Normal-dispersion Microcombs Enabled by Controllable Mode Interactions
Xiaoxiao Xue, Yi Xuan, Pei-Hsun Wang, Yang Liu, Dan E. Leaird, Minghhao Qi, Andrew M. Weiner
aa r X i v : . [ phy s i c s . op ti c s ] M a r Normal-dispersion Microcombs Enabled by Controllable Mode Interactions
Xiaoxiao Xue, ∗ Yi Xuan,
1, 2
Pei-Hsun Wang, Yang Liu, Dan E. Leaird, Minghhao Qi,
1, 2 and Andrew M. Weiner
1, 2, † School of Electrical and Computer Engineering, Purdue University,465 Northwestern Avenue, West Lafayette, Indiana 47907-2035, USA. Birck Nanotechnology Center, Purdue University,1205 West State Street, West Lafayette, Indiana 47907, USA.
We demonstrate a scheme incorporating dual coupled microresonators through which mode inter-actions are intentionally introduced and controlled for Kerr frequency comb (microcomb) generationin the normal dispersion region. Microcomb generation, repetition rate selection, and mode lockingare achieved with coupled silicon nitride microrings controlled via an on-chip microheater. Ourresults show for the first time that mode interactions can be programmably tuned to facilitatebroadband normal-dispersion microcombs. The proposed scheme increases freedom in microres-onator design and may make it possible to generate microcombs in an extended wavelength range(e.g., in the visible) where normal material dispersion is likely to dominate.
Microresonator-based Kerr frequency comb (micro-comb) generation is a promising technique with manyadvantages including very compact size, high repetitionrate, and (sometimes) wide bandwidth [1]. Many ap-plications can potentially benefit from this revolution-ary technique, such as optical communications [2], pho-tonic radio-frequency signal processing [3], and opticalclocks [4]. The initial stage of comb formation inside themicroresonator is triggered by modulational instabilitywhich is enabled by Kerr nonlinearity and group veloc-ity dispersion. Anomalous dispersion has been widelyexploited [5–17], while normal dispersion has often beenthought unsuitable for microcomb generation due to thelack of modulational instability on the upper branchof the bistable pump field in the normal dispersion re-gion [18–20]. Nevertheless, comb generation in normal-dispersion microresonators has by now been reported sev-eral times [21–29]. Normal-dispersion microcombs are ofparticular interest as normal dispersion is easy to accessin most nonlinear materials. It has been found that mod-ulational instability may occur in the normal dispersionregion with the aid of coupling between different familymodes [23, 27, 28, 30]. However, the mode interactionsemployed so far in a single microresonator are related toaccidental degeneracies associated with different spatialmodes and are hence very difficult to control and modify.In this letter, we demonstrate a novel scheme which forthe first time permits programmable and reliable controlof mode interactions to achieve repetition-rate-selectableand mode-locked combs from normal dispersion microres-onators.Figure 1(a) shows the microscope image of our devicewhich is based on the well-known coupled-microresonatorstructure [31, 32]. Two silicon nitride (SiN) microrings(main and auxiliary) are coupled to each other. Eachring is also coupled to its own bus waveguide, which al-lows either transmission measurements or pump injec-tion. Figure 1(b) shows the linear transmission curves ofthe two rings measured at room temperature by scan- (a)
MainAux. Heater
FIG. 1. Dual coupled silicon nitride microrings. (a) Mi-croscope image. The radii of the main and auxiliary ringsare 60 µ m and 58 µ m, respectively. An integrated micro-heater shifts the resonances of the auxiliary ring via thethermo-optic effect. (b) Linear transmission spectra measuredwith a low-power frequency scanning laser at the bus waveg-uide of either the main or auxiliary ring. The FSRs of themain and auxiliary rings are 378 GHz and 391 GHz, respec-tively. (c) FSR versus the relative mode number for the mainring. Mode 0 corresponds to the resonance around 191.9 THzwhich is marked in subplot (b) with × . The dispersion is β ≈
