Mid-infrared frequency comb based on a quantum cascade laser. Power. Carrier-envelope offset frequency. Modal gain (cm 1 )

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1 doi:1.138/nture116 Mid-infrred frequency com sed on quntum cscde lser Andres Hugi 1, Gustvo Villres 1, Stéphne Blser, H. C. Liu 3 &Jérôme Fist 1 Opticl frequency coms 1 ct s rulers in the frequency domin nd hve opened new venues in mny fields such s fundmentl time metrology, spectroscopy nd frequency synthesis. In prticulr, spectroscopy y mens of opticl frequency coms hs surpssed the precision nd speed of Fourier spectrometers. Such spectroscopy technique is especilly relevnt for the mid-infrred rnge, where the fundmentl rottionl virtionl nds of most light molecules re found. Most mid-infrred com sources re sed on down-conversion of ner-infrred, mode-locked, ultrfst lsers using nonliner crystls 3. Their use in frequency com spectroscopy pplictions hs resulted in n unequlled comintion of spectrl coverge, resolution nd sensitivity 4 7. Another mens of com genertion is pumping n ultrhighqulity fctor microresontor with continuous-wve lser 8 1. However, these coms depend on chin of opticl components, which limits their use. Therefore, to widen the spectroscopic pplictions of such mid-infrred coms, more direct nd compct genertion scheme, using electricl injection, is preferle. Here we present compct, rodnd, semiconductor frequency com genertor tht opertes in the mid-infrred. We demonstrte tht the modes of continuous-wve, free-running, rodnd quntum cscde lser 11 re phse-locked. Comining mode prolifertion sed on four-wve mixing with gin provided y the quntum cscde lser leds to phse reltion similr to tht of frequency-modulted lser. The com centre crrier wvelength is 7 micrometres. We identify nrrow drive current rnge with intermode et linewidths nrrower thn 1 hertz. We find com ndwidths of 4.4 per cent with n intermode stility of less thn or equl to hertz. The intermode et cn e vried over frequency rnge of 65 kilohertz y rdio-frequency injection. The lrge gin ndwidth nd independent control over the crrier frequency offset nd the mode spcing open the wy to rodnd, compct, ll-solid-stte mid-infrred spectrometers. Unlike the sitution in internd semiconductor lsers 1, modelocked opertion of typicl high-performnce, room-temperture quntum cscde lsers with emission of short single pulses is difficult to chieve ecuse the gin recovery time (t <.3 ps) is much shorter thn the time required y the pulse to complete one round-trip in the cvity (the round-trip time, t rt 5 64 ps), which defines the mode spcing. Such pulsed opertion hs so fr only een chieved t cryogenic tempertures 13 over locking ndwidth of 15 cm 1 t 77 K y incorporting n ctive region tht used digonl trnsition with very long upper-stte lifetime 14. Similrly, mode locking of ten modes hs lso een chieved t cryogenic temperture in terhertz quntum cscde lsers 15. It should e noted, however, tht the only requirement for com opertion in spectroscopy pplictions is the periodicity of the wveform t the round-trip frequency, not the genertion of highintensity pulses. Even though microcvity-sed frequency coms hve shown true com opertion with millihertz stility, their output is sometimes nerly unmodulted in time 16,17. In fct, ecuse the intensity of perfectly frequency-modulted lser is constnt, the power envelope of such em would not e pertured y the fst gin recovery of the quntum cscde lser nd the spectrum of such lser would lso e composed of eqully spced nd discrete spectrl lines. Furthermore, s in rdio communiction, frequency-modulted signl my e more roust to noise thn n mplitude-modulted signl. In ddition, constnt output power cn e preferle for liner spectroscopy pplictions, to void dditionl