Although the electromagnetic spectrum is a continuum, a

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1 Progress rticle Pulished online: 29 octoer 2 doi:.38/nphoton.2.96 Opticl ritrry wveform genertion Steven T. Cundiff * nd Andrew M. Weiner 2 Opticl ritrry wveform genertion will llow wveforms to e synthesized t opticl frequencies ut with the flexiility currently ville t rdiofrequencies. This technique is enled y comining frequency com technology, which produces trins of opticl pulses with well-defined frequency spectrum, with pulse shping methods, which re used to trnsform trin of ultrshort pulses into n ritrry wveform. To produce wveform tht fills time, the resolution of the shper must mtch the repetition rte of the originl pulse trin, which in turn must hve com spectrum tht is locked to the shper. Here, we review the current efforts towrds chieving opticl ritrry wveform genertion nd discuss the possile pplictions of this technology. Although the electromgnetic spectrum is continuum, strong distinction is typiclly drwn etween electronics nd optics. This distinction is due, in prt, to the very different technologies used for electronics nd optics. A further distinction is tht electronic devices typiclly generte nd mesure electric field wveforms, wheres opticl devices cn generte nd mesure only intensity wveforms ecuse the frequencies involved re much higher. For ny intensity wveform there is continuous fmily of electric field wveforms tht differ y the overll phse. Furthermore, in optics there hve een significnt limits on wht wveforms cn e generted, wheres electronic devices hve een used to generte ritrry wveforms for severl decdes. Over the pst decde, dvnces in optics hve llowed the phse of n electric field, with respect to the corresponding intensity wveform, to e mesured nd controlled. These techniques re referred to s opticl frequency coms ecuse the evolution of the electric field phse in trin of pulses cuses shift in the corresponding frequency spectrum, which is com of eqully spced shrp spectrl lines. Opticl frequency com technology hs revolutionized opticl frequency metrology nd opticl tomic clocks 2, nd hs enled the production of ttosecond pulses 3. The development of com technology hs lso spurred recent work on the genertion of ritrry wveforms t opticl frequencies. Techniques for shping ultrshort opticl pulses hve existed for round two decdes 4. However, these techniques hve significnt limittions. First, the durtion of the output pulses is limited y the spectrl resolution of the pulse shper nd is less thn the time etween pulses. Thus, the output pulse trin does not fill time; tht is, there re gps etween pulses. Second, typiclly the pulses re ll identicl. An ritrry wveform cnnot e produced within these limittions. Producing wveform tht fills time requires pulse shper with spectrl resolution tht mtches the spcing of the com lines of the input pulse trin. Such high resolution is only useful if the frequency com is stle nd ligned with the pulse shper 5 hence the need for frequency com technology. Sometimes known s line-y-line pulse shping, pulse shping with resolution mtching the com ws demonstrted few yers go 5 7. However, the phse nd/or mplitude of the individul com lines were mnipulted y msks tht re essentilly sttic. To produce truly ritrry opticl wveforms requires tht the pulse shper cn e updted for ech pulse gol tht hs not yet een reched, ut is eing ctively pursued in mny lortories round the world. Genertion of com spectr There re two min sources of frequency coms: mode-locked lsers nd opticl frequency com genertors sed on the electro-optic modultion of continuous-wve lser. Although modelocked lsers dominte in most pplictions, oth sources re currently eing used for efforts towrds opticl ritrry wveform genertion. Mode-locked lsers produce regulr trin of ultrshort opticl pulses 8,9, with typicl pulse durtions rnging from ~ fs to few picoseconds. Repetition rtes, f r, rnge from tens of meghertz to few tens of gighertz. Although Ti:Spphire lsers using Kerr-lens mode-locking re the most common in ultrfst optics lortories, other technologies such s fire lsers mode-locked y nonliner polriztion rottion re lso used extensively. Prior to the development of frequency com technology, mode-locked lsers were primrily used in pplictions exploiting either the high time resolution or the high pek power provided y ultrshort pulses. These pplictions were sensitive to the properties of n isolted pulse, nd the fct