130 ps / km, which is extracted from the slope of theFSR curve in subplot (c). The jumps in FSR around mode − ning the frequency of a low-power laser. The cross-section of the waveguide from which the microrings areformed is 1 . µ m ×
600 nm. Unlike most on-chip mi-croresonators that have been used for comb generation,this waveguide dimension supports only single transversemode. The radii of the two rings are different (main:60 µ m; auxiliary: 58 µ m), corresponding to different freespectral ranges (FSRs) (main: 378 GHz; auxiliary: 391 H e a t e r p o w e r ( m W ) (a) 193.38 193.39 193.4 193.41150200250 Frequency (THz)193.76 193.77 193.78 193.79 T r a n s m i ss i o n ( a . u . ) H e a t e r p o w e r ( m W ) (b) 193.38 193.39 193.4 193.41150200250 Frequency (THz)193.76 193.77 193.78 193.79 T r a n s m i ss i o n ( a . u . ) FIG. 2. Transmission spectra versus heater power, showing that the resonances can be selectively split. (a) Auxiliary ring; (b)main ring. Three consecutive resonances are shown. The thermal tuning efficiency of the auxiliary ring is −
600 MHz / mW, whilethe main ring shifts only slightly at a rate of −
30 MHz / mW. By changing the heater power, the strongest mode interactionmoves from one resonance to the next. GHz). Figure 1(c) shows the FSR of the main ring versusthe relative mode number measured by using frequencycomb assisted spectroscopy [33]. The dispersion is de-termined from the slope of the curve and is given by D / (2 π ) ≈ −
16 MHz, where the D parameter signifiesthe change in FSR from one pair of resonances to thenext [13, 16]. This corresponds to β ≈
130 ps / km andis clearly in the normal dispersion regime.It can be observed in Fig. 1(c) that the approximatelylinear variation of the FSR curve is disturbed aroundmode −
6. This is a signature of coupling between themodes of the two rings when their resonant frequenciesare close to each other [28, 30, 33] (see the mode cross-ing area around 189.5 THz in Fig. 1(b)). The reso-nances of the auxiliary ring can be thermally shifted viaa microheater. Figures 2(a) and 2(b) show the zoomed-in transmission spectra versus the heater power for theauxiliary ring and the main ring, measured at their re-spective bus waveguides. The thermal shifting efficiencyof the auxiliary ring is −
600 MHz / mW. The resonancesof the main ring are also shifted slightly ( −
30 MHz / mW)as no special efforts were made to optimize the thermalisolation. The resonances in the mode crossing regionare split due to the coupling between the rings, a be-havior similar to that in quantum mechanical perturba-tion theory [34]. The two new resonances evident in thetransmission spectra push each other leading to avoidedcrossings. The effect of mode interaction decreases for heater powers at which the (unperturbed) resonant fre-quencies of the main ring and auxiliary ring are furtherseparated. Away from the mode-crossing region, one ofthe resonant features disappears from the transmissionspectrum; the remaining resonance recovers to the casewith nearly no mode coupling. Naturally, which reso-nant feature remains outside of the mode-crossing regiondepends on whether the spectrum is measured from theupper or lower bus waveguide. By changing the heaterpower, we are able to selectively split and shift an indi-vidual resonance.Denote the field amplitude in the main and auxiliaryrings a and a with time dependences exp ( jω t ) andexp ( jω t ), respectively. The fields obey the followingcoupled-mode equations [35, 36]d a d t = (cid:18) jω − τ (cid:19) a + jκ a , (1)d a d t = (cid:18) jω − τ (cid:19) a + jκ a , (2)where 1 /τ , 1 /τ are the decay rates of the main andauxiliary ring, respectively; κ = κ ∗ = κ is the couplingrate. τ and τ are related to the loaded cavity qualityfactors ( Q ’s) by Q = ω τ / Q = ω τ / FIG. 3. Resonant frequencies, measured at the bus waveguideattached to the main ring or to the auxiliary ring, respectively,in the mode-splitting region around 193.77 THz. Branch “b1”is red shifted, while branch “b2” is blue shifted with respectto the resonant frequencies assuming no mode coupling (thegray dashed lines, derived through linearly fitting the resonantfrequencies versus the heater power in the region away fromthe mode splitting area).