complexities cused y nonliner interctions. Nonliner effects in quntum cscde lsers, triggering the onset of multimode opertion, hve een studied in detil 18. As in internd lsers 19, sptil hole urning ws found to hve key role in the onset of multimode instilities. Two counterpropgting wves t frequencies v 1 nd v crete grting tht ets t frequency dv 5 v 1 v, trnsferring energy etween modes seprted y tht frequency difference. This gin mechnism is phse sensitive. In ddition, intersund trnsitions feture strong third-order opticl nonlinerities, x (3), due to the lrge opticl mtrix element etween the excited stte nd the empty lower sttes, llowing prmetric processes due to fourwve mixing. It is importnt to stress tht ecuse these processes re qusi-resonnt, the coupling etween the modes will occur with nontrivil phse dely. As shown schemticlly in Fig. 1, the result of Power Dispersed Fry Pérot modes Eqully spced modes generted y four-wve mixing Locked frequency com Com opertion Crrier-envelope offset frequency Modl gin (cm 1 ) , Locking rnge 1, 1,4 1,6 1,8 ) ω 1 + ω 3 = ω + ω 4 1) ω 1 = ω + ω 3 ω ω 1 ω 3 ω 4, 1, 5 5 1, Brod gin Nrrow gin Totl GVD rod gin GVD ctive region rod gin GVD ctive region nrrow gin GVD (fs mm 1 ) c Intensity (.u.) 1 nm (Hz) χ (3) 3 1,41 1,4 1,43 Figure 1 Opticl frequency com in quntum cscde lser., The dispersed Fry Pérot resontor modes lock to the eqully spced modes generted y four-wve mixing processes., Gin nd GVD simultions of nrrownd (dotted) nd rodnd (solid lines) quntum cscde lser. c, Mgnified view of the lser spectr t I 5 74 ma, mesured using highresolution Fourier trnsform infrred spectrometer (.6 cm 1, 78 MHz)..u., ritrry units. 1 Institute for Quntum Electronics, ETH Zurich, 893 Zurich, Switzerlnd. Alpes Lsers SA, 1 3 Mximilien-de-Meuron, 1 Neuchâtel, Switzerlnd. 3 Key Lortory of Artificil Structures nd Quntum Control, Deprtment of Physics, Shnghi Jio Tong University, Shnghi 4, Chin. 13 DECEMBER 1 VOL 49 NATURE 9 1 Mcmilln Pulishers Limited. All rights reserved

2 RESEARCH LETTER these nonlinerities will e prolifertion of modes due to degenerte nd non-degenerte four-wve mixing processes, in similr fshion to wht occurs in microcvity resontors 1. The ility to lock longitudinl modes is limited y the mteril group velocity dispersion (GVD). Our heterogeneous quntum cscde lser is expected to hve much lower GVD in comprison with conventionl devices 3. It opertes close to the zero-gvd point of our device, InGAs/InAlAs heterostructure grown on InP; the low doping of the ctive region nd the wveguide design decrese the contriution from these components. In ddition, s shown in Fig. 1, nd in contrst to conventionl quntum cscde lsers, the computed GVD hs rod minimum in the centre of the gin curve owing to the flt top shpe of the gin curve of the rodnd lser. The rodnd quntum cscde lser used in this work ws composed of three different sustcks nd operted t wvelength of round 7 mm. The lser spectr prtly displyed in Fig. 1c were mesured using high-resolution Fourier trnsform infrred spectrometer nd show single set of longitudinl modes extending over 1.1 mm, with no mesurle dispersion within the resolution (.6 cm 1, 78 MHz) of the spectrometer over the whole dynmic rnge (Supplementry Fig. 1). All instilities relted to multiple trnsverse modes cn e completely neglected. A selected set of spectr indicting the power per mode (etween 1 mw nd 3 mw) is displyed in Supplementry Fig.. The totl output power s function of current t uc is shown in Supplementry Fig.. The device switches to multimode opertion t I 5 46 ma, shortly ove threshold (I th 5 4 ma). The spectrum, which is initilly spred over dv 5 4 cm 1,rodens progressively to dv 5 3 cm 1 t the mximum current. To investigte to wht extent the modes re coupled, we