Abstract

Phase coherently linking optical-to-radio frequencies with femtosecond mode-locked laser frequency combs has enabled counting the cycles of light and is the basis of optical clocks, absolute frequency synthesis, tests of fundamental physics, and improved spectroscopy. Using an optical microresonator frequency comb to establish a coherent link between optical and microwave frequencies will extend optical frequency synthesis and measurements to areas requiring compact form factor, on-chip integration, and comb line spacing in the microwave regime, including coherent telecommunications, astrophysical spectrometer calibration, or microwave photonics. Here we demonstrate a microwave-to-optical link with a microresonator. By using a temporal dissipative single soliton state in an ultrahigh-Q crystalline microresonator that is broadened in highly nonlinear fiber, an optical frequency comb is generated that is self-referenced, allowing us to phase coherently link a 190 THz optical carrier directly to a 14 GHz microwave frequency. Our work demonstrates that precision optical frequency measurements can be realized with compact high-Q microresonators.

© 2015 Optical Society of America

1. INTRODUCTION

The development of the optical frequency comb (OFC) based on femtosecond pulsed mode-locked lasers [13] in conjunction with nonlinear spectral broadening constituted a dramatic simplification over large-scale harmonic frequency chains [4]. In the frequency domain, OFCs give equidistant optical lines, where the frequency of each component obeys fn=n·frep+f0. The spacing between the lines is determined by the pulse repetition rate of the laser frep (n being an integer). Knowledge of the comb’s overall offset frequency f0 (also referred to as the carrier envelope offset frequency) along with frep and n allows linking the optical frequency fn to the electronically countable frequency frep and f0 in the radio frequency or microwave domain. In this way the measurement of frep and f0 corresponds to counting the cycles of light. Self-referencing of the comb, i.e., a self-contained measurement of f0 and frep, has been achieved using nonlinear interferometers, whereby the comb’s bandwidth needs to be broadened to encompass typically two-thirds of or a full octave [58]. This measurement is a key prerequisite for many applications of OFCs. For example, referencing one of the comb lines of an OFC to an atomic frequency standard [9] allows the comb to function as a “gearbox,” realizing the next generation of atomic clocks based on optical transitions. Self-referenced frequency combs can also be used for optical frequency synthesis, and have enabled the most accurate frequency measurements [10,11]. Frequency combs with large mode spacings (10GHz), which are challenging to obtain via mode-locked lasers [12], can be used in a growing number of applications, including astronomical spectrometer calibration [13], dual-comb coherent Raman imaging [14], high-speed optical sampling or coherent telecommunications [15]. In each of these applications, having a line spacing 10GHz is either beneficial or even required.

Different from mode-locked lasers, microresonator frequency combs (MFCs) [16,17] are generated using parametric frequency conversion [18,19], of a continuous-wave (CW) laser. This approach exhibits several attractive features that have the potential to extend further the use of OFCs to new areas in precision optical measurement, spectroscopy, astronomy, telecommunications, and industrial applications. Fundamentally different from mode-locked laser systems, MFCs offer high repetition rates (>10GHz), compact form factors, broadband parametric gain that can be generated in wavelength regimes ranging from the visible [20] to the mid-infrared [21,22], CMOS-compatible microresonator platforms, and high power per comb line. Some unique characteristics of MFCs are that the pump laser constitutes a comb line and that there is no active laser gain medium in the system. These properties have encouraged in recent years the intense investigation of microresonator-based frequency combs with the ultimate goal of realizing a self-referenced system. Progress in recent years includes new microresonator platforms in crystalline materials [23], fused silica microtoriods [16], and photonic chips (based on silicon nitride [24,25], aluminum nitride [26], Hydex, [27,28] and diamond [29]). In addition, MFCs without self-referencing have been used for coherent telecommunications [15], compact atomic clocks [30], stabilized oscillators [31], and optical pulse generation [3234]. The dynamics of microresonator frequency combs have been investigated, and regimes with low noise frequency comb operation have been identified based on intrinsic low phase noise regimes, or via tuning mechanisms such as δΔ matching [35], parametric seeding [36], and injection locking [36,37], or via the observation of phase locking [33]. Moreover recently, low noise frequency combs have been generated via temporal dissipative soliton formation [34,3840] and numerical tools to simulate comb dynamics emerged based on the Lugiato–Lefever equation [4143] and the coupled-modes equation [34,44].