tht mode-locked lsers produce trin of pulses ws not importnt. An individul ultrshort pulse hs rod opticl spectrum with width tht is inversely proportionl to the minimum (chirp-free) durtion. Becuse the output of mode-locked lser consists of regulr trin of pulses, the opticl spectrum is ctully com of shrp spectrl lines eneth n envelope tht is the spectrum of single pulse. The com lines re spced y f r, mking them only oservle in very high resolution spectrum. If ll of the pulses in the trin hve n identicl electric field, then the com line frequencies would simply e integer multiples of f r. However, the pulses re not ll identicl ecuse the pulse circulting inside the lser experiences shift etween the phse of the crrier wve, which trvels t the phse velocity, nd the pek of the intensity envelope, which trvels t the group velocity. The evolution of this phse, known s the crrier envelope phse, ϕ ce, shifts the com spectrum y the offset frequency to give f = f r Δϕ ce /2π, where Δϕ ce is the pulse-topulse chnge in ϕ ce. Thus, the opticl frequencies of the com lines re ν n = nf r + f, where n is n integer. The reltionship etween the time nd frequency domins is shown in Fig.. The development of methods to mesure f ws the key rekthrough in producing useful frequency coms using mode-locked lsers 2. The sic ide, known s self-referencing, is to compre the low- nd high-frequency wings of the spectrum y frequency douling the low-frequency wing through second-hrmonic JILA, Ntionl Institute of Stndrds nd Technology nd University of Colordo, Boulder, Colordo , USA. 2 Deprtment of Electricl nd Computer Engineering, Purdue University, West Lfyette, Indin , USA. *e-mil: cundiff@jil.colordo.edu 76 nture photonics VOL 4 NOVEMBER Mcmilln Pulishers Limited. All rights reserved.

2 Nture photonics doi:.38/nphoton.2.96 progress rticle Time domin Δφ ce Δ2φ ce. 5 Idel Electric field τ Time Pulse mgnitude (.u.). 5 High resolution Frequency domin /f r. 5 Low resolution Time (/f rep ) Current Grting f r Output wveform Lens f Sptil light modultor ν n = nf r + f Lens Frequency genertion. The frequency difference etween high-frequency com line nd the closest douled low-frequency com line is f, which is esily mesured through heterodyne methods. This mesurement cn e used in phse-locked loop 3 to fix f nd thus produce stle com with specified com line frequencies. Selfreferencing requires very rod spectrum to ensure tht there is significnt power t two wvelengths seprted y n octve (tht is, seprted y fctor of two in frequency). Such spectrum cn e chieved y externl rodening in nonliner medium such s microstructure fire 4,5, or it cn e produced directly y the mode-locked lser 6 9. Alterntive methods of producing coms re lso of interest, prticulrly for generting coms t high rtes (> GHz). For exmple, mode-locked lsers t rtes of GHz or even 4 GHz hve een demonstrted, in which the opticl frequency is not self-referenced ut is insted referenced to n intrcvity etlon 2 or n externl moleculr sorption cell 2. Other pproches strt with continuous-wve lser nd use phse modultor to produce multiple sidends spced y the modultor frequency 22. In one recent exmple, very lrge modultion index ws otined using totl of three telecommunictions phse modultors, yielding 6 com lines, ech spced y 25 GHz (ref. 23). Such sources could potentilly replce the rrys /τ Input pulse Grting Figure Opticl ritrry wveform genertion., The correspondence etween the time (top) nd frequency (ottom) domins for pulse trin with evolving phse nd durtion τ., Schemtic of pulse shper sed on spectrl decomposition. Figure 2 Interply etween spectrl resolution nd temporl response. The repetition rte should doule if n mplitude msk tht locks every other com line is introduced. However, this idel cse (top) is not relizle, nd the ctul wveform depends on the resolution, which is djustle y the spot size in this simultion. At high resolution the switching is slow, while the fidelity of the msked wveform is good (middle). At low resolution the switching is fst, ut the wveform fidelity is poor (ottom). A compromise etween resolution nd fidelity must e mde. Figure reproduced with permission from ref. 32, 28 OSA. of distriuted feedck lsers currently used to generte the multitude of crrier frequencies required for wvelength-division-multiplexed opticl communictions. A lrger numer of sidends cn e produced if the modultor is plced in n opticl cvity tht hs free spectrl rnge commensurte with the modultion frequency 24,25. Compred