first mesure the intermode et, tht is, the rdio-frequency spectrum of the intensity ner the round-trip frequency, n rt, using fst quntum-well infrred photodetector 4. Uncoupled modes (such s those originting from two free-running lsers driven in similr wy to our device) would generte spectrum with 5 1-MHz linewidth 5. In contrst, s shown in Fig., such mesurement performed just ove the onset of multimode opertion shows linewidth with full-width t hlf-mximum of only dn Hz. For this current, the spectrum is lredy dv 5 15 cm 1 wide nd contins 6 modes. This very nrrow intermode et is oserved over the current rnge I < ma. At higher tempertures (13 uc), this regime is more dominnt nd the com spns up to 6 cm 1 (4 modes) with n intermode et linewidth of # Hz. At current of $48 ma, the intermode et ruptly ecomes wider: dn < 48 khz. The intensity of the modultion of the lser output is never greter thn %, indicting mostly constnt mplitude. The rupt chnge in intermode et linewidth is lso reflected in the mplitude noise spectr shown in Supplementry Fig. 3. When the current is incresed to 5 ma, the spectrum spns,1 cm 1 nd the intermode et widens to dn, 5 khz. Aove 51 ma, the single nrrow intermode et splits into two distinct rodened peks spced y 14 MHz. The ssessment of the coherence properties of mode-locked lser is usully performed y n utocorreltion mesurement on nonliner crystl to revel the time structure of the opticl pulse. This technique cnnot e used in our cse, ecuse we do not expect the respective phses of the longitudinl modes to yield single opticl pulse with high pek intensity, suitle for nonliner optics. To gin Spectrum nlyser power (W) Power (dbm) Hz 14 Frequency (Hz) GHz Intensity interferogrm Scn 1 t ν rt Scn t ν rt QWIP is current (μa) c Simultion Mesurement Simultion Mesurement.4 Intensity interferogrm FM lser.6 intermode et interferogrm.8 Conventionl mode-locked intermode et interferogrm Normlized intensity (.u.) d Log normlized intensity (.u.) cm ,3 1,35 1,4 1,45 1,5 1,55 Intermode et spectrum Intensity spectrum Figure Intermode et spectroscopy., Nrrow intermode et, with full-width t hlf-mximum of,1 Hz t the onset of the multimode emission. The resolution ndwidth of the spectrum nlyser is set to 1 Hz., Intensity interferogrm nd intermode et interferogrms mesured in two successive scns seprted y 9 min, t 49 ma. The resolution ndwidth is 1 khz. QWIP, Quntum-well infrred photodetector. c, Comprison of the mesured intermode et interferogrm t 48 ma with two intermode et interferogrm simultions of perfectly frequency-modulted (FM) signl nd fundmentlly mode-locked lser. Inset, mgnified view of region t zero dely. d, Comprison of the intermode et spectrum, J (n rt,v), nd the intensity spectrum, J (,v), t n injection current of 5 ma. 3 NATURE VOL DECEMBER 1 Mcmilln Pulishers Limited. All rights reserved 1

3 RESEARCH insight into the respective phses nd coherence properties of the modes, we present here n interferometric technique wherey the utocorreltion of the intermode et is mesured using Michelson interferometer. The quntity mesured is Iðn,tÞ~ F jet ðþzeðtztþ ð1þ which is the solute vlue of the Fourier component of the intensity t the detector t frequency n over chosen resolution ndwidth of the spectrum nlyser. Here E denotes the time-dependent mplitude of the electric field nd F stnds for the Fourier trnsform tht is pplied to the resulting intensity. The norml intensity interferogrm mesured in Fourier trnsform infrred spectrometer is I(, t). In contrst to the intensity interferogrm, the intermode et interferogrm, I(n rt, t), is function of oth the mplitude nd the reltive phse of the modes. Furthermore, in nlogy with Fourier spectroscopy, the Fourier trnsform J ðn rt,vþ~f ðiðn rt,tþþ ðþ will yield the