However, despite the rapid progress in understanding, simulations, applications, and platforms, there is a milestone that has not yet been reached: a self-referenced microresonator system, capable of phase coherently linking the microwave and the optical frequency domain. So far, knowledge of the absolute frequency of all comb lines of a MFC has been achieved only by using an auxiliary self-referenced fiber laser frequency comb as a Ref. [45], as well as via locking of two comb teeth to a rubidium transition [30]. Self-referencing, however, has never been achieved. One reason for this is the high repetition rate of the microresonators, leading to correspondingly low pulse peak intensities. This makes external spectral broadening using nonlinear fiber, which is widely employed in mode-locked lasers, difficult to apply. While octave spanning combs [46,47] have been attained directly from MFCs, they have not been suitable for self-referencing techniques due to excess noise associated with subcomb formation [35].

Here, we demonstrate a coherent microwave-to-optical link using temporal dissipative soliton formation in a crystalline microresonator in conjunction with external spectral broadening, measuring simultaneously both frep and f0, which are necessary for linking the optical to the radio frequency domain. Our approach uses the newly discovered class of temporal dissipative cavity solitons in microresonators [34,39,48,49] and marks the first time that the carrier envelope offset frequency of such a soliton has been measured, to our knowledge. Our results demonstrate that MFCs generated by soliton formation are suitable for absolute frequency measurements. In particular, the pulse-to-pulse timing jitter is sufficiently low to enable precise measurement of the carrier envelope offset frequency via self-referencing. Although not demonstrated here, it has already been shown that microresonator comb parameters frep and f0 can be stabilized by controlling the pump laser frequency and by actuating the resonator free spectral range (FSR) by heating or mechanical stress [45,50].

2. EXPERIMENT AND RESULTS

Optical microresonators support different azimuthal optical whispering gallery modes (WGMs). The FSR between modes of a particular mode family is determined by material and geometric dispersion. It has been shown that WGMs can have quality factors exceeding 1010 [51,52]. When a CW pump laser is coupled to a WGM, the resonator’s Kerr nonlinearity can lead to efficient nonlinear frequency conversion. The resonator used in this work is a crystalline ultrahigh-Q resonator made by polishing crystalline MgF2 [5355] (see Fig. 1), and can support WGMs [51] confined in one of the protrusions that extend around the circumference of the resonator. The mode used has a quality factor of 109 and a FSR of 14.0939 GHz. Light from a CW fiber laser at 1553 nm with 150mW can be coupled into and out of the resonator via evanescent coupling using a tapered optical fiber [56]. To form the solitons in the cavity, the pump laser’s frequency is scanned over the resonance and stopped when the appropriate conditions are met [34]. The duration of the pulse inside the resonator depends mainly on the coupling and detuning of the pump laser to the resonator mode, and can be estimated from the bandwidth of the spectrum shown in Fig. 1, to be 130fs. The optical spectrum generated by the soliton is not yet sufficiently broad for self-referencing; however, the spectrum can be broadened via supercontinuum generation [57].

 figure: Fig. 1.

Fig. 1. Crystalline MgF2 microresonator and temporal dissipative soliton generation. (a) Optical image of the employed ultrahigh-Q crystalline whispering gallery optical microresonators on a magnesium fluoride pillar with a diameter of several millimeters. The ultrahigh-Q whispering gallery optical modes are confined in the fabricated protrusions that extend around the circumference. The top resonator was used in the experiments and the mode of interest has a FSR of 14.0939 GHz and a loaded Q109. (b) The hyperbolic-secant shaped spectrum (fit: red dotted line) of the single temporal soliton produced inside the resonator by the CW pump laser. The inset shows the ability to resolve the microresonator comb lines on a grating-based spectrometer.

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The experimental setup after the resonator is shown in Fig. 2. A portion of the pulse train produced by the resonator is sent to an optical spectrum analyzer (OSA). The rest of the pulse train then has the CW background, which consists of the residual pump laser [34] minimized by fiber optic filters. Then another small amount is sent to a photodetector and an electronic spectrum analyzer (ESA) to detect frep. The pulse is then preamplified with an erbium-doped fiber amplifier (EDFA). The main type of fiber in the experiment is SMF28, which has anomalous group velocity dispersion in the wavelength range of the soliton. Before being sent into a high power EDFA, the soliton pulse is prechirped using dispersion compensating fiber (DCF), which has normal group velocity dispersion, to minimize nonlinear effects in the EDFA. In this way the average power of the pulse train is increased to 2 W. After the EDFA, the pulse is recompressed using SMF28 fiber via the cut-back method to a duration of 300fs with an energy of 150pJ. This pulse is subsequently sent through approximately 2 m of highly nonlinear fiber (HNLF) (Menlo Systems), where supercontinuum generation occurs. The resulting spectrum can be seen in Fig. 3. The blue trace shows the soliton spectrum after the optical microresonator, and the red after the HNLF fiber. The latter spectrum exceeds two-thirds of an octave, which is sufficient for self-referencing via a 2f3f interferometer [58]. Importantly, the broadened spectrum is coherent. This is verified by using a heterodyne beat with additional external lasers at the two ends of the comb, as detailed below. Figure 3(b) shows a zoom into the spectrum taken after the HNLF fiber, where the individual comb lines are clearly visible, even with the limited resolution of the OSA (0.02 nm).

 figure: Fig. 2.

