical fiber, a multimode (here two modes) nonlinear waveguide (mm-NLWG), and a demultiplexer (m-MUX/m-deMUX) to convert single mode input from the fibers/VGCs to appropriate mode multiplexer and demultiplexer (m-MUX/m-deMUX) to convert single mode input from the modes that propagate in the mm-NLWG and vice versa. fibers/VGCs to appropriate modes that propagate in the mm-NLWG and vice versa.

Figure 13. (a) Schematic of mode selective nonlinear device (MSND) comprising vertical grating Figurecouplers 13. (a )(VGCs), Schematic mode of modemultiplexer selective and nonlineardemultiplexer device (m-MUX/m-deMUX), (MSND) comprising and verticalmultimode grating couplersnonlinear (VGCs), waveguide mode multiplexer (mm-NLWG); and ( demultiplexerb) asymmetric directional (m-MUX/m-deMUX), couplers (ADC) and structure; multimode (c) cross nonlinear waveguidesection (mm-NLWG);of silicon waveguide; (b) asymmetric (d) intra-channel directional and couplers inter-channel (ADC) structure;transmittance (c) cross(i.e., linear section of siliconinter-channel waveguide; cross-talk) (d) intra-channel over the wa andvelength inter-channel span from transmittance 1500 to 1600 (i.e., nm. linear inter-channel cross-talk) over the wavelength span from 1500 to 1600 nm. Figure 13b shows the design of the m-MUX and m-deMUX, which are based on asymmetric directional couplers (ADCs) [44,45]. The principle of operation is as follows. An optical signal that is Figure 13b shows the design of the m-MUX and m-deMUX, which are based on asymmetric launched into Port #3 will propagate as a transverse electric (TE0) or fundamental mode in the upper directional couplers (ADCs) [44,45]. The principle of operation is as follows. An optical signal that is waveguide on the input side of the ADC and be converted to the TE1 mode on the output side. It launchedthen intopropagates Port #3 as will a TE propagate1 mode in as the a transversemm-NLWG. electric On the (TE other0) or hand, fundamental an optical mode signal in that the is upper waveguidelaunched on into the inputPort #1, side i.e., of in the the ADC lower and waveguide be converted on the to input the TEside1 modeof the onADC the will output maintain side. its It then propagatesmode profile as a TE (TE1 mode0) at the in ADC the mm-NLWG.output and then On propagate the other as hand, a TE0 an mode optical in the signal mm-NLWG. that is launched The into Portwidth #1, of i.e., the inupper the lowerwaveguide waveguide in the ADC on the is input360 nm side while of thethat ADCof the will lower maintain waveguide its modeextends proﬁle

(TE0) at the ADC output and then propagate as a TE0 mode in the mm-NLWG. The width of the upper Photonics 2017, 4, 44 13 of 20 waveguide in the ADC is 360 nm while that of the lower waveguide extends linearly from 700 nm to 800 nm; this allows for phase matching between the TE0 and TE1 modes for mode transformation. The coupling gap and length of the ADCs are chosen to be 100 nm and 30 µm, respectively; this gives a coupling efficiency of up to 91% over a wavelength range of 100 nm from 1500 nm to 1600 nm. The mm-NLWG has a width of 800 nm and supports the TE0 and TE1 modes as well as the first two transverse magnetic modes that are not excited due to the specific designs of the VGCs we used (which are optimized for TE mode operation). Table1 summarizes the characteristics of the modes in the mm-NLWG.

Table 1. Characteristics of the TE modes in the multimode nonlinear waveguide (mm-NLWG) calculated using Mode Solver from Lumerical MODE Solutions and using a nonlinear index −18 2 n2 = 4.5 × 10 m /W.

Parameter TE0 Mode TE1 Mode Dispersion @ 1550 nm, ps/(nm·cm) −5.55 × 10−4 1.56 × 10−3 Dispersion slope @ 1550 nm, ps/(nm·cm2) 1.75 × 10−6 −1.51 × 10−5 Effective area, µm2 0.094 0.122 Nonlinear parameter, m−1·W−1 194 150

In the MSND, we denote the transmission from Port #1 to Port #2 as Channel #1 and that from Port #3 to Port #4 as Channel #2. The measured intra-channel transmissions within Channel #1 or #2 and inter-channel transmission between Channel #1 and #2 are shown in Figure 13d. These measurements account for coupling loss (~6 dB/coupler) and propagation loss. The linear inter-channel cross-talk (i.e., either from Port #1 to #4 or from Port #3 to #2) is more than 15 dB less than the corresponding intra-channel cases. Nonlinear optical effects (e.g., FWM or XPM) occur when both a high power pump and a CW probe propagate in the same mode in the mm-NLWG. In particular, if a high power pump and a CW probe are input at Port #1, they will propagate as a TE0 mode in the mm-NLWG (or equivalently, on Channel #1). Similarly, if the pump and CW probe are input at Port #3, they will propagate as a TE1 mode in the mm-NLWG (or on Channel #2). However, no nonlinear interactions occur if the pump and the CW probe are input on separate ports because they will propagate as different modes in the mm-NLWG and the inter-modal nonlinear interaction is very limited. To characterize the nonlinear crosstalk, we compare the highest XPM-induced power around the probe when both pump and probe are input on the same channel (e.g., both are on Channel #1) to when they are launched on different channels (e.g., the pump is on Channel #2 whereas the probe is on Channel #1). Measurements show that the nonlinear inter-channel crosstalk at 1540 nm and 1560 nm is −30 dB. We can then infer the nonlinear coefﬁcients for inter-modal interactions to be ~0.15 m−1·W−1 −1 −1 from the TE0 to TE1 modes and ~0.19 m ·W from the TE1 to TE0 modes.