intermode et spectrum, which roughly indictes the spectrl regions contriuting to the intermode et. Figure shows two successive scns of I(n rt, t) cquired with resolution ndwidth of 1 khz t the round-trip frequency, mesured t 9-min intervls nd n injection current of 49 ma. These scns (lue nd red) re compred with the zero-frequency component I(, t) (green). Rndomly vrying phses would generte n intermode et interferogrm roughly proportionl to the zero-frequency component round zero time dely (Supplementry Fig. 4). In contrst, the mesured I(n rt, t) shows long-term stility with minimum t zero time dely, proving tht there is well-defined phse reltion etween the modes. The phse reltion cnnot e esily inferred from the mesurement of I(n rt, t), however. To help us do so, we compre the mesured I(n rt, t) to the respective signls predicted for purely frequency-modulted signl nd conventionl mode-locked lser (Fig. c; see Supplementry Fig. 5 for mesurement of n intermode et interferogrm of mode-locked fire lser). The phses re such tht the mplitude modultion of the signl is strongly dmped t zero dely (t 5 ), s it would e for frequency-modulted lser. In generl, the comprison emphsizes the frequency modultion chrcteristics of the output of the lser, s expected from the short lifetime of the excited stte. A minimum of the intermode et is lwys oserved for t 5 over ll injected currents, indicting tht the device never produces single pulses. To confirm further the frequencymodulted nture of the lser, we put sheet of polyethylene, which hs strong wvelength-dependent sorption, etween the lser nd the detector. This sheet cts s n opticl discrimintor tht cn convert the frequency modultion of the lser output to n mplitude modultion signl. As expected from frequency-modulted signl, we find tht the mplitude of the intermode et t the detector increses. This mplifiction fctor ws mesured to e The intermode et spectrum, J ðn rt,vþ, nd the intensity spectrum, J ð,vþ, re compred in Fig. d nd show tht the entire lser spectrum contriutes to the intermode et. Regrdless of the kilohertz intermode et linewidth, we hve com-like spectrum ecuse the mode spcing does not fluctute more thn the chosen resolution ndwidth of the spectrum nlyser over the whole lser spectrum. The mesurement of the whole rdio-frequency spectrum round n rt s function of t yields importnt informtion out the mechnisms tht destilize the com. An exmple of such chrcteristics is shown in Supplementry Fig. 6 t high current (I ma) where the intermode et hs two peks nd wide rdio-frequency spectrum. By further incresing the size of the region with low GVD, it should e strightforwrd to increse the com ndwidth. To chrcterize the com further, we did heterodyne et experiment etween com line nd single-mode distriuted-feedck quntum cscde lser (Supplementry Fig. 7). The inset of Fig. 3 shows the spectrum of the single-mode quntum cscde lser longside the com spectrum tht covers 6 cm 1 nd hs n intermode et linewidth of # Hz. Figure 3 shows the corresponding heterodyne signl. A nrrow linewidth of 1.3 MHz is mesured, which simply reflects the temperture nd current stility of our set-up. The incresed phse noise directly trnsltes into roder linewidth of out MHz in com-like spectr. Our mesurements show tht the low GVD, s well s the existence of nonlinerities, tends to lock the modes together. This locking cn lso e enhnced through rdio-frequency injection. Such injection locking hs lredy een successfully pplied to terhertz quntum cscde lser, enling the demonstrtion of pulsed mode-locked opertion. In our experiment, rdio-frequency power of 11 dbm is injected close to the round-trip frequency of 7.5 GHz, with n estimted injection loss of 34.5 db. The direct current is set to 494 ma. While Normlized intensity (.u.) DFB quntum-cscde-lser spectrum Quntum-cscde-lser com spectrum 6 cm 1 1,38 1,4 1,4 1, MHz Frequency (GHz) Figure 3 Linewidth mesurement nd rdio-frequency injection., Heterodyne et mesurement etween single-mode distriuted-feedck (DFB) quntum cscde lser nd quntum-cscde-lser com line. The inset shows the two spectr. The mesured heterodyne signl hs linewidth of 1.3 MHz. The resolution ndwidth is 5 khz nd the integrtion time is 5 ms., Heterodyne et mesurement of com-like line nd stle Heterodyne et (dbm) Heterodyne et frequency (MHz) 1,175 1,17 1,165 1,16 1,155 1,15 1,145 1,14 1,135 1,13 1,15 Intermode et (dbm) khz 11 MHz RF injection frequency (GHz) Frequency (GHz) single-mode quntum cscde lser while sweeping the rdio-frequency (RF) injection frequency round the cvity round-trip frequency. When sweeping cross the resonnce of the cvity round-trip, the heterodyne signl cn e shifted in frequency y 11 MHz. Inset, mesured intermode et t three different chrcteristic injection frequencies t resonnce. 13 DECEMBER 1 VOL 49 NATURE 31 1 Mcmilln Pulishers Limited. All rights reserved

4 RESEARCH LETTER sweeping the rdio frequency, we mesure the heterodyne et etween one com-like line nd the single-mode quntum cscde lser (Supplementry Fig. 7). Figure 3 shows the chnge in the heterodyne et position nd proves tht we re le to chnge the mode spcing ctively. The intermode et with rdio-frequency injection round resonnce is shown in the inset of Fig. 3. Unlike previous ttempts 6, our mesurements show the expected collpse of the intermode et t the round-trip frequency to the resolution of the spectrum nlyser. The round-trip frequency cn e vried over rnge of more thn 65 khz. There re pproximtely 167 modes etween the pek of the lser nd the mode tht ets with the single-mode quntum cscde lser. Chnging the round-trip frequency y 65 khz should therefore result in chnge of khz MHz in the heterodyne et signl, which grees with the mesured 11 MHz. It should e noted tht the crrier frequency offset cn e djusted y the injected direct current (Supplementry Fig. 7), wheres the mode spcing cn e set through the rdio-frequency injection. Therefore, it is possile to stilize quntum-cscde-lser frequency coms fully 7. However, s the injected rdio-frequency power is incresed to 6.6 dbm, the intermode et interferogrm resemles tht of fundmentlly mode-locked lser, nd, unlike the cse for 11 dbm, the intermode et spectrum shows tht only smll frction (18%) of the modes contriute to the injection-locked intermode et (Supplementry Fig. 8). We hve presented mid-infrred quntum-cscde-lser freerunning opticl frequency com covering 6 cm 1 (38 nm) t centre wvenumer of 1,43 cm 1 (7 mm). The mesured linewidth of the com lines is #1.3 MHz with nrrow intermode et linewidth of # Hz. At higher currents, we mesure com-like emission spectr tht spn 1 cm 1 nd hve roder intermode et linewidths (5 5 khz). Further mesurements using metrologicl techniques will give deeper insight into this system 8. We hve shown tht the crrierenvelope offset frequency s well s the repetition frequency cn e set independently y chnging the direct current nd through rdiofrequency injection. The phse signture of the com strongly resemles tht of frequency-modulted signl nd is stle over time. We identify the locking mechnism responsile for the formtion of the frequency com to e four-wve mixing. Key physicl properties of mterils used in quntum cscde lsers in frequency coms re therefore strong third-order opticl nonlinerities nd low GVD. Further investigtion of the GVD nd its sign is necessry 9. Altogether, this system offers remrkle freedom of design, ecuse it llows control over the electronic trnsitions, gin fltness, opticl nonlinerities nd dispersion through nd structure engineering. The ndwidth