Fig. 2. Experimental setup and 2f3f microresonator self-referencing scheme. (a) The frequency domain picture showing the relevant frequency components used to self-reference the comb and to determine the carrier envelope offset frequency (f0). (b) The simplified experimental setup used for self-referencing. A portion of the solitons that are outcoupled from the resonator are sent to an OSA to measure the spectrum, then residual pump light is filtered out using fiber optic filters before a portion is picked off and sent to a photodetector (PD) to measure the repetition rate on an ESA. The pulse is first preamplified in an EDFA and then prechirped to temporally broaden it with a DCF before being amplified by a high-power EDFA. The pulse is subsequently recompressed and coupled into a HNLF where the coherent supercontinuum is generated. A fraction of the spectrum is mixed with light from the 1908 nm thulium fiber laser and sent through a 1908 nm bandpass filter to a PD and ESA to measure Δ1908. The same is done with the 1272 nm external cavity diode laser to measure Δ1272 and a servo loop is used to phase lock the laser to the optical frequency comb and fix Δ1272 where a signal from an atomic clock is used as a reference. To create the 2f3f interferometer light from the 1272 nm laser is frequency doubled in a periodically poled lithium niobate crystal (PPLN) to produce light at 636 nm. Light from the 1908 nm laser is frequency doubled to 954 nm in a PPLN crystal, and subsequently combined with 1908 nm and sent through a PPLN crystal phase matched for sum frequency generation, creating light at 636 nm. The generated visible light is optically heterodyned on a PD with the frequency doubled light from the 1272 nm laser, permitting us to measure Δ2f3f on an ESA. This offset frequency is fixed by phase locking the 1908 nm laser via the 2f3f interferometer. With this scheme the carrier envelope frequency is measured by recording Δ1908.

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 figure: Fig. 3.

Fig. 3. Optical spectrum of the microresonator before and after external broadening. (a) The blue trace shows the optical spectrum generated in the crystalline optical microresonator by the temporal dissipative soliton state. The large central spike originates from residual light from the pump laser. The spectrum after the supercontinuum generation is denoted in red. It is composed of data taken from two different OSAs as result of the limited bandwidth of the individual instruments. (b) Zoom into the broadened spectrum revealing the widely spaced comb lines. (c) Heterodyne beatnote of a laser at 1272 nm with the broadened comb demonstrating a SNR exceeding 40 dB in the resolution bandwidth (RBW) of 300 kHz. (d) Heterodyne beatnote at the long wavelength end of the comb at 1900 nm (RBW 100 kHz).

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Self-referencing is achieved by measuring frep and f0 of the generated frequency comb. By picking off a small portion of the light after it leaves the resonator and sending it to a photodetector, frep can be directly measured (see Fig. 2). The broadened spectrum is sufficiently wide and allows employing a 2f3f interferometer [5] to determine f0. This is traditionally implemented by frequency tripling a component of the low-frequency part of the spectrum fL=n·frep+f0 using a combination of second-harmonic and sum-frequency generation to give 3fL=3n·frep+3f0, where n is an integer. In addition, a component of the higher frequency part of the spectrum fH=m·frep+f0 is frequency doubled using second-harmonic generation to give 2fH=2m·frep+2f0, where m is an integer. Mixing the doubled and the tripled light and detection on a photodetector gives the offset frequency 3fL2fH=f0, granted 3n=2m, i.e., necessitating a spectrum that covers two-thirds of an octave. Here a scheme involving two transfer lasers is implemented, which has the advantage of allowing independent verification of the coherence of the supercontinuum generation at the two ends of the spectrum. The coherence of the generated broadband OFC is verified by optically heterodyning the two reference lasers at 1272nm (external cavity diode laser) and 1908nm (thulium fiber laser) with the supercontinuum and detecting the optical heterodyne beat signal on a photodetector (see Fig. 3). The beatnote frequencies can be written in terms of the frequency comb parameters and an offset as