3.3. Bandwidth Measurements The maximum bandwidth for a photonic implementation of RFSA is given by [12]

1 ∆ f = , (5) max L|2D∆λ + S · ∆λ2| where D is the dispersion and S the dispersion slope of the nonlinear waveguide (both at the central wavelength of the signal under test), and ∆λ is the wavelength detuning between the CW probe and the signal. From the simulated dispersion properties of the mm-NLWG, the maximum theoretical bandwidths on Channel #1 and #2 are 4.5 THz and 1.5 THz, respectively, for a 10 nm detuning in a 2 cm long waveguide. This estimate does not account for higher order dispersion, which will reduce this bandwidth. Photonics 2017, 4, 44 14 of 20

Photonics 2017, 4, 44 14 of 20 We measured the bandwidth of our RFSA using the setup illustrated in Figure 14. The pump (or signal under test) is the beat signal from two CW lasers whose wavelengths are located about 1562.5 nm; the probe is a CW signal at λp = 1535 nm. λs and λp were chosen according to the spectral λ Photonics 2017, 4, 44 λ λ λ 14 of 20 responsess = 1562.5 of nm; the theVCGs probe and is the a CW availability signal at ofp opti= 1535cal nm.filters sandand amplifiers.p were chosen We adjusted according the to beat the spectral responses of the VCGs and the availability of optical filters and amplifiers. We adjusted s frequency1562.5 nm; (df )the by probe detuning is a CW the signal two atCW λp =lasers 1535 nm.symmetrically λs and λp were about chosen λ . accordingThe bandwidth to the spectral on each the beat frequency (df ) by detuning the two CW lasers symmetrically about λs. The bandwidth on channelresponses of the of theRFSA VCGs was and then the obtained availability by of exam optiiningcal filters the andvariation amplifiers. in the We power adjusted level the ofbeat the each channel of the RFSA was then obtained by examining the variation in the power level of the XPM-inducedfrequency ( dfsidebands) by detuning at ±df thefrom two λp CWas a functionlasers symmetrically of df (for these about measurements, λs. The bandwidth we used on an each OSA XPM-induced sidebands at ±df from λ as a function of df (for these measurements, we used an OSA withchannel 0.1 nm of theresolution RFSA was bandwidth). then obtainedp To avoidby exam nonlinearining the absorptionvariation in inthe the power mm-NLWG, level of the we with 0.1 nm resolution bandwidth). To avoid nonlinear absorption in the mm-NLWG, we maintained maintainedXPM-induced the total sidebands power at launched ±df from intoλp as Channel a function #1 of to df be (for 23.4 these mW measurements, (the probe alone we usedaccounted an OSA for the total power launched into Channel #1 to be 23.4 mW (the probe alone accounted for 8.9 mW) and 8.9 withmW) 0.1and nm into resolution Channel #2bandwidth). to 37.1 mW To (the avoid probe nonlinear alone accounted absorption for in 15.1 the mW).mm-NLWG, Figure 15a,bwe into Channel #2 to 37.1 mW (the probe alone accounted for 15.1 mW). Figure 15a,b show the spectral showmaintained the spectral the total evolution power launchedabout λp intoas dfChannel is increased #1 to be while 23.4 mW 15c (theshows probe the alone response accounted for bothfor df channelsevolution8.9 mW) (the about and traces intoλp as areChannel basedis increased #2 on to a 37.12nd-order while mW 15c (the polynomial shows probe the alone responsefit accountedto the formeasured bothfor 15.1 channels values). mW). (theFigure Note traces that,15a,b are in based on a 2nd-order polynomial fit to the measured values). Note that, in Figure 15c, optical powers Figureshow 15c, the optical spectral powers evolution at higher about frequencies λp as df is are increased all normalized while 15c to theshows optical the powerresponse at 0.125for both THz (i.e.,at higherchannels a wavelength frequencies (the traces detuning are are all based normalized between on a 2nd-order the to thetwo optical CWpolynomial pump power signalsfit at to 0.125 the of THzmeasured 1 nm). (i.e., The avalues). wavelength fluctuations Note detuningthat, in inthe measuredbetweenFigure the 15c,responses two optical CW powers pumpare due signalsat higherto the of frequencies 1ripples nm). The in are fluctuationsth alle normalizedspectral in responses the to measuredthe optical of the responsespower VGCs at 0.125 are(e.g., dueTHz the to peak-to-peakthe(i.e., ripples a wavelength in ripple the spectral for detuning a VGC-to-VCG responses between of the testthe VGCs structuretwo CW (e.g., pumpis the 3.6 peak-to-peak dB).signals The of 3 1dB nm). ripple bandwidths The for fluctuations a VGC-to-VCG for Channel in the test #1 structuremeasured is 3.6 responses dB). The 3are dB due bandwidths to the ripples for Channel in the #1spectral and Channel responses #2 areof >2.0the THzVGCs and (e.g., 0.5 the THz, and Channel #2 are >2.0 THz and 0.5 THz, respectively. With the chosen values of λs and λp, the peak-to-peak ripple for a VGC-to-VCG test structure is 3.6 dB). The 3 dB bandwidths ±for Channel #1 XPM-inducedrespectively. With spectral the chosen tones valuesat ±df ofwillλs overlapand λp, thewith XPM-induced the FWM idlers spectral from tones the at twodf beatingwill overlap CW and Channel #2 are >2.0 THz and 0.5 THz, respectively. With the chosen values of λs and λp, the signalswith the for FWM a detuning idlers fromgreater the than two 11 beating nm; this CW restricts signals the for effective a detuning bandwidth greater thanof the 11 MSND nm; this to 1.4 restricts THz. XPM-induced spectral tones at ±df will overlap with the FWM idlers from the two beating CW Thethe effectivemeasured bandwidth bandwidths of the are MSND generally to 1.4 THz.smaller The than measured those bandwidths estimated areusing generally Equation smaller (5). thanThe signals for a detuning greater than 11 nm; this restricts the effective bandwidth of the MSND to 1.4 THz. differencesthose estimated arise usingfrom Equation(1) the fact (5). that The the differences calculated arise values from only (1) the account fact that for the the calculated dispersion values and onlyThe account measured for thebandwidths dispersion are and generally dispersion smaller slope than of the those waveguide estimated and using not higherEquation order (5). valuesThe dispersiondifferences slope arise of thefrom waveguide (1) the fact and that not the higher calcul atedorder values values only of dispersion account for and the (2) dispersion limitations and on measuringof dispersion the and output (2) limitationspower of the on beat measuring signal du thee to output ripples, power the bandwidth, of the beat signaland the due shape to ripples, of the thedispersion bandwidth, slope and of the the shape waveguide of the VGCand not spectral higher response. order values of dispersion and (2) limitations on VGCmeasuring spectral response.the output power of the beat signal due to ripples, the bandwidth, and the shape of the VGC spectral response.