with coms generted y mode-locked lsers, these continuous-wve pproches hve the dvntge tht the frequencies of the com lines re known reltive to the opticl frequency of the lser, nd lso tht it is esier to generte coms with lrge spcing (typicl vlues re 5 25 GHz). The min disdvntge is tht self-referencing cnnot e implemented ecuse of the nrrow com ndwidth, nd thus the solute frequencies re not known. However, current efforts towrds opticl ritrry wveform genertion (OAWG) mnipulte only reltively smll numer of com lines, nd the solute frequency does not mtter; thus, coms produced y phse modultion cn e esier to use thn those produced y mode-locked lser. Pulse shping In pulse shping, powerful Fourier synthesis methods re used to generte user-defined femtosecond opticl wveforms. As shown in Fig., n incident femtosecond pulse is decomposed into its constituent spectrl components y spectrl disperser (usully grting) nd focusing element ( lens or curved mirror). A sptilly ptterned msk then modultes the phse nd mplitude (nd sometimes the polriztion) of the sptilly dispersed spectrl components. A shped output pulse is otined fter the spectrl components re recomined y second lens nd grting, with the pulse shpe given y the Fourier trnsform of the pttern trnsferred y the msk onto the spectrum. This 4f pulse shping rrngement is lso frequently implemented in reflection geometry, in which mirror plced fter the sptil msk directs the field ck through the first lens nd grting. Pulse shping msks were originlly implemented through microlithogrphic ptterning techniques 26, nd susequently using progrmmle sptil light modultors 4,27,28, cousto-optic modultors 29, hologrphic msks, deformle mirrors nd micromirror rrys. Pulse shping is most commonly implemented using progrmmle liquid-crystl modultor rrys 4,27,28, which llow independent, simultneous grey-level control of oth spectrl mplitude nd phse. A nture photonics VOL 4 NOVEMBER Mcmilln Pulishers Limited. All rights reserved.

3 progress rticle Nture photonics doi:.38/nphoton.2.96 c 8.5 GHz,54.7,54.9,542. Wvelength (nm) GHz π d Frequency (GHz) 2 c Frequency (GHz) π,54.7,54.9,542. Wvelength (nm) 2 2 Figure 3 Offset frequency sensitivity in line-y-line pulse shping.,, Opticl spectrum nlyser mesurement of two reltively stle spectrl lines t 8.5 GHz (), long with smpling scope trces with phse modultions of nd π on single spectrl line (). The trces re scnned times. c,d, Opticl spectrum nlyser mesurement of two reltively unstle spectrl lines t GHz (c), long with smpling scope trces with phse modultions of nd π on single spectrl line (d). The trces re scnned times. Figure reproduced with permission from ref. 5, 25 OSA. detiled theoreticl discussion of pulse shping is given in ref. 9. Some reviews of pulse shping nd its pplictions re given in refs 4,3,3. Using these methods, femtosecond pulses cn e engineered into complex opticl signls, lmost ritrrily nd ccording to specifiction. A key point is tht wveform synthesis is chieved y prllel modultion in the frequency domin, which is chieved y sptil modultion of the dispersed opticl frequency spectrum. Thus, wveforms with seril modultion ndwidths s high s hundreds of terhertz cn e generted nd mnipulted without ny ultrfst modultors. Recent reserch hs imed to extend pulse shping to hyperfine spectrl resolution of few gighertz nd elow, which requires the mnipultion of wveforms with time pertures extending to hundreds of picoseconds or longer. This is in strk contrst with tody s conventionl resolutions of tens or hundreds of gighertz nd time pertures of picoseconds or tens of picoseconds. Such resolution cpility is criticl for processing opticl signls t dt rtes of tens of gigits per second, s well s for line-y-line shping of frequency com sources for OAWG, which is discussed in the following section. Note tht the term OAWG is often used inconsistently in the literture. Line-y-line shping is sometimes clled sttic OAWG, with the sttic often eing omitted. In this cse, the term dynmic OAWG is used to refer to true OAWG, in which the wveform is updted for every pulse. Opticl ritrry wveform genertion The strting point for producing n ritrry opticl wveform is trin of identicl opticl pulses with sufficient ndwidth. As discussed ove, the pulse trin my e produced either y modelocked lser or through modultion of continuous-wve lser. If the pulse trin is to e converted into n ritrry wveform y spectrl decomposition (s is typiclly done), the spectrum must e decomposed with