f1272=n·frep+f0+Δ1272
and
f1908=m·frep+f0Δ1908,
where n and m are integers and Δ1272 and Δ1908 are the frequency offsets (>0) of the transfer lasers from the generated OFC (see Fig. 3). The offset frequencies Δ1272 and Δ1908 are chosen to both be positive by convention. The 2f3f interferometry is constructed with reference lasers in which one arm of the interferometer serves for second-harmonic generation of light at 1272 nm to give light at 636 nm, written as (see Fig. 2)
2f1272=2n·frep+2f0+2Δ1272.
The other interferometer arm serves for frequency tripling of the light at 1908 nm via second-harmonic generation to create light at 954 nm followed by sum-frequency generation of the 954 and 1908 nm light to give light at 636 nm, and the frequency can be written as
3f1908=3m·frep+3f03Δ1908.
The doubled light and tripled light are mixed and detected on a photodetector, giving an optical heterodyne signal at the difference frequency:
Δ2f3f=2f12723f1908.
The offset frequency f0 is related to the beats of the transfer lasers with the generated frequency comb:
Δ2f3f=(2n3m)frepf03Δ1908+2Δ1272.
The transfer laser at 1272 nm is phase locked to a frequency comb component with Δ1272=10MHz offset frequency. The frequency tripled 1908 nm transfer laser is phase locked via the 2f3f interferometer signal to 20 MHz below the frequency doubled 1272 nm transfer laser at Δ2f3f=20MHz. Both phase locks are referenced to a commercial atomic clock. For 2n3m=0 (which can readily be achieved by locking the 1272 nm transfer laser to the appropriate comb line), the beat Δ1908 between the 1908 nm transfer laser and the OFC corresponds to
Δ1908=f03.
With this measurement technique, we measure an offset frequency of f03=3.543GHz (see Fig. 4). The signal-to-noise ratio (SNR) of f0 of >30dB in a 100 kHz resolution bandwidth (RBW), as well as a SNR of >60dB in a 100 Hz RBW of frep, is sufficient for accurate, i.e., real-time counting of the cycles of the two radio frequency beats (and making the use of, e.g., tracking oscillators unnecessary). This, along with the knowledge of the comb teeth number, provides the ability to directly count the cycles of the pump laser as well as the other comb teeth.

 figure: Fig. 4.

Fig. 4. Repetition rate and carrier envelope frequency signals of the self-referenced microresonator comb. (a) The offset frequency (f0) of the optical microresonator frequency comb divided by three as described in Eq. (7). The measured optical heterodyne beat frequency has a center frequency of 3.543 GHz and exhibits a SNR that exceeds 30 dB in a 100 kHz RBW. (b) The repetition rate frep of the soliton in the optical microresonator with a center frequency (CF) of 14.0939 GHz and a SNR >60dB measured in a resolution bandwidth of 100 Hz. The large SNRs are sufficient for accurate phase tracking of the two microwave signals.

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It should be noted that the determination of the comb line index with a mode-locked laser frequency comb with repetition rates <1GHz can be challenging. Here the much denser comb spectrum does not normally permit resolving the comb line with a grating-based OSA, and moreover, the sensitivity to drifts in repetition rate is significantly higher, making it necessary to fully phase stabilize the comb in order to determine the comb line index. In contrast, the comb line index can be obtained in the present work with a low-resolution wavemeter without requiring locking of either frep or f0. In this way, the comb line number of the pump laser was determined to be npump=13,696. Self-referencing, along with knowledge of the comb line numbers, implies that the absolute laser frequency of the pump laser (fpump, as well as any other comb teeth) can be directly determined via the repetition rate beatnote (frep) and the recorded beatnote (Δ1908), since the absolute laser frequency is related to the two quantities via

fpump=3Δ1908+npump·frep,
establishing the ability to count the cycles of light via the crystalline microresonator.

3. CONCLUSIONS

Our results constitute the first phase-coherent link from the microwave to the optical domain using a microresonator, by demonstrating measurement of the carrier envelope frequency of a temporal dissipative soliton in a microresonator. These results demonstrate that microresonator-based frequency combs can provide accurate and precise absolute optical frequency standards for a wide range of applications in optical frequency metrology, optical atomic clocks, optical frequency synthesis, or low-noise microwave generation by frequency division. In terms of soliton dynamics, this demonstration constitutes the first measurement of the carrier envelope offset frequency of a temporal dissipative Kerr cavity soliton, to our knowledge. This opens a new route to studying nonlinear dynamics of solitons. A further important step in the future will be to phase lock both frep and f0 to an external radio frequency reference, and thereby achieve a phase-stabilized self-referenced microresonator frequency comb. This can be achieved by controlling both frep and f0 independently via changing the pump frequency detuning along with either the pump power [45] or by applying a stress to the resonator with a piezoelectric crystal [50]. The crystalline-microresonator-based microwave-to-optical link can be made more compact with almost all optical components being fiber optic based, and aside from the optical microresonator, the non-fiber-based components (filters and sum-frequency generation stages) can be replaced with fiber-based components in the future. Finally, the external broadening stage itself, required in the present case, can, in suitably dispersion engineered optical microresonators, be avoided when making use of soliton-induced higher order spectral broadening [42,47,58]. Eventually, this provides a path to counting the cycles of light using chip-scale microresonators.