OBF OBF

Figure 14. Experimental setup for measuring the RFSA bandwidth. FigureFigure 14. 14.Experimental Experimental setup setup for for measuringmeasuring the RFSA bandwidth. bandwidth.

FigureFigure 15. 15.Evolution Evolution of ofthe the output output spectrum spectrum from from the the MSND MSND asas the pump detuningdetuning increases increases for for (a ()a ) Figure 15. Evolution of the output spectrum from the MSND as the pump detuning increases for ChannelChannel #1 and#1 and (b )( bChannel) Channel #2; #2; (c )( cvariation) variation in in output output power power ofof thethe XPM-induced tone tone as as a afunction function (a) Channel #1 and (b) Channel #2; (c) variation in output power of the XPM-induced tone as a function of dfof from df from which which the the bandwidth bandwidth of of th the ephotonic photonic RFSA RFSA is is estimated. estimated. of df from which the bandwidth of the photonic RFSA is estimated. 3.4.3.4. Multi-Channel Multi-Channel Results Results WeWe demonstrate demonstrate simultaneous simultaneous characterization characterization of of thethe RFRF spectrumspectrum forfor twotwo ultrahigh ultrahigh repetition repetition raterate optical optical pulse pulse trains, trains, one one at at 160 160 GHz GHz and and the the ot otherher atat 640640 GHz, using thethe setupsetup in in Figure Figure 16. 16. A A mode-lockedmode-locked laser laser at at1550 1550 nm nm and and having having a a repetitionrepetition raterate of 10 GHz isis firstfirst divideddivided into into two two