resolution equl to the repetition rte of the pulse trin. This condition is necessry for the output wveform to fill time. In ddition, the elements used to modulte the individul frequency components must e updted t the repetition rte; Figure 4 Frequency coms spred in two dimensions using VIPA nd diffrction grting., Frequency com from GHz repetition rte Ti:Spphire lser. Ech spot corresponds to com line. Horizontl spcing etween columns is 25 GHz nd verticl spcing is GHz (imge courtesy of J. Willits)., GHz com otined y modulting continuouswve lser followed y spectrl rodening in fire. Horizontl spcing etween columns is 2 GHz (VIPA free spectrl rnge), verticl spcing is 2 GHz (every other com line is eliminted). The offset etween columns is introduced to relize shped wveform. c, 2,2 individul modes from GHz repetition rte lser filtered y cvity to 3 GHz. The dt repet every 5 GHz in the verticl direction, nd suset of unique dt is enclosed y the lck ox. Imge cquired fter pssing through n iodine cell. Numerous modes re ttenuted y the iodine vpour, thus providing unique fingerprint. The circled modes re reference lser used for clirtion. Figure reproduced with permission from:, ref. 62, 28 OSA; c, ref. 36, 27 NPG. otherwise the wveform is limited to repeting every period of the input pulse trin. From technologicl perspective, these two criteri re in direct competition. The spectrl resolution requirement is more esily chieved t higher repetition rtes, wheres the modultion requirement is more esily chieved t lower repetition rtes. Currently, it seems tht frequencies of round GHz re the est compromise etween the two. An ovious concern is tht modultion occurs t the sme frequency t which the spectrum is eing resolved. Although the modultors will generte new frequency components on given com line, these components will e t the wrong sptil loction nd hence do not recomine properly. Simultions show tht firly good wveforms cn e produced for n pproprite choice of resolution 32. If the resolution is too low, then the wveform fidelity is compromised, wheres if it is too high, then the switching speed is limited. An exmple clcultion of this compromise is shown in Fig. 2 for the cse of rupt switching on msk tht locks every other com line, thus douling the repetition rte of the pulse trin. The resolution is vried y chnging the spot size in the pulse shper. If the resolution is too low, then the fidelity of the wveform is low; in this cse the pulses in the doule-repetition-rte trin re unequl. If the resolution is too high, then the trnsition etween wveforms extends over mny pulse periods. An pproch to ddress the competition etween resolution nd 762 nture photonics VOL 4 NOVEMBER Mcmilln Pulishers Limited. All rights reserved.

4 Nture photonics doi:.38/nphoton.2.96 progress rticle Mesurement Clcultion Unwrpped phse (rd) 5π 2 2 c 5 π,535 2π,536,537,538,539,54 Wvelength (nm) d Wrpped phse (rd) π,535,536,537,538,539,54 Wvelength (nm) Phse ( rd div ) e Intensity (5 db div ) Phse ( rd div ) f g 2 2 Frequency (GHz) Phse ( rd div ) Intensity (5 db div ) Phse ( rd div ) Time (5 ps div ) Frequency ( GHz div ) Figure 5 Sttic OAWG wveforms. c, Spectrl phse shping of > lines t 5 GHz spcing: liner spectrl phse (delyed pulse) in hlf of spectrum nd cuic spectrl phse in other hlf. Both wrpped (ctul) phse nd unwrpped phse re shown. d g, Genertion of communictions wveforms. 9-it 36 G s dt pcket (d) nd corresponding spectrum (e); 4-it 4 G s dt pcket (f) nd corresponding spectrum (g). For time domin wveforms (d,f), intensity nd phse dt re shown s lue nd red solid lines, respectively, with trgets shown s dots or dshes. For spectr (e,g), intensity nd phse dt re lue stems nd red circles, respectively, with trgets indicted s x. Figure reproduced with permission from: c, ref. 7, 27 NPG; d g, ref. 33, 29 OSA. switching speed is suggested in ref. 33, in which wveforms re synthesized in prtilly overlpping spectrl slices nd pre-distorted to ccount for spectrl filtering effects. If the spectrl resolution of the pulse shping is equl to the repetition rte of the input trin known s line-y-line pulse shping then lignment etween the frequency com of the pulse trin nd the modultor elements ecomes n issue. A sttic mislignment cn increse losses, nd my even render the pulse shper opque. Furthermore, fluctutions in the com offset frequency will mp onto fluctutions in the generted wveform. Figure 3 shows simple demonstrtion of the sensitivity to the com offset frequency. Achieving