Funding

Defense Advanced Research Projects Agency (DARPA), PULSE program (W31PQ-13-1-0016); European Space Agency (ESA); Eurostars Program; Marie Curie IEF; Marie Curie IIF; Swiss National Science Foundation.

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39. F. Leo, S. Coen, P. Kockaert, S.-P. P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010). [CrossRef]  

40. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012). [CrossRef]  

41. L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987). [CrossRef]  

42. S. Coen, H. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38, 37–39 (2013). [CrossRef]  

43. M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs,” Opt. Lett. 38, 3478–3481 (2013). [CrossRef]  

44. Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010). [CrossRef]  

45. P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008). [CrossRef]  

46. P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011). [CrossRef]  

47. Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (2011). [CrossRef]  

48. N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 72, 809–818 (1987). [CrossRef]  

49. N. Akhmediev and A. Ankiewicz, Dissipative Solitons: From Optics to Biology and Medicine (Springer, 2008).

50. S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3, 031003 (2013).

51. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989). [CrossRef]  

52. I. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006). [CrossRef]  

53. J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82, 031804 (2010). [CrossRef]  

54. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92, 043903 (2004). [CrossRef]  

55. T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014). [CrossRef]  

56. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003). [CrossRef]  

57. J. M. Dudley and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]  

58. V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” arXiv:1410.8598 (2014).

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    [Crossref]
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  43. M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs,” Opt. Lett. 38, 3478–3481 (2013).
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    [Crossref]
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    [Crossref]
  47. Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (2011).
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  49. N. Akhmediev and A. Ankiewicz, Dissipative Solitons: From Optics to Biology and Medicine (Springer, 2008).
  50. S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3, 031003 (2013).
  51. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
    [Crossref]
  52. I. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
    [Crossref]
  53. J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82, 031804 (2010).
    [Crossref]
  54. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92, 043903 (2004).
    [Crossref]
  55. T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
    [Crossref]
  56. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
    [Crossref]
  57. J. M. Dudley and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
    [Crossref]
  58. V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” arXiv:1410.8598 (2014).

2015 (1)

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015).
[Crossref]

2014 (5)

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1, 10–14 (2014).
[Crossref]

P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (2014).
[Crossref]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
[Crossref]

2013 (10)

S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3, 031003 (2013).

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5  μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

S. Coen, H. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38, 37–39 (2013).
[Crossref]

M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs,” Opt. Lett. 38, 3478–3481 (2013).
[Crossref]

N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, and A. D. Ludlow, “An atomic clock with 10−18 instability,” Science 341, 1215–1218 (2013).
[Crossref]

K. Saha, Y. Okawachi, B. Shim, J. S. Levy, M. A. Foster, R. Salem, A. R. Johnson, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Modelocking and femtosecond pulse generation in chip-based frequency combs,” Opt. Express 21, 1335–1343 (2013).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

A. A. Savchenkov, D. Eliyahu, W. Liang, V. S. Ilchenko, J. Byrd, A. B. Matsko, D. Seidel, and L. Maleki, “Stabilization of a Kerr frequency comb oscillator,” Opt. Lett. 38, 2636–2638 (2013).
[Crossref]

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picque, and T. W. Hansch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502, 355–358 (2013).
[Crossref]

H. Jung, C. Xiong, K. Y. Fong, X. Zhang, and H. X. Tang, “Optical frequency comb generation from aluminum nitride microring resonator,” Opt. Lett. 38, 2810–2813 (2013).
[Crossref]

2012 (4)

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref]

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Low-pump-power, low-phase-noise, and microwave to millimeter-wave repetition rate operation in microcombs,” Phys. Rev. Lett. 109, 233901 (2012).
[Crossref]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[Crossref]

2011 (6)

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (2011).
[Crossref]

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[Crossref]

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
[Crossref]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref]

2010 (3)

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82, 031804 (2010).
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F. Leo, S. Coen, P. Kockaert, S.-P. P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
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Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
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2009 (3)

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
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J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
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2008 (4)

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
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T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kenitscher, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
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T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
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P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[Crossref]

2007 (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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2006 (2)

I. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
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J. M. Dudley and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
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2004 (3)

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92, 043903 (2004).
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T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
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A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
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2003 (3)

J. Ye, H. Schnatz, and L. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9, 1041–1058 (2003).
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S. Diddams, A. Bartels, T. Ramond, C. Oates, S. Bize, E. Curtis, J. Bergquist, and L. Hollberg, “Design and control of femtosecond lasers for optical clocks and the synthesis of low-noise optical and microwave signals,” IEEE J. Sel. Top. Quantum Electron. 9, 1072–1080 (2003).
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S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
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2001 (2)