The eigenvalues of Eqs. (1) and (2) are jω ′ , where ω ′ , = ω + ω j (cid:18) τ + 1 τ (cid:19) ± s(cid:20) ω − ω j (cid:18) τ − τ (cid:19)(cid:21) + | κ | . (3)The real parts of ω ′ , are the new resonant frequenciesaffected by mode coupling, and the imaginary parts arethe decay rates. Figure 3 shows the resonant frequen-cies of the main and auxiliary rings in the mode-splittingregion around 193.77 THz. Also shown are the calcu-lated results with Q = 7 . × , Q = 3 . × , and κ = 1 . × s − . Here the Q ’s are extracted fromthe linewidths of the transmission resonances measuredaway from the mode-crossing region, while κ is adjustedto fit the data of Fig. 3. The agreement between calcula-tion and measurement is excellent. Note that the curvesacquired by measuring the transmission at either the topor bottom waveguide agree essentially perfectly, whichis expected since in either case we are probing the samehybridized resonances. One of the hybridized resonancesis red shifted (branch “b1”) with respect to the originalresonances assuming no mode splitting, while the other isblue shifted (branch “b2”). In comb generation, the res-onance shifts play a key role in creating phase matchedconditions enabling modulational instability.For comb generation, the pump laser is slowly tunedinto resonant mode 0 of the main ring from the blueside. In this process, the intracavity pump field stayson the upper branch of the bistability curve where mod-ulational instability is absent in a normal-dispersion mi-croresonator undisturbed by mode interactions [18–20].With our coupled-microring scheme, interactions are in-tentionally introduced and controlled by thermally tun- ing the auxiliary ring to facilitate comb generation. Atthe initial stage of comb formation, essentially only threeresonant modes are involved: the pumped mode ω andthe two sideband modes ω ± µ where new frequency com-ponents first start to grow. The effect of dispersion cor-responds to unequal distances between these three modes( ω µ − ω = ω − ω − µ ). Define the resonance asymmetryfactor by ∆ ω = ω µ − ω − ( ω − ω − µ ) which is a gener-alization of the D parameter to a form relevant to mod-ulational instability at the ± µ th resonant modes. Notethat positive ∆ ω corresponds to an anomalous disper-sion, for which modulational instability may occur, whilenegative ∆ ω corresponds to normal dispersion. By se-lectively splitting one of the sideband modes − µ or µ , theasymmetry factor may be changed so that an equivalentanomalous dispersion is achieved (∆ ω becomes positive)involving the blue shifted sideband mode (branch “b2”in Fig. 3). Modulational instability thus becomes pos-sible, leading to generation of initial comb lines. Morecomb lines can be generated through cascaded four-wavemixing resulting in a broadband frequency comb.Note that the equivalent dispersion achieved with ourscheme is different from the general microresonator dis-persion which is represented to the first order by anFSR change linear in mode number. As pointed outabove, splitting and shifting of just one resonance isenough for the modulational instability to occur; thisis distinct from the usual smooth change of FSR overa series of resonant modes. As a result our scheme iseasy to implement and offers an alternative to widebanddispersion engineering [8, 37]. The equivalent disper-sion is related to the resonance asymmetry factor by β , eff = − n ∆ ω/ (cid:0) π c · µ FSR (cid:1) where n is the refrac-tive index, c the speed of light in vacuum, and FSR isthe FSR (Hz) at ω . For the dual coupled SiN microringswe employed, the resonance shifts due to mode splittingcan be several GHz. When µ = 1, this corresponds to anequivalent dispersion change on the order of 10 ps / km,which is very difficult to achieve by tailoring the microres-onator geometry [8, 37]. The large equivalent dispersionmakes it possible to directly generate 1-FSR combs as thepeak frequency of modulational instability gain is inverseto the dispersion [18, 20]. This may prove especially use-ful for large microresonators with small FSRs [28], wherewithout mode interactions achieving direct 1-FSR combgeneration is difficult. Direct generation of 1-FSR combsoffers the advantage of easy to access phase locked states[13, 21, 22, 25].By controlling the mode interaction location, the initialcomb lines can be selectively generated at specified res-onances, giving rise to a repetition-rate-selectable comb.Figure 4 shows the results when the off-chip pump poweris 1 W (0.5 W on chip). The comb repetition rate is tunedfrom 1-FSR ( ∼