of mid-infrred quntum-cscde-lser frequency coms cn e improved through detiled understnding of the phse-locking mechnism nd y ppropritely engineering the GVD using wveguide design nd fcet cotings. The lrge ndwidth, in comintion with independent control over the crrier frequency offset nd the mode spcing, opens the wy to metrologicl nd sensing pplictions. Thus, the mid-infrred quntum-cscde-lser frequency com could ecome stndrd technology for rodnd, compct, ll-solid-stte mid-infrred spectrometers. METHODS SUMMARY Clcultion of the GVD. We include three contriutions to the GVD in our clcultions. First, the verticl nd lterl modl GVDs of the guided mode (GVD vert nd GVD lt ). GVD vert includes the dispersion of the doped lyers due to free-crrier sorption nd mteril dispersion. Second, the GVD due to the gin nd loss in the ctive region. These produce chnge in the refrctive index, Dn, clculted through Krmers Kronig reltions. The gin is clculted using softwre sed on density mtrix model extended to the whole structure, which lso includes second-order gin nd loss mechnism etween ll su-nd pirs 3. The totl losses re set to.5 cm 1. Becuse the rodnd ctive region is composed of three sustcks, ech individul stck is simulted gin including the loss introduced through cross-sorption. This tkes into ccount the inhomogeneous rodening of these devices. Third, we ccount for the GVD due to mteril dispersion. The totl GVD is clculted s sum of the individul terms weighted y the modl overlp. Intermode et spectroscopy set-up. Supplementry Fig. 9 shows the intermode et spectroscopy set-up. The lser light is collimted through n ntireflectioncoted ZnSe lens. The light psses through n ntireflection-coted qurter-wve plte to reduce the effect of feedck originting from reflections from opticl components. The light psses through Fourier trnsform infrred spectrometer (Bruker IFS66/S) nd is focused through n ntireflection-coted ZnSe lens on 8 mm 3 8 mm quntum-well infrred photodetector cooled to the temperture of liquid nitrogen. The Fourier trnsform infrred spectrometer is run in step-scn mode. At ech step, we record the rdio-frequency spectrum t the round-trip frequency of the lser. Concurrently, we record the intensity component of the interferogrm through the is current of the photodetector. Received 5 My; ccepted 5 Septemer Udem, T., Holzwrth, R. & Hänsch, T. W. Opticl frequency metrology. Nture 416, ().. Keilmnn, F., Gohle, C. & Holzwrth, R. Time-domin mid-infrred frequencycom spectrometer. Opt. Lett. 9, (4). 3. Adler, F. et l. Phse-stilized, 1.5 W frequency com t mm. Opt. Lett. 34, (9). 4. Johnson, T. A. & Diddms, S. A. Mid-infrred upconversion spectroscopy sed on Y:fier femtosecond lser. Appl. Phys. B 17, (1). 5. Foltynowicz, A., Bn, T., Msl / owski, P., Adler, F. & Ye, J. Quntum-noise-limited opticl frequency com spectroscopy. Phys. Rev. Lett. 17, 33 (11). 6. Adler, F., Thorpe, M. J., Cossel, K. C. & Ye, J. Cvity-enhnced directfrequency com spectroscopy: technology nd pplictions. Annu. Rev. Anl. Chem. 3, (1). 7. Vodopynov, K. L., Sorokin, E., Sorokin, I. T. & Schunemnn, P. G. Mid-IR frequency com source spnning mm sed on suhrmonic GAs opticl prmetric oscilltor. Opt. Lett. 36, (11). 8. Del Hye, P. et l. Opticl frequency com genertion from monolithic microresontor. Nture 45, (7). 9. Wng, C. Y. et l. Mid-infrred opticl frequency coms sed on crystlline microresontors. Preprint t (11). 1. Kippenerg, T. J., Holzwrth, R. & Diddms, S. A. Microresontor-sed opticl frequency coms. Science 33, (11). 11. Fist, J. et l. Quntum cscde lser. Science 64, (1994). 1. Derickson, D. J. et l. Short pulse genertion using multisegment mode-locked semiconductor lsers. IEEE J. Quntum Electron. 8, 186 (199). 13. Wng, C. Y. et l. Mode-locked pulses from mid-infrred quntum cscde lsers. Opt. Express 17, (9). 