Photonics 2017, 4, 44 15 of 20

3.4. Multi-Channel Results We demonstrate simultaneous characterization of the RF spectrum for two ultrahigh repetition rate optical pulse trains, one at 160 GHz and the other at 640 GHz, using the setup in Figure 16. Photonics 2017, 4, 44 15 of 20 A mode-locked laser at 1550 nm and having a repetition rate of 10 GHz is first divided into two branches. In one branch, we use a commercial opticaloptical multiplexer (OMUX) to increase the repetition 7 rate to 160 GHz. The OMUX is designed nominallynominally to increase thethe datadata raterate ofof aa 227–1 pseudo-random 7 7 bit sequence (PRBS), i.e., to obtain a 27–1–1 PRBS PRBS at at 40 40 Gb/s, Gb/s, 80 80 Gb/s, Gb/s, or or 160 160 Gb/s Gb/s from from a 2 a7–1 2 –1PRBS PRBS at 10 at 10Gb/s. Gb/s. In this In thissense, sense, we do we not do nothave have a true a true 160 160GHz GHz pulse pulse train, train, i.e., the i.e., OMUX the OMUX does does not perform not perform true truepulse pulse repetition repetition rate multiplication. rate multiplication. This can This be can verified be verified by observing by observing the optical the opticalspectrum spectrum of the 160 of theGHz 160 pulse GHz train, pulse which train, exhibits which exhibits 10 GHz 10spectral GHz spectral tones as tones opposed as opposed to only totones only separated tones separated by 160 byGHz. 160 In GHz. the second In the branch, second we branch, filter wetwo filter tones two separated tones separated by 640 GHz by to 640 create GHz a to640 create GHz asinusoidal 640 GHz sinusoidalwaveform waveformby optical by heterodyning. optical heterodyning. These two These ultr twoahigh ultrahigh repetition repetition rate (bandwidth) rate (bandwidth) signals signals are areamplified amplified and and filtered filtered and and used used as asseparate separate pu pumpmp signals signals before before being being combined combined with with the CW probes usingusing wavelength-division-multiplexing wavelength-division-multiplexing (WDM) (WDM) couplers. couplers. The wavelengthsThe wavelengths of the of CW the probes CW launchedprobes launched into Channel into #1Channel and Channel #1 and #2 Channel are 1540 nm#2 are and 1540 1559 nm nm, and respectively. 1559 nm, The respectively. average powers The launchedaverage powers into the launched MSND into are thethe following:MSND are the 69.2 fo mWllowing: and 69.2 31.6 mW mW, and respectively, 31.6 mW, respectively, for Channel for #1, andChannel 63.1 mW#1, and and 63.1 32.3 mW mW, and respectively, 32.3 mW, forrespective Channelly, #2. for The Channel estimated #2. The nonlinear estimated phase nonlinear shifts for phase both channelsshifts for areboth ~0.12 channels radians are which ~0.12 ensures radians accuracy which ensures for the extractionaccuracy offor the the RF extraction spectrum. of At the these RF powerspectrum. levels, At wethese again power observe levels, negligible we again nonlinear observe absorption negligible in the nonlinear mm-NLWG. absorption We measure in the outputmm-NLWG. spectra We on measure each channel the output using thespectra OCSA on (with each 0.16 channel pm or using 20 MHz the resolution),OCSA (with which 0.16 pm provides or 20 moreMHz resolution), details on the which photonic provides RF spectrummore details of theon th signalse photonic under RF test. spectrum Note thatof the the signals scanning under rate test. of photonicNote that RFSA the scanning depends onrate that of ofphotonic the OSA RFSA used which,depends in turn,on that depends of the on OSA settings used such which, as sensitivity. in turn, Ourdepends measurements on settings with such the as OCSA sensitivity. were obtained Our meas withurements a relatively with high the sensitivity OCSA were (typically obtained−70 with dBm) a andrelatively a sweep high would sensitivity take a (typically few seconds. −70 dBm) and a sweep would take a few seconds.

Figure 16. Experimental setupsetup forfor multi-channelmulti-channel RFSA RFSA with with a a 640 640 GHz GHz waveform waveform on on Channel Channel #1 #1 and and a pulsea pulse train train with with a 160a 160 GHz GHz repetition repetition rate rate on on Channel Channel #2. #2. WSS: WSS: Finisar Finisar waveshaper. waveshaper.

The results are summarized in Figure 17: Figure 17a,b show the optical spectra measured at the The results are summarized in Figure 17: Figure 17a,b show the optical spectra measured at output for Channel #1 and #2, respectively, during simultaneous RFSA operation; Figure 17c,d the output for Channel #1 and #2, respectively, during simultaneous RFSA operation; Figure 17c,d highlight the corresponding RF spectra (i.e., half of the sideband measured from the probe highlight the corresponding RF spectra (i.e., half of the sideband measured from the probe wavelength). wavelength). The red curves are obtained when both channels are active, i.e., for simultaneous The red curves are obtained when both channels are active, i.e., for simultaneous characterization characterization of the two signals, whereas the blue curves correspond to the case when only the of the two signals, whereas the blue curves correspond to the case when only the observed channel observed channel is active. For Channel #1, a 640 GHz tone is detected properly. For Channel #2, the is active. For Channel #1, a 640 GHz tone is detected properly. For Channel #2, the RF spectrum of RF spectrum of the 160 GHz pulse train shows harmonics at 10 GHz; as explained previously, this is the 160 GHz pulse train shows harmonics at 10 GHz; as explained previously, this is due to the fact due to the fact that the multiplexer does not perform true pulse repetition rate multiplication. Nevertheless, we can identify a 160 GHz tone along with one at 320 GHz. We can see that the 640 GHz tone in Channel #1 is not impacted whether or not the signal in Channel #2 is active; more specifically, when Channel #2 is active, the 160 GHz spectral tone does not appear at the output of Channel #1. Similarly, the 640 GHz tone from the signal on Channel #1 does not appear in the spectral output of Channel #2. These results verify the fact that we can perform simultaneous RFSA for each channel in the MSND with negligible inter-channel interference.