S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293, 825–828 (2001).
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U. Morgner, R. Ell, G. Metzler, T. Schibli, F. Kärtner, J. Fujimoto, H. Haus, and E. Ippen, “Nonlinear optics with phase-controlled pulses in the sub-two-cycle regime,” Phys. Rev. Lett. 86, 5462–5465 (2001).
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2000 (2)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
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S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
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1999 (2)

J. Reichert, R. Holzwarth, T. Udem, and T. W. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
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H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
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1993 (1)

1989 (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
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1987 (2)

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 72, 809–818 (1987).
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L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
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1973 (1)

K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, and G. W. Day, “Accurate frequencies of molecular transitions used in laser stabilization: the 3.39-μm transition in CH4 and the 9.33- and 10.18-μm transitions in CO2,” Appl. Phys. Lett. 22, 192 (1973).
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P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
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N. Akhmediev and A. Ankiewicz, Dissipative Solitons: From Optics to Biology and Medicine (Springer, 2008).

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Arcizet, O.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
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P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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Bartels, A.

A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
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S. Diddams, A. Bartels, T. Ramond, C. Oates, S. Bize, E. Curtis, J. Bergquist, and L. Hollberg, “Design and control of femtosecond lasers for optical clocks and the synthesis of low-noise optical and microwave signals,” IEEE J. Sel. Top. Quantum Electron. 9, 1072–1080 (2003).
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Beha, K.

P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (2014).
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S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1, 10–14 (2014).
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N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, and A. D. Ludlow, “An atomic clock with 10−18 instability,” Science 341, 1215–1218 (2013).
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Bergquist, J.

S. Diddams, A. Bartels, T. Ramond, C. Oates, S. Bize, E. Curtis, J. Bergquist, and L. Hollberg, “Design and control of femtosecond lasers for optical clocks and the synthesis of low-noise optical and microwave signals,” IEEE J. Sel. Top. Quantum Electron. 9, 1072–1080 (2003).
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T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
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S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293, 825–828 (2001).
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T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picque, and T. W. Hansch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502, 355–358 (2013).
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S. Diddams, A. Bartels, T. Ramond, C. Oates, S. Bize, E. Curtis, J. Bergquist, and L. Hollberg, “Design and control of femtosecond lasers for optical clocks and the synthesis of low-noise optical and microwave signals,” IEEE J. Sel. Top. Quantum Electron. 9, 1072–1080 (2003).
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V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
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T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).
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J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
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T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
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V. Brasch, T. Herr, M. Geiselmann, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip based optical frequency comb using soliton induced Cherenkov radiation,” arXiv:1410.8598 (2014).

Brusch, A.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
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B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
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Chembo, Y. K.

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
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Chen, L.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
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T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
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Coen, S.

S. Coen, H. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38, 37–39 (2013).
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J. M. Dudley and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
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D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
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S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
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S. Diddams, A. Bartels, T. Ramond, C. Oates, S. Bize, E. Curtis, J. Bergquist, and L. Hollberg, “Design and control of femtosecond lasers for optical clocks and the synthesis of low-noise optical and microwave signals,” IEEE J. Sel. Top. Quantum Electron. 9, 1072–1080 (2003).
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S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293, 825–828 (2001).
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Danielson, B. L.

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K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, and G. W. Day, “Accurate frequencies of molecular transitions used in laser stabilization: the 3.39-μm transition in CH4 and the 9.33- and 10.18-μm transitions in CO2,” Appl. Phys. Lett. 22, 192 (1973).
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P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (2014).
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S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1, 10–14 (2014).
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P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
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P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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Diddams, S. A.

S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1, 10–14 (2014).
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P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (2014).
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S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3, 031003 (2013).

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A. Bartels, D. Heinecke, and S. A. Diddams, “10-GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref]

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
[Crossref]

S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293, 825–828 (2001).
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S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
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T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
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Duchesne, D.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
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J. M. Dudley and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
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H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
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N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 72, 809–818 (1987).
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S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

Razzari, L.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[Crossref]

Reichert, J.

J. Reichert, R. Holzwarth, T. Udem, and T. W. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Riemensberger, J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

Rosenband, T.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
[Crossref]

Saha, K.

Salem, R.

Savchenkov, A. A.

A. A. Savchenkov, D. Eliyahu, W. Liang, V. S. Ilchenko, J. Byrd, A. B. Matsko, D. Seidel, and L. Maleki, “Stabilization of a Kerr frequency comb oscillator,” Opt. Lett. 38, 2636–2638 (2013).
[Crossref]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref]

I. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92, 043903 (2004).
[Crossref]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Schibli, T.