the spectrl resolution needed to seprte com lines is chllenge. The ruled diffrction grtings typiclly used in trditionl ulk optics pulse shping cn only resolve com lines from reltively high repetition rte source (~ 5 GHz), nd to do so requires em dimeter of severl centimetres, lrge grtings nd long focl length lens (~ m). These requirements result in ulky experimentl set-up. The most common pproch for chieving even higher spectrl resolution in more compct rrngement is to use virtul imged phsed rry (VIPA), which is essentilly side-entrnce Fry Pérot etlon 34. A VIPA provides very high ngulr dispersion, ut lso hs free spectrl rnge (just s for regulr etlon), with frequencies seprted y free spectrl rnge going in the sme output direction s ech other. However, the free spectrl rnge is typiclly lrge enough such tht the com lines going in given direction cn e seprted with n ordinry grting. A VIPA grting pir is typiclly configured such tht they provide ngulr dispersion t right ngles to one nother 35 nd spred the input spectrum cross two dimensions; thus, the frequency com ecomes frequency rush 36. Exmples demonstrting the resolution of individul com lines spred in two dimensions re shown in Fig. 4. High spectrl resolution hs lso een chieved using n rryed wveguide router 6, This pproch hs the dvntge of eing esily integrted with other wveguide devices such s modultors to form pulse-shper chips. Opertion in the line-yline regime is n especilly suitle ppliction of such devices, nture photonics VOL 4 NOVEMBER Mcmilln Pulishers Limited. All rights reserved.

5 progress rticle s the opticl com my e plced t the centre of their discrete trnsmission chnnels. However, the minimum repetition rte is currently limited to GHz, ecuse incresing the resolution requires incresing the re of the chip, which ecomes incomptile with the need for very low phse errors in the wveguide rry. On the other hnd, high-speed modultion is esier to chieve in wveguide device thn with ulk opticl modultors, provided tht the wveguides re formed from mterils tht support highspeed modultion, such s certin compound semiconductors (InP, for exmple). Recent reserch includes implementtion of n InP tunle integrted pulse shper with corse (2 GHz) chnnel spcing 4 nd the friction methods suitle for relizing InP-sed rryed wveguide routers with close chnnel spcing ( 2 GHz) tht is pproprite for OAWG 4. However, high-fidelity pulse shping in the line-y-line regime hs so fr een limited to devices sed on the more mture silic-sed technology, which relies on thermo-optic modultion nd is consequently slow. Full OAWG, including simultneous spectrl resolution t the com spcing nd modultion t the repetition rte, hs not yet een chieved. Line-y-line pulse shping hs een chieved for s mny s com lines spced y 5 GHz using trditionl diffrction grtings nd liquid-crystl sptil modultor 7. Line-y-line pulse shping hs lso een chieved with 32 nd 4 com lines using silic-sed rryed wveguide router pulse shper with resistive-heter-sed Mch Zehnder phse nd mplitude modultion for ech wvelength 6,33. Exmples of wveforms generted y oth techniques re shown in Fig. 5. Opticl ritrry wveform mesurement Methods for the full chrcteriztion of ultrshort-pulse fields re well-estlished 9,42 44, nd include self-referenced techniques such s frequency-resolved opticl gting nd spectrl shering interferometry (known s SPIDER in conventionl ultrfst optics 42 ) nd non-self-referenced techniques such s spectrl interferometry. However, the unique ttriutes of the fields generted y line-yline pulse shping led to new chllenges in wveform chrcteriztion. For exmple, these fields my exhiit % duty cycle, with shped wveforms spnning the full time-domin repetition period of the frequency com, spectrl mplitude nd phse chnging ruptly from line-to-line, nd lrge time ndwidth products. In contrst, conventionl methods for chrcterizing ultrshort pulse fields re typiclly used to mesure low-duty-cycle pulses tht re isolted in time nd hve smoothly vrying spectr nd reltively low time ndwidth product. These methods re gered towrds low spectrl resolution nd re not generlly comptile with the rpid spectrl chnges tht re hllmrk of line-y-line pulse shping. Severl efforts hve een mde to dpt ultrfst mesurement techniques for the chrcteriztion of sttic OAWG wveforms. For exmple, frequency-resolved opticl gting hs een dpted for mesuring reltively simple OAWG signls 45. Severl recent ppers focus on pplying frequency-domin ultrshort-pulse chrcteriztion