Photonics 2017, 4, 44 16 of 20 that the multiplexer does not perform true pulse repetition rate multiplication. Nevertheless, we can identify a 160 GHz tone along with one at 320 GHz. We can see that the 640 GHz tone in Channel #1 is not impacted whether or not the signal in Channel #2 is active; more speciﬁcally, when Channel #2 is active, the 160 GHz spectral tone does not appear at the output of Channel #1. Similarly, the 640 GHz tone from the signal on Channel #1 does not appear in the spectral output of Channel #2. These results verify the fact that we can perform simultaneous RFSA for each channel in the MSND with negligible inter-channelPhotonics 2017, 4, interference.44 16 of 20

Figure 17. Simultaneous multi-channel RFSA when the probe wavelengths are separated by 19 nm. Figure 17. Simultaneous multi-channel RFSA when the probe wavelengths are separated by 19 nm. XPM-induced sidebands are observed on (a) Channel #1 and (b) Channel #2; the half sideband RF XPM-induced sidebands are observed on (a) Channel #1 and (b) Channel #2; the half sideband RF spectrum is illustrated in (c) for Channel #1 and (d) for Channel #2. Insets: enlarged spectra around spectrum is illustrated in (c) for Channel #1 and (d) for Channel #2. Insets: enlarged spectra around the the 640 GHz and 160 GHz tones. The resolutions of the RF spectra shown are set by the resolution of 640 GHz and 160 GHz tones. The resolutions of the RF spectra shown are set by the resolution of the the optical complex spectrum analyzer (OCSA); in this case, 20 MHz. optical complex spectrum analyzer (OCSA); in this case, 20 MHz. 3.5. Discussion 3.5. Discussion There are two primary factors that determine the number of channels that can be processed, i.e., There are two primary factors that determine the number of channels that can be processed, the number of spatial modes that can be supported by the MSND: (1) the number of modes that can i.e., the number of spatial modes that can be supported by the MSND: (1) the number of modes that be multiplexed using the ADC and (2) the ability to obtain sufficient nonlinear optical effects in the can be multiplexed using the ADC and (2) the ability to obtain sufﬁcient nonlinear optical effects in the higher order spatial modes. First, while it is possible to obtain phase matching so that the TE0 mode higher order spatial modes. First, while it is possible to obtain phase matching so that the TE mode can can be transformed to many higher order modes, the smaller difference in effective indices0 of the be transformed to many higher order modes, the smaller difference in effective indices of the modes can modes can induce greater inter-channel cross-talk during mode conversion. ADCs capable of induce greater inter-channel cross-talk during mode conversion. ADCs capable of exciting eight modes exciting eight modes in a multi-mode waveguide (TE0–TE3 and TM0–TM3) have been realized [45]; in a multi-mode waveguide (TE –TE and TM –TM ) have been realized [45]; however, scaling to however, scaling to a greater0 number3 of 0modes3 may require new and/or more complex a greater number of modes may require new and/or more complex m-MUX/m-deMUX designs. m-MUX/m-deMUX designs. Second, the effective area of higher order modes is greater than for the Second, the effective area of higher order modes is greater than for the fundamental and lower order fundamental and lower order modes. As such, the peak power required for higher order modes to modes. As such, the peak power required for higher order modes to achieve a similar nonlinear phase achieve a similar nonlinear phase change for lower order modes will be greater. This can create change for lower order modes will be greater. This can create problems in terms of nonlinear absorption, problems in terms of nonlinear absorption, especially if SiP is considered for developing the MSND. especially if SiP is considered for developing the MSND. In this context, a material platform such as In this context, a material platform such as silicon-rich nitride may be more suitable, as it does not silicon-rich nitride may be more suitable, as it does not show nonlinear absorption effects [46,47]. show nonlinear absorption effects [46,47]. While the results shown in this paper focused on photonic RFSA of high repetition rate optical pulse trains, and, in particular, identification of the associated RF frequency tones, we can also monitor impairments such as the impact of dispersion on these pulse trains (see, e.g., [13–17,43]). Moreover, as demonstrated in [48], we can obtain the RF spectra of more arbitrary waveforms such as pulse bursts having uniform, apodized, and ramped envelopes/profiles and frequency content at 40 GHz and 80 GHz. Ultimately, a trade-off between bandwidth and resolution must be made; unless a high resolution OSA is used, the resolution might be limited even if very high bandwidth signals can be characterized.

Photonics 2017, 4, 44 17 of 20

While the results shown in this paper focused on photonic RFSA of high repetition rate optical pulse trains, and, in particular, identiﬁcation of the associated RF frequency tones, we can also monitor impairments such as the impact of dispersion on these pulse trains (see, e.g., [13–17,43]). Moreover, as demonstrated in [48], we can obtain the RF spectra of more arbitrary waveforms such as pulse bursts having uniform, apodized, and ramped envelopes/proﬁles and frequency content at 40 GHz and 80 GHz. Ultimately, a trade-off between bandwidth and resolution must be made; unless a high resolution OSA is used, the resolution might be limited even if very high bandwidth signals can be characterized.