U. Morgner, R. Ell, G. Metzler, T. Schibli, F. Kärtner, J. Fujimoto, H. Haus, and E. Ippen, “Nonlinear optics with phase-controlled pulses in the sub-two-cycle regime,” Phys. Rev. Lett. 86, 5462–5465 (2001).
[Crossref]

Schindler, P.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

Schioppo, M.

N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, and A. D. Ludlow, “An atomic clock with 10−18 instability,” Science 341, 1215–1218 (2013).
[Crossref]

Schliesser, A.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5  μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82, 031804 (2010).
[Crossref]

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Schmidt, P. O.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
[Crossref]

Schmidt, W.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kenitscher, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref]

Schmogrow, R.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

Schnatz, H.

J. Ye, H. Schnatz, and L. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9, 1041–1058 (2003).
[Crossref]

Seidel, D.

A. A. Savchenkov, D. Eliyahu, W. Liang, V. S. Ilchenko, J. Byrd, A. B. Matsko, D. Seidel, and L. Maleki, “Stabilization of a Kerr frequency comb oscillator,” Opt. Lett. 38, 2636–2638 (2013).
[Crossref]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref]

Sherman, J. A.

N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, and A. D. Ludlow, “An atomic clock with 10−18 instability,” Science 341, 1215–1218 (2013).
[Crossref]

Shim, B.

Solomatine, I.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref]

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[Crossref]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

Srinivasan, K.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[Crossref]

Stalnaker, J. E.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
[Crossref]

Steinmetz, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kenitscher, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref]

Steinmeyer, G.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[Crossref]

Stenger, J.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[Crossref]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

Strekalov, D.

I. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Low threshold optical oscillations in a whispering gallery mode CaF2 resonator,” Phys. Rev. Lett. 93, 243905 (2004).
[Crossref]

Sutter, D. H.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[Crossref]

Swann, W. C.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
[Crossref]

Sylvestre, T.

Tang, H. X.

Telle, H. R.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[Crossref]

Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
[Crossref]

Udem, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kenitscher, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref]

S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293, 825–828 (2001).
[Crossref]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

J. Reichert, R. Holzwarth, T. Udem, and T. W. Hänsch, “Measuring the frequency of light with mode-locked lasers,” Opt. Commun. 172, 59–68 (1999).
[Crossref]

Vahala, K.

Vahala, K. J.

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Low-pump-power, low-phase-noise, and microwave to millimeter-wave repetition rate operation in microcombs,” Phys. Rev. Lett. 109, 233901 (2012).
[Crossref]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[Crossref]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

Varghese, L. T.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[Crossref]

Venkataraman, V.

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

Vogel, K. R.

S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293, 825–828 (2001).
[Crossref]

Wabnitz, S.

Wang, C. Y.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[Crossref]

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5  μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

Wang, J.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[Crossref]

Wegner, D.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

Weimann, C.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

Weiner, A. M.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[Crossref]

Wells, J. S.

K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, and G. W. Day, “Accurate frequencies of molecular transitions used in laser stabilization: the 3.39-μm transition in CH4 and the 9.33- and 10.18-μm transitions in CO2,” Appl. Phys. Lett. 22, 192 (1973).
[Crossref]

Wen, Y. H.

Wilken, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kenitscher, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Windeler, R. S.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

Wineland, D. J.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
[Crossref]

S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293, 825–828 (2001).
[Crossref]

Xiong, C.

Ye, J.

J. Ye, H. Schnatz, and L. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9, 1041–1058 (2003).
[Crossref]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300  THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

Yu, M.

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015).
[Crossref]

Yu, N.

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
[Crossref]

Yu, Y.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref]

Zhang, X.

Appl. Phys. B (1)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[Crossref]

Appl. Phys. Lett. (1)

K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, and G. W. Day, “Accurate frequencies of molecular transitions used in laser stabilization: the 3.39-μm transition in CH4 and the 9.33- and 10.18-μm transitions in CO2,” Appl. Phys. Lett. 22, 192 (1973).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

S. Diddams, A. Bartels, T. Ramond, C. Oates, S. Bize, E. Curtis, J. Bergquist, and L. Hollberg, “Design and control of femtosecond lasers for optical clocks and the synthesis of low-noise optical and microwave signals,” IEEE J. Sel. Top. Quantum Electron. 9, 1072–1080 (2003).
[Crossref]

J. Ye, H. Schnatz, and L. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9, 1041–1058 (2003).
[Crossref]

Nat. Commun. (3)

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5  μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015).
[Crossref]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref]