378 GHz) to 6-FSR ( ∼ .
27 THz) whilemaintaining a similar comb spectral envelope. All thecombs exhibit low intensity noise (below our experimen- R e l a t i v e po w e r ( d B / d i v ) FIG. 4. Repetition rate selectable comb. The laser pumpsmode 0 of the main ring (marked with × ) and the frequencyis fixed after tuning into the resonance. The off-chip pumppower is 1 W (0.5 W on chip). The auxiliary ring is ther-mally tuned to facilitate comb generation. The heater poweris 108 mW (1-FSR), 95 mW (2-FSR), 68 mW (3-FSR), 44 mW(4-FSR), 20 mW (5-FSR), and 0 mW (6-FSR), respectively.The frequencies at which strong mode interactions occur aremarked with ▽ . tal sensitivity) directly upon generation. High coherenceis thus anticipated [21, 22].Mode-locking transitions, in which the comb firstshows high intensity noise and then transitions to a low-noise state, are also observed. Figure 5 shows the re-sults with 1.8 W off-chip pump power. The strongestmode interaction is experienced by the first mode to thered side of the pump. By changing the heater power,the spectrum first shows no comb (Fig. 5(a) I and Fig.5(b) I), then a 1-FSR comb which at this pump poweris generated with high intensity noise (Fig. 5(a) II, IIIand Fig. 5(b) II, III). By further optimizing the heaterpower, the comb intensity noise suddenly drops below theequipment level (Fig. 5(a) IV and Fig. 5(b) IV). The low-noise comb is relatively broad with a 10-dB bandwidthof around 15 THz (120 nm). To further verify the mode-locked state of the comb, a fraction of the comb spectrumis selected and phase compensated line-by-line by usinga pulse shaper in the lightwave C+L band. The auto-correlation trace of the compressed pulse, shown in Fig.5(c), is in good agreement with the calculated result as-suming ideal phase compensation (autocorrelation width200 fs, corresponding to 130-fs pulse width). The abilityto fully compress to a transform-limited pulse suggestshigh coherence of the low-noise comb [21].In summary, we have demonstrated a novel scheme in-corporating coupled microresonators for Kerr frequencycomb generation in the normal dispersion region. The dy-namics of comb formation can be controlled by adjustingthe interactions between the microresonators. Repetitionrate selection and broadband mode-locking transitionsare achieved with coupled SiN microrings. By incorpo- (a) I II R e l a t i v e po w e r ( d B / d i v ) III
180 190 200 210
Frequency (THz) IV Shapingrange
ESA background Comb intensity noise(b) I II R e l a i v e po w e r ( d B / d i v ) III
Frequency (GHz) IV -4 -3 -2 -1 0 1 2 3 4 Measured Calculated A u t o c o rr e l a t i on ( a . u . ) Delay (ps)(c)