4. Conclusions In this review paper, we described approaches to generate simultaneously two chirped microwave waveforms as well as to perform simultaneous RFSA of two ultrahigh repetition rate optical pulse trains. In terms of simultaneous generation of multiple chirped microwave waveforms, the AWGSI incorporating linearly chirped BGs achieves the same functionality and capability as having multiple Sagnac interferometers, each incorporating its own grating (regardless of whether a fiber-based or photonic integrated circuit based approach is considered). While both approaches use the same number of gratings, the AWGSI achieves its ‘parallel’ nature by exploiting the wavelength domain, which, in turn, reduces complexity and the number of components needed for its implementation. Parallel operation via the wavelength domain can also be applied to other spectral shaping techniques, such as the Fabry–Pérot cavity with distributed resonances. Harnessing nonlinear optical effects in a mode selective manner represents another way to achieve parallel operation via spatial modes. In this paper, we considered RFSA based on XPM as the nonlinear optical effect. FWM is another nonlinear optical effect that has been used to perform IFM for microwave sensing applications [49–51]. Simultaneous wavelength conversion of two optical signals based on FWM has been demonstrated using the MSND [41]. As such, we can also expect to perform simultaneous IFM for at least two microwave signals. Moreover, as different nonlinear effects are excited in a mode selective manner, and as the inter-channel nonlinear effects are minimal, it should also be possible to realize multi-functional operation with the MSND, e.g., RFSA can be performed on one channel with IFM on the other. Such multi-channel and multi-functional microwave signal processing can only be enabled through photonics. While scaling the number of channels that can be processed will be constrained by (1) the number of spatial modes that can be multiplexed/demultiplexed and (2) the nonlinear coefficient associated with the higher order modes (effectively, the amount of power required to obtain a sufficient nonlinear interaction), we can nonetheless take advantage of bidirectional propagation and orthogonal polarizations to increase by a factor of four the number of channels that can be processed via different spatial modes. The most direct approach for multi-channel microwave photonic signal processing is to duplicate the processing block that performs the processing function, i.e., there will be as many processing blocks as there are channels to be processed. While this form of ‘parallel’ processing can indeed be implemented readily, it may not result in the most practical realization. This, in turn, may impose limits on scalability. The solutions and approaches presented in this paper demonstrate how simple ‘tricks’ can be used to process multiple signals simultaneously without the need for ‘brute force’ duplication and should stimulate further work on the topic.

Acknowledgments: This funding was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) CREATE NGON, NSERC CREATE Si-EPIC, and the Fonds de Recherche du-Nature et Technologies (FRQNT). The silicon photonic devices were fabricated by Richard Bojko at the University of Washington Nanofabrication Facility, a member of the National Science Foundation National Nanotechnology Infrastructure Network. We also thank Prof. Martin Rochette, Marwan Chehade, and Muhammad Anees of McGill University for their contributions to experimental work. Photonics 2017, 4, 44 18 of 20

Author Contributions: L.R.C. conceived the ideas and supervised the work. P.M., M.M. and R.A. performed the experiments. M.M. designed the integrated silicon photonics device. All authors contributed to data analysis and manuscript writing. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Capmany, J.; Novak, D. Microwave photonics combines two worlds. Nat. Photonics 2007, 1, 319–330. [CrossRef] 2. Yao, J.P. Microwave photonics. IEEE/OSA J. Lightw. Technol. 2009, 27, 314–335. [CrossRef] 3. Iezekiel, S.; Burla, M.; Klamkin, J.; Marpaung, D.; Capmany, J. RF engineering meets optoelectronics. IEEE Microw. Mag. 2015, 16, 28–45. [CrossRef] 4. Yao, J.P. Photonic generation of microwave arbitrary waveforms. Opt. Commun. 2011, 284, 3723–3736. [CrossRef] 5. Rashidinejad, A.; Li, Y.; Weiner, A.M. Recent Advances in Programmable Photonic-Assisted Ultrabroadband Radio-Frequency Arbitrary Waveform Generation. IEEE J. Quantum Electron. 2016, 52, 1–17. [CrossRef] 6. Capmany, J.; Mora, J.; Gasulla, I.; Sancho, J.; Lloret, J.; Sales, S. Microwave photonic signal processing. IEEE/OSA J. Lightw. Technol. 2013, 31, 571–586. [CrossRef] 7. Minasian, R.A.; Chan, E.W.H.; Yi, X. Microwave photonic signal processing. Opt. Express 2013, 21, 22918–22936. [CrossRef][PubMed] 8. Ng, W. Photonics for microwave systems and ultra-wideband signal processing. Opt. Commun. 2016, 373, 2–15. [CrossRef] 9. Jiang, H.; Marpaung, D.; Pagani, M.; Vu, K.; Choi, D.-Y.; Madden, S.J.; Yan, L.; Eggleton, B.J. Wide-range, high-precision multiple microwave frequency measurement using a chip-based photonic Brillouin ﬁlter. Optica 2016, 3, 30–34. [CrossRef] 10. Pan, S.; Yao, J.P. Photonics-based broadband microwave measurement. IEEE/OSA J. Lightw. Technol. 2017, 35, 3498–3513. [CrossRef] 11. Zmuda, H.; Toughlian, E.N. Photonic Aspects of Modern Radar; Artech House: Norwood, MA, USA, 1994. 12. Dorrer, C.; Maywar, D.N. RF Spectrum Analysis of Optical Signals Using Nonlinear Optics. J. Light. Technol. 2004, 22, 266–274. [CrossRef] 13. Pelusi, M.; Luan, F.; Vo, T.D.; Lamont, M.R.E.; Madden, S.J.; Bulla, D.A.; Choi, D.-Y.; Luther-Davies, B.; Eggleton, B.J. Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth. Nat. Photonics 2009, 3, 139–143. [CrossRef] 14. Vo, T.D.; Pelusi, M.D.; Schröder, J.; Luan, F.; Madden, S.J.; Choi, D.Y.; Bulla, D.A.P.; Luther-Davies, B.; Eggleton, B.J. Simultaneous multi-impairment monitoring of 640 Gb/s signals using photonic chip based RF spectrum analyzer. Opt. Express 2010, 18, 3938–3945. [CrossRef][PubMed] 15. Corcoran, B.; Vo, T.D.; Pelusi, M.D.; Monat, C.; Xu, D.-X.; Densmore, A.; Ma, R.; Janz, S.; Moss, D.J.; Eggleton, B.J. Silicon nanowire based radio-frequency spectrum analyzer. Opt. Express 2010, 18, 20190–20200. [CrossRef][PubMed] 16. Vo, T.D.; Corcoran, B.; Schroder, J.; Pelusi, M.D.; Xu, D.X.; Densmore, A.; Ma, R.; Janz, S.; Moss, D.J.; Eggleton, B.J. Silicon-chip-based real-time dispersion monitoring for 640 Gbit/s DPSK signals. IEEE/OSA J. Lightw. Technol. 2011, 29, 1790–1796. [CrossRef] 17. Ferrera, M.; Reimer, C.; Pasquazi, A.; Peccianti, M.; Clerici, M.; Caspani, L.; Chu, S.T.; Little, B.E.; Morandotti, R.; Moss, D.J. CMOS compatible integrated all-optical radio frequency spectrum analyzer. Opt. Express 2014, 22, 21488–21498. [CrossRef][PubMed] 18. Weiner, A.M. Optical pulse shaping: A tutorial review. Opt. Commun. 2011, 284, 3669–3692. [CrossRef] 19. Chen, L.R. Photonic generation of chirped microwave and millimeter wave pulses based on optical spectral shaping and wavelength-to-time mapping in silicon photonics. Opt. Commun. 2016, 373, 70–81. [CrossRef] 20. Wang, C.; Yao, J.P. Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped ﬁber Bragg grating. IEEE Trans. Microw. Theory Tech. 2008, 56, 542–553. [CrossRef] Photonics 2017, 4, 44 19 of 20