pproches, such s spectrl interferometry nd spectrl shering interferometry, to OAWG signls, therey llowing prllel dt cquisition. Such techniques mesure spectrl phse through frequency-dependent interference with delyed uxiliry pulse. Conventionlly, the need to unmiguously retrieve oth qudrtures of the spectrl interference mens tht the dely must exceed the pulse durtion. However, for OAWG wveforms with intrinsiclly lrge time pertures, this results in very difficult spectrl resolution requirements. Accordingly, zerodely versions of these techniques, in which oth qudrtures of the interference signl re cquired seprtely, hve recently een implemented, therey relxing spectrl resolution requirements to the com spcing nd enling prcticl implementtion The Nture photonics doi:.38/nphoton.2.96 spectrl interferometry flvour of such mesurements hs een demonstrted to llow high-precision dispersion mesurements for fire spns of up to 5 km (ref. 48) orders of mgnitude greter thn the distnces over which interferometric mesurements of spectrl phse hve previously een chieved. A key point here is the use of frequency coms s the light source, s the periodicity nd long coherence time of com permits successful interferometry even with lrge dely imlnce etween the interferometer rms. Single-shot chrcteriztion of individul OAWG wveform frmes hs een chieved using spectrl interferometry pproches, which cn chieve the required high sensitivity ecuse they only use liner optics 46,49. This cpility will e needed for dynmic OAWG mesurement, in which wveforms will e updted on pulse-y-pulse sis, nd should enle oth the intensity nd phse of non-recurring trnsient events to e cptured in dvnced lightwve systems (not possile with tody s smpling-sed chrcteriztion methods). Demonstrtions of dynmic wveform mesurement 46,49 hve so fr relied on externl switching etween two different sttic wveforms, such s tht otined from two different sttic pulse shpers, rther thn on the true pulse-y-pulse updte of single shper. Time lens pproches, which mgnify the timescle of urst wveforms to durtions comptile with rel-time oscilloscope technology, hve lso een demonstrted for the single-shot cpturing of OAWG intensity profiles, ut not phse profiles 5,5. Finlly, rel-time mesurement over extended record lengths hs recently een demonstrted y opticl homodyne detection followed y high-speed digitiztion of in-phse nd qudrture field components similr to techniques now populr in stte-of-the-rt lightwve communictions receivers, ut extended to multiple overlpping wvelength nds using frequency com s the locl oscilltor 52. Applictions OAWG is still in its infncy, nd its pplictions re still mtter of specultion. Mny of the pplictions of trditionl pulse shping will enefit from the superior cpilities provided y OAWG. These include coherent control over quntum mechnicl processes such s ultrfst chemicl rections, the mnipultion of high-field lser mtter interctions such s the genertion of ttosecond pulses, nd photoniclly enled genertion nd processing of ultrrodnd rdiofrequency electricl signls. There my of course e new, unknown pplictions tht will e enled y the unique cpilities of OAWG. A recent exmple of coherent control is the cretion of high phse-spce density of polr molecules 53 using pir of continuous-wve lsers locked to the frequency com produced y mode-locked lser. OAWG techniques could llow the sme result to e chieved y directly producing the desired phse-coherent wveform, rther thn y using continuous-wve lser. Coherent control of cold ruidium toms using com of pulses shped through conventionl techniques hs lso een demonstrted 54. OAWG will dd new dimension to this control scheme y llowing the pulse shpe to chnge dynmiclly. OAWG my lso impct new high-sensitivity rodnd spectroscopy techniques sed on femtosecond com enhncement cvities 55 nd mssively prllel red-out 36 y llowing the genertion of interrogtion fields optimized for the detection of prticulr species. One possile ppliction of OAWG is in opticl communictions, where it enles the synthesis of terit-per-second signls y exploiting complex modultion formts such s qudrture mplitude modultion. This concept hs recently een demonstrted using sttic line-y-line shping to generte repeted wveforms 33. With the dvent of OAWG, in which the wveform cn e chnged for every pulse, it will ecome possile to trnsmit dt t terit-per-second rtes using single light source. The long 764 nture photonics VOL 4 NOVEMBER Mcmilln Pulishers Limited. All rights reserved.