14. Fist, J. et l. Lser ction y tuning the oscilltor strength. Nture 387, (1997). 15. Brieri, S. et l. Coherent smpling of ctive mode-locked terhertz quntum cscde lsers nd frequency synthesis. Nture Photon. 5, (11). 16. Del Hye, P., Arcizet, O., Schliesser, A., Holzwrth, R. & Kippenerg, T. Full stiliztion of microresontor-sed opticl frequency com. Phys. Rev. Lett. 11, 5393 (8). 17. Ferdous, F. et l. Spectrl line-y-line pulse shping of on-chip microresontor frequency coms. Nture Photon. 5, (11). 18. Gordon, A. et l. Multimode regimes in quntum cscde lsers: from coherent instilities to sptil hole urning. Phys. Rev. A 77, 5384 (8). 19. Ymd, M. Theoreticl nlysis of nonliner opticl phenomen tking into ccount the eting virtion of the electron density in semiconductor lsers. J. Appl. Phys. 66, (1989).. Wlrod, D., Auyng, S. Y., Wolff, P. A. & Sugimoto, M. Oservtion of third order opticl nonlinerity due to intersund trnsitions in AlGAs/GAs superlttices. Appl. Phys. Lett. 59, (1991). 1. Rosencher, E. et l. Quntum engineering of opticl nonlinerities. Science 71, (1996).. Bnerjee, S. & Shore, K. A. MIR nd NIR nonliner opticl processing using intersund x (3) in triple quntum well structures. Semicond. Sci. Technol. 18, (3). 3. Prz, W. et l. Intersund gin-induced dispersion. Opt. Lett. 34, 8 1 (9). 4. Grnt, P. D., Dudek, R., Buchnn, M. & Liu, H. C. Room-temperture heterodyne detection up to 11 GHz with quntum-well infrred photodetector. IEEE Photon. Technol. Lett. 18, 18 (6). 5. Aellen, T. et l. Direct mesurement of the linewidth enhncement fctor y opticl heterodyning of n mplitude-modulted quntum cscde lser. Appl. Phys. Lett. 89, 9111 (6). 6. Soiel, A. et l. Active mode locking of rodnd quntum cscde lsers. IEEE J. Quntum Electron. 4, (4). 7. Telle, H. et l. Crrier-envelope offset phse control: novel concept for solute opticl frequency mesurement nd ultrshort pulse genertion. Appl. Phys. B 69, (1999). 8. Brje, D., Hollerg, L. & Diddms, S. Brillouin-enhnced hyperprmetric genertion of n opticl frequency com in monolithic highly nonliner fier cvity pumped y cw lser. Phys. Rev. Lett. 1, 1939 (9). 9. Herr, T. et l. Universl formtion dynmics nd noise of Kerr-frequency coms in microresontors. Nture Photon. 6, (1). 3 N AT U R E VO L D E C E M B E R 1 Mcmilln Pulishers Limited. All rights reserved 1

5 RESEARCH 3. Terzzi, R. & Fist, J. A density mtrix model of trnsport nd rdition in quntum cscde lsers. N. J. Phys. 1, 3345 (1). Supplementry Informtion is ville in the online version of the pper. Acknowledgements We thnk M. Quck nd E. Miloglydov for their help with the high-resolution Fourier trnsform infrred spectrometer mesurements, U. Keller nd V. Wittwer for providing scientific equipment, nd J. Khurgin for discussions. This work ws finncilly supported y the Quntum Photonics Ntionl Center of Competence in Reserch of the Swiss Ntionl Science Foundtion. H.C.L. cknowledges support from the Ntionl Mjor Bsic Reserch Projects (11CB9563) nd the Shnghi Municipl Mjor Bsic Reserch Project (9DJ141). Author Contriutions A.H. crried out the mesurements. Simultions nd ides were developed y A.H. nd J.F. G.V. contriuted to the heterodyne et mesurements s well s the mplitude noise mesurements. S.B. provided oth quntum cscde lsers. H.C.L. provided the quntum-well infrred photodetector. All the work ws done under the supervision of J.F. Author Informtion Reprints nd permissions informtion is ville t The uthors declre no competing finncil interests. Reders re welcome to comment on the online version of the pper. Correspondence nd requests for mterils should e ddressed to J.F. (jfist@ethz.ch) or H.C.L. (h.c.liu@sjtu.edu.cn). 13 DECEMBER 1 VOL 49 NATURE 33 1 Mcmilln Pulishers Limited. All rights reserved