FIG. 5. Mode-locking transition in the normal dispersion re-gion with dual coupled microrings. The laser pumps mode 0of the main ring. The off-chip pump power is 1.8 W (0.9 W onchip). (a) Comb spectra when the heater power is 98 mW (I),109 mW (II), 115 mW (III), and 118 mW (IV), respectively.(b) Corresponding comb intensity noise. ESA: electrical spec-trum analyzer. (c) Autocorrelation of the transform-limitedpulse after line-by-line shaping. The lines in the lightwaveC+L band are shaped. The pump line is suppressed by 10dB to increase the extinction ratio of the compressed pulse. rating a microheater to tune the dual rings into resonanceand avoiding accidental degeneracies associated with few-moded waveguides, our scheme shows for the first timea reliable design strategy for normal-dispersion micro-combs. As normal dispersion is easy to access in mostnonlinear materials, the proposed scheme facilitates mi-crocomb generation and is of particular importance inwavelength ranges (e.g., the visible) where the materialdispersion is likely to dominate.This work was supported in part by by the Air ForceOffice of Scientific Research under grant FA9550-12-1-0236 and by the DARPA PULSE program through grantW31P40-13-1-0018 from AMRDEC. ∗ [email protected] † [email protected][1] T. J. Kippenberg, R. Holzwarth, and S. A. Diddams,Science , 555 (2011).[2] J. Pfeifle et al. , Nature Photon. , 375C (2014).[3] X. Xue et al. , J. Lightwave Technol. , 3557 (2014).[4] S. B. Papp et al. , Optica , 10 (2014).[5] P. Del’Haye et al. , Nature , 1214 (2007).[6] J. S. Levy et al. , Nature , 37 (2010). [7] L. Razzari et al. , Nature , 41 (2010).[8] A. A. Savchenkov et al. , Nature Photon. , 293 (2011).[9] M. A. Foster et al. , Opt. Express , 14233 (2011).[10] Y. Okawachi et al. , Opt. Lett. , 3398 (2011).[11] S. B. Papp and S. A. Diddams, Phys. Rev. A , 053833(2011).[12] I. Grudinin, L. Baumgartel, and N. Yu, Opt. Express , 6604 (2012).[13] T. Herr et al. , Nature Photon. , 480 (2012).[14] C. Wang et al. , Nature Comm. , 1345 (2013).[15] S. Saha et al. , Opt. Express , 1335 (2013).[16] T. Herr et al. , Nature Photon. , 145 (2014).[17] P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams,Phys. Rev. Lett. , 043905 (2014).[18] M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Com-mun. , 401 (1992).[19] S. Coen and M. Haelterman, Phys. Rev. Lett. , 4139(1997).[20] T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A , 023819 (2013).[21] F. Ferdous et al. , Nature Photon. , 770 (2011).[22] P.-H. Wang et al. , Opt. Express , 29284 (2012). [23] A. A. Savchenkov et al. , Opt. Express , 27290 (2012).[24] A. Coillet et al. , IEEE Photonics J. , 6100409 (2013).[25] P.-H. Wang et al. , Opt. Express , 22441 (2013).[26] W. Liang et al. , Opt. Lett. , 2920 (2014).[27] X. Xue et al. , arXiv:1404.2865v4.[28] Y. Liu et al. , Optica , 137 (2014).[29] S.-W. Huang et al. , Phys. Rev. Lett. , 053901 (2015).[30] S. Ramelow et al. , Opt. Lett. , 5134 (2014).[31] M. A. Popovi´c, C. Manolatou, and M. R. Watts, Opt.Express , 1208 (2006).[32] C. M. Gentry, X. Zeng, and M. A. Popovi´c, Opt. Lett. , 5689 (2014).[33] P. Del’Haye et al. , Nature , 529 (2009).[34] L. D. Landau and E. M. Lifshitz, Quantum mechanics:nonrelativistic theory (3rd ed) (Butterworth-Heinemann,2003).[35] H. A. Haus and W. Huang, Proceedings of the IEEE ,1505 (1991).[36] L. Novotny, Am. J. Phys. , 1199 (2010).[37] J. Riemensberger et al. , Opt. Express20