6 Nture photonics doi:.38/nphoton.2.96 coherence times ssocited with frequency coms will enle new pproches for coherent detection y serving s the locl oscilltor t the receiver 56. Comined with trnsmitter tht utilizes OAWG, this pproch my led to significnt improvements in communiction ndwidth. OAWG trnsmitters my lso impct new concepts for crrier-phse-locked opticl communictions, where they re proposed to exploit interchnnel coherence to mitigte liner nd nonliner interference etween different wvelength chnnels 57,58. Light detection nd rnging (LIDAR) uses rodnd opticl wveforms to chieve high-precision distnce mesurements, with precision tht improves s the ndwidth increses. One common choice for such systems is to use wveforms with simple frequency sweep (or chirp), lthough this sweep must e very liner. The current stte-of-the-rt LIDAR systems re sed on sweeping the frequency of continuous-wve lser using self-heterodyne technique to chieve resolution of 86 nm t rnge of.5 m (ref. 59). Recent experiments tht simultneously exploited the opticl phse nd rdiofrequency timing coherence of pir of fire-lser-sed frequency coms hve demonstrted rnging precision down to 5 nm (ref. 6). Using OAWG, it should e possile to generte perfectly liner frequency sweep over greter ndwidth nd t higher chirp rte, yielding improved resolution nd fster updte for chirp-sed systems, or generte wveforms tht llow the designer to mnipulte the trde-off, or miguity function, etween rnge nd velocity resolution in com-sed lser rdr, much like trditionl rdr engineers select rdiofrequency wveforms sed on their miguity function performnce. A very specultive ppliction of OAWG is to implement the ides of synthetic perture rdr t opticl frequencies. In synthetic perture rdr, wveform is emitted nd the return signl recorded coherently while the trnsmitter nd receiver move long known trjectory (typiclly on n irplne or stellite) 6. Becuse the signl is recorded coherently, it is possile to numericlly produce n imge with resolution limited y the distnce trvelled rther thn the collection perture. Using OAWG, similr concept could e implemented t opticl frequencies, which would void the lrge lenses usully needed for producing highresolution imges. Outlook nd summry The ility to generte opticl ritrry wveforms hs ecome conceivle due to enling dvnces in the genertion of opticl frequency coms nd high-resolution spectrl dispersers. Although OAWG hs not yet een chieved, the intermedite gol of sttic line-y-line pulse shping hs lredy een demonstrted. OAWG will e demonstrted in the ner future, lthough proly for only smll numer of com lines. Such demonstrtion will trigger new pplictions, including the trnsltion of ides from the rdiofrequency domin to opticl frequencies. References. Ye, J. & Cundiff, S. T. Femtosecond opticl frequency com technology (Springer, 25). 2. Cundiff, S. T. & Ye, J. Femtosecond opticl frequency coms. 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7 progress rticle 4. Bek, J. H. et l. -GHz nd 2-GHz chnnel spcing high-resolution AWGs on InP. IEEE Photon. Tech. Lett. 2, (29). 42. Iconis, C. & Wlmsley, I. A. Spectrl phse interferometry for direct electricfield reconstruction of ultrshort opticl pulses. Opt. Lett. 23, (998). 43. Lepetit, L., Cheriux, G. & Joffre, M. Liner techniques of phse mesurement y femtosecond spectrl interferometry for pplictions in spectroscopy. J. Opt. Soc. Am. B 2, (995). 