21. Chi, H.; Yao, J.P. Chirped RF pulse generation based on optical spectral shaping and wavelength-to-time mapping using a nonlinearly chirped fiber Bragg grating. IEEE/OSA J. Lightw. Technol. 2008, 26, 1282–1287. [CrossRef] 22. Wang, C.; Yao, J.P. Simultaneous optical spectral shaping and wavelength-to-time mapping for photonic microwave arbitrary waveform generation. IEEE Photonics Technol. Lett. 2009, 21, 793–795. [CrossRef] 23. Spasojevic, M.; Chen, L.R. Discretely tunable optical delay lines using serial and step-chirped sidewall Bragg gratings in SOI. Electron. Lett. 2013, 49, 608–610. [CrossRef] 24. Wang, C.; Yao, J.P. Photonic generation of chirped microwave pulses using superimposed chirped fiber Bragg gratings. IEEE Photonics Technol. Lett. 2008, 20, 882–884. [CrossRef] 25. Ma, M.; Rochette, M.; Chen, L.R. Generating chirped microwave pulses using an integrated distributed Fabry–Pérot cavity in silicon-on-insulator. IEEE Photonics J. 2015, 7, 5500706. [CrossRef] 26. Zhang, W.; Yao, J.P. Photonic generation of linearly chirped microwave waveforms using a silicon-based on-chip spectral shaper incorporating two linearly chirped waveguide Bragg gratings. IEEE/OSA J. Lightw. Technol. 2015, 33, 5047–5054. [CrossRef] 27. Zhang, W.; Yao, J.P. Silicon-based on-chip electrically-tunable spectral shaper for continuous tunable linearly chirped microwave waveform generation. IEEE/OSA J. Lightw. Technol. 2016, 34, 4644–4672. [CrossRef] 28. Wang, C.; Yao, J. Chirped microwave pulse generation based on optical spectral shaping and wavelength-to-time mapping using a Sagnac loop mirror incorporating a chirped fiber Bragg grating. IEEE/OSA J. Lightw. Technol. 2009, 27, 3336–3341. [CrossRef] 29. Wang, J.; Ashrafi, R.; Rochette, M.; Chen, L.R. Chirped microwave pulse generation using an integrated silicon photonic spectral shaper. IEEE Photonics Technol. Lett. 2015, 27, 1876–1879. [CrossRef] 30. Shu, X.; Yu, L.; Zhao, D.; Zhang, L.; Sugden, K.; Bennion, I. Transmission characteristics of Sagnac interferometers based on fiber Bragg gratings. J. Opt. Soc. Am. B 2002, 19, 2770–2780. [CrossRef] 31. Moslemi, P.; Chen, L.R. Simultaneously generating multiple chirped microwave pulses with superimposed FBGs. IEEE Photonics Technol. Lett. 2017, 29, 1387–1390. [CrossRef] 32. Capmany, J.; Muñoz, P.; Sales, S.; Pastor, D.; Ortega, B.; Martinez, A. Arrayed waveguide Sagnac interferometer. Opt. Lett. 2003, 28, 197–199. [CrossRef][PubMed] 33. Moslemi, P.; Chen, L.R.; Rochette, M. Simultaneously generating multiple chirped microwave waveforms using an arrayed waveguide Sagnac interferometer. IET Electron. Lett. 2017, 53, 1534–1535. [CrossRef] 34. Bolger, J.A.; Littler, I.C.M.; Eggleton, B.J. Optimization of superimposed chirped fiber Bragg gratings for the generation of ultra-high speed optical pulse trains. Opt. Commun. 2007, 271, 524–531. [CrossRef] 35. Shahoei, H.; Li, M.; Yao, J. Continuously tunable time delay using an optically pumped linear chirped fiber Bragg grating. IEEE/OSA J. Lightw. Technol. 2011, 29, 1465–1472. [CrossRef] 36. Cheung, S.; Su, T.; Okamoto, K.; Yoo, S.J.B. Ultra-compact silicon photonic 512 × 512 25 GHz arrayed waveguide grating router. IEEE J. Sel. Top. Quantum Electron. 2014, 20, 8202207. [CrossRef] 37. Burla, M.; Cortés, L.R.; Li, M.; Wang, X.; Chrostowski, L.; Azaña, J. Integrated waveguide Bragg gratings for microwave photonics signal processing. Opt. Express 2013, 21, 25120–25147. [CrossRef][PubMed] 38. LaRochelle, S.; Simard, A.D. Silicon photonic Bragg grating devices. In Proceedings of the Conference on Optical Fiber Communication, Los Angeles, CA, USA, 19–23 March 2017. 39. Provost, L.; Parmigiani, F.; Petropoulos, P.; Richardson, D.J. Investigation of simultaneous 2R regeneration of two 40-Gb/s channels in a single optical fiber. IEEE Photonics Technol. Lett. 2008, 20, 270–272. [CrossRef] 40. Provost, L.; Parmigiani, F.; Petropoulos, P.; Richardson, D.J.; Mukasa, K.; Takahashi, M.; Hiroishi, J.; Tadakuma, M. Investigation of four-wavelength regenerator using polarization- and direction-multiplexing. IEEE Photonics Technol. Lett. 2008, 20, 1676–1678. [CrossRef] 41. Ding, Y.; Xu, J.; Ou, H.; Peucheret, C. Mode-selective wavelength conversion based on four-wave mixing in a multimode silicon waveguide. Opt. Express 2014, 22, 127–135. [CrossRef][PubMed] 42. Ma, M.; Chen, L.R. Harnessing mode-selective nonlinear optics for on-chip multi-channel all-optical signal processing. APL Photonics 2016, 1, 086104. [CrossRef] 43. Ma, M.; Adams, R.; Chen, L.R. Integrated photonic chip enabled simultaneous multi-channel ultra-wideband radio frequency spectrum analyzer. IEEE/OSA J. Lightw. Technol. 2017, 35, 2622–2628. [CrossRef] 44. Ding, Y.; Xu, J.; Da Ros, F.; Huang, B.; Ou, H.; Peucheret, C. On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer. Opt. Express 2013, 21, 10376–10382. [CrossRef][PubMed] Photonics 2017, 4, 44 20 of 20