Nat. Photonics (10)

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[Crossref]

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
[Crossref]

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
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Figures (4)

Fig. 1.
Fig. 1. Crystalline MgF 2 microresonator and temporal dissipative soliton generation. (a) Optical image of the employed ultrahigh- Q crystalline whispering gallery optical microresonators on a magnesium fluoride pillar with a diameter of several millimeters. The ultrahigh- Q whispering gallery optical modes are confined in the fabricated protrusions that extend around the circumference. The top resonator was used in the experiments and the mode of interest has a FSR of 14.0939 GHz and a loaded Q 10 9 . (b) The hyperbolic-secant shaped spectrum (fit: red dotted line) of the single temporal soliton produced inside the resonator by the CW pump laser. The inset shows the ability to resolve the microresonator comb lines on a grating-based spectrometer.
Fig. 2.
Fig. 2. Experimental setup and 2 f 3 f microresonator self-referencing scheme. (a) The frequency domain picture showing the relevant frequency components used to self-reference the comb and to determine the carrier envelope offset frequency ( f 0 ). (b) The simplified experimental setup used for self-referencing. A portion of the solitons that are outcoupled from the resonator are sent to an OSA to measure the spectrum, then residual pump light is filtered out using fiber optic filters before a portion is picked off and sent to a photodetector (PD) to measure the repetition rate on an ESA. The pulse is first preamplified in an EDFA and then prechirped to temporally broaden it with a DCF before being amplified by a high-power EDFA. The pulse is subsequently recompressed and coupled into a HNLF where the coherent supercontinuum is generated. A fraction of the spectrum is mixed with light from the 1908 nm thulium fiber laser and sent through a 1908 nm bandpass filter to a PD and ESA to measure Δ 1908 . The same is done with the 1272 nm external cavity diode laser to measure Δ 1272 and a servo loop is used to phase lock the laser to the optical frequency comb and fix Δ 1272 where a signal from an atomic clock is used as a reference. To create the 2 f 3 f interferometer light from the 1272 nm laser is frequency doubled in a periodically poled lithium niobate crystal (PPLN) to produce light at 636 nm. Light from the 1908 nm laser is frequency doubled to 954 nm in a PPLN crystal, and subsequently combined with 1908 nm and sent through a PPLN crystal phase matched for sum frequency generation, creating light at 636 nm. The generated visible light is optically heterodyned on a PD with the frequency doubled light from the 1272 nm laser, permitting us to measure Δ 2 f 3 f on an ESA. This offset frequency is fixed by phase locking the 1908 nm laser via the 2 f 3 f interferometer. With this scheme the carrier envelope frequency is measured by recording Δ 1908 .
Fig. 3.
Fig. 3. Optical spectrum of the microresonator before and after external broadening. (a) The blue trace shows the optical spectrum generated in the crystalline optical microresonator by the temporal dissipative soliton state. The large central spike originates from residual light from the pump laser. The spectrum after the supercontinuum generation is denoted in red. It is composed of data taken from two different OSAs as result of the limited bandwidth of the individual instruments. (b) Zoom into the broadened spectrum revealing the widely spaced comb lines. (c) Heterodyne beatnote of a laser at 1272 nm with the broadened comb demonstrating a SNR exceeding 40 dB in the resolution bandwidth (RBW) of 300 kHz. (d) Heterodyne beatnote at the long wavelength end of the comb at 1900 nm (RBW 100 kHz).
Fig. 4.
Fig. 4. Repetition rate and carrier envelope frequency signals of the self-referenced microresonator comb. (a) The offset frequency ( f 0 ) of the optical microresonator frequency comb divided by three as described in Eq. (7). The measured optical heterodyne beat frequency has a center frequency of 3.543 GHz and exhibits a SNR that exceeds 30 dB in a 100 kHz RBW. (b) The repetition rate f rep of the soliton in the optical microresonator with a center frequency (CF) of 14.0939 GHz and a SNR > 60 dB measured in a resolution bandwidth of 100 Hz. The large SNRs are sufficient for accurate phase tracking of the two microwave signals.

Equations (8)

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f 1272 = n · f rep + f 0 + Δ 1272
f 1908 = m · f rep + f 0 Δ 1908 ,
2 f 1272 = 2 n · f rep + 2 f 0 + 2 Δ 1272 .
3 f 1908 = 3 m · f rep + 3 f 0 3 Δ 1908 .
Δ 2 f 3 f = 2 f 1272 3 f 1908 .
Δ 2 f 3 f = ( 2 n 3 m ) f rep f 0 3 Δ 1908 + 2 Δ 1272 .
Δ 1908 = f 0 3 .
f pump = 3 Δ 1908 + n pump · f rep ,

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