44. Treino, R. Frequency-resolved opticl gting: The mesurement of ultrfst lser pulses (Kluwer, 2). 45. Scott, R. P. et l. High-fidelity line y line opticl wveform genertion nd complete chrcteriztion using FROG. Opt. Express 5, (27). 46. Fontine, N. K., Scott, R. P., Heritge, J. P. & Yoo, S. J. B. Ner quntum-limited, single-shot coherent ritrry opticl wveform mesurements. Opt. Express 7, (29). 47. Mio, H. X., Leird, D. E., Lngrock, C., Fejer, M. M. & Weiner, A. M. Opticl ritrry wveform chrcteriztion vi dul-qudrture spectrl shering interferometry. Opt. Express 7, (29). 48. Suprdeep, V. R., Leird, D. E. & Weiner, A. M. Opticl ritrry wveform chrcteriztion vi dul-qudrture spectrl interferometry. Opt. Express 7, (29). 49. Suprdeep, V. R., Leird, D. E. & Weiner, A. M. Single shot mplitude nd phse chrcteriztion of opticl ritrry wveforms. Opt. Express 7, (29). 5. Bennett, C. V., Morn, B. D., Lngrock, C., Fejer, M. M. & Isen, M. 64 GHz rel-time recording using temporl imging. Conf. on Lsers nd Electro-Optics/Quntum Electronics nd Lser Science Conf. pper CTuA6 (28). 5. Foster, M. A. et l. Silicon-chip-sed ultrfst opticl oscilloscope. Nture 456, 8 84 (28). 52. Fontine, N. K. et l. Rel-time full-field ritrry opticl wveform mesurement. Nture Photon. 4, (2). 53. Ni, K. K. et l. A high phse spce density gs of polr molecules. Science 322, (28). Nture photonics doi:.38/nphoton Stowe, M. C., Cruz, F. C., Mrin, A. & Ye, J. High resolution tomic coherent control vi spectrl phse mnipultion of n opticl frequency com. Phys. Rev. Lett. 96, 53 (26). 55. Thorpe, M. J., Moll, K. D., Jones, R. J., Sfdi, B. & Ye, J. Brodnd cvity ringdown spectroscopy for sensitive nd rpid moleculr detection. Science 3, (26). 56. Lee, W., Izdpnh, H., Delfyett, P. J., Menendez, R. & Etemd, S. Coherent pulse detection nd multi-chnnel coherent detection sed on single lnced homodyne receiver. Opt. Express 5, (27). 57. Ellis, A. D. & Gunning, F. C. G. Spectrl density enhncement using coherent WDM. IEEE Photon. Tech. Lett. 7, (25). 58. Ymzki, E., Inuzuk, F., Yoneng, K., Tkd, A. & Kog, M. Compenstion of interchnnel crosstlk induced y opticl fier nonlinerity in crrier phselocked WDM system. IEEE Photon. Tech. Lett. 9, 9 (27). 59. Roos, P. A. et l. Ultrrodnd opticl chirp lineriztion for precision metrology pplictions. Opt. Lett. 34, (29). 6. Coddington, I., Swnn, W. C., Nendovic, L. & Newury, N. R. Rpid nd precise solute distnce mesurements t long rnge. Nture Photon. 3, (29). 6. Gens, R. & VnGenderen, J. L. SAR interferometry issues, techniques, pplictions. Int. J. Remote Sens. 7, (996). 62. Suprdeep, V. R., Hung, C. B., Leird, D. E. & Weiner, A. M. Femtosecond pulse shping in two dimensions: Towrds higher complexity opticl wveforms. Opt. Express 6, (28). Acknowledgements S.T.C. ws supported y NIST. A.M.W. ws supported in prt y the Nvl Postgrdute School under grnt N through the Ntionl Security Science nd Engineering Fculty Fellowship progrmme. Any opinions, findings, conclusions or recommendtions expressed in this puliction re those of the uthors nd do not necessrily reflect the views of the sponsors. Additionl informtion The uthors declre no competing finncil interests. 766 nture photonics VOL 4 NOVEMBER Mcmilln Pulishers Limited. All rights reserved.