45. Wang, J.; He, S.; Dai, D. On-chip silicon 8-channel hybrid (de)multiplexer enabling simultaneous mode- and polarization-division-multiplexing. Laser Photonics Rev. 2014, 8, L18–L22. [CrossRef] 46. Krückel, C.J.; Fülöp, A.; Klintberg, T.; Bengtsson, J.; Andrekson, P.A.; Torres-Company, V. Linear and nonlinear characterization of low-stress high conﬁnement silicon-rich nitride waveguides. Opt. Express 2015, 23, 25827–25837. [CrossRef][PubMed] 47. Rezagholipour Dizaji, M.; Krückel, C.J.; Fülöp, A.; Andrekson, P.A.; Torres-Company, V.; Chen, L.R. Silicon-rich nitride waveguides for ultra-broadband nonlinear signal processing. Opt. Express 2017, 25, 12100–12108. [CrossRef][PubMed] 48. Samadi, P.; Chen, L.R.; Callender, C.L.; Dumais, P.; Jacob, S.; Celo, D. RF arbitrary waveform generation using tunable planar lightwave circuits. Opt. Commun. 2011, 284, 3737–3741. [CrossRef] 49. Bui, L.A.; Pelusi, M.D.; Vo, T.D.; Sarkhosh, N.; Emami, H.; Eggleton, B.J.; Mitchell, A. Instantaneous frequency measurement system using optical mixing in highly nonlinear ﬁber. Opt. Express 2009, 17, 22983–22991. [CrossRef][PubMed] 50. Pagani, M.; Morrison, B.; Zhang, Y.; Casas-Bedoya, A.; Aalto, T.; Harjanne, M.; Kapulainen, M.; Eggleton, B.J.; Marpaung, D. Low-error and broadband microwave frequency measurement in a silicon chip. Optica 2015, 2, 751–756. [CrossRef] 51. Pagani, M.; Vu, K.; Choi, D.-Y.; Madden, S.J.; Eggleton, B.J.; Marpaung, D. Instantaneous microwave frequency measurement using four-wave mixing in a chalcogenide chip. Opt. Commun. 2016, 373, 100–104. [CrossRef]

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).