Abstract

Compact optical frequency comb sources with gigahertz repetition rates are desirable for a number of important applications including arbitrary optical waveform generation and direct comb spectroscopy. We report the generation of phase-locked, gigahertz repetition rate optical frequency combs in a chalcogenide photonic chip. The combs are formed via the interplay of stimulated Brillouin scattering and Kerr-nonlinear four-wave mixing in an on-chip Fabry–Perot waveguide resonator incorporating a Bragg grating. Phase-locking of the comb is confirmed with real-time measurements, and a chirp of the comb repetition rate within the pump pulse was observed. These results represent a significant step towards the realization of integrated optical frequency comb sources with gigahertz repetition rates.

© 2014 Optical Society of America

Compact optical frequency comb sources with gigahertz repetition rates have applications ranging from arbitrary optical waveform generation [1] and direct comb spectroscopy [2] to advanced telecommunications. In practice, however, such sources are difficult to achieve: conventional passively mode-locked lasers have repetition rates on the order of 10–100 MHz [3], whereas most Kerr combs generated in microresonators have repetition rates on the order of terahertz [1,4]. The nonlinear optical process of stimulated Brillouin scattering (SBS) enables the generation of highly coherent gigahertz-frequency shifted waves [5]. It is based on inelastic scattering on acoustic phonons, leading to the generation of Stokes waves, which are Doppler shifted by the acoustic resonance frequency (νB711GHz for most glasses).

In the presence of cavity feedback, the threshold of SBS is reduced and SBS can be cascaded, leading to the formation of Brillouin frequency combs (BFCs) with a comb line spacing equal to the Brillouin frequency shift νB [611]. In contrast to both passively mode-locked lasers and Kerr combs generated in microresonators, the frequency spacing of BFCs is determined by the acoustic properties of the medium and is independent of the resonator dimensions.

Phase-locking of the spectral components of BFCs is required for most applications. The SBS process, however, does not provide a mechanism for phase-locking. Recently, phase-locked generation of BFCs in a Fabry–Perot (FP) fiber resonator was reported [12]. The phase-locking mechanism was attributed to Kerr-nonlinear four-wave mixing (FWM). Due to the long resonator length (38 cm), however, the demonstrated device was very sensitive to environmental fluctuation, limiting its performance. Furthermore, the fiber-based resonator is not compatible with integration of other functionalities such as on-chip lasers [13].

Here, we report for the first time to our knowledge chip-based generation of phase-locked BFCs. The BFCs were generated in a novel configuration consisting of a low-finesse FP resonator incorporating an on-chip Bragg grating. The FP resonator was formed by the facet reflections of a 6.5 cm long As2S3 chalcogenide glass [14] rib waveguide. Enhancement of nonlinear interactions by the Bragg grating was essential for the comb generation, due to the small feedback from the facets. Phase-locking of the comb was confirmed by real-time measurements. The RF spectrum of the BFC was analyzed, revealing a chirp (130kHz/ns) of the comb repetition rate within the pump pulse without loss of phase-locking.

Figure 1(a) illustrates the generation of phase-locked BFCs in FP resonators. The frequency combs are generated via the interplay of SBS of counterpropagating and FWM of copropagating comb components. Initially, a narrow band optical pump with frequency ν0 is coupled into the resonator. If the pump power is above a certain threshold value, it can excite the first-order Stokes wave via SBS at frequency ν1=ν0νB (at longer wavelength). This initial frequency shift determines the repetition rate of the comb. Copropagating pump and first-order Stokes waves can then generate anti-Stokes waves (j>0) and higher-order Stokes waves (j<1) via FWM at frequencies νj=ν0+jνB, where j is an integer [6]. These newly generated frequencies are also coupled by SBS since they inherit the initial frequency shift of the Stokes wave νB.

 

Fig. 1. (a) Illustration of BFC generation via the interplay of SBS and Kerr-nonlinear FWM (P, pump laser). (b) Schematic of the experiment. OSA, optical spectrum analyzer; PD, photodiode; RT-Scope, real-time oscilloscope.

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SBS by itself would not lead to phase-locking of BFCs as it only couples adjacent comb components and is independent of the spectral phase [12,15]. Unequally spaced frequency components would also be expected in the absence of an additional nonlinear effect than SBS. The comb frequency components have a linewidth much narrower than the Brillouin gain bandwidth [16] ΔνB1580MHz due to cavity feedback [17], and their exact frequencies are individually subject to frequency pulling arising from the interplay of gain, cavity resonances, and nonlinear phase shifts [12,15]. On the other hand, FWM is sensitive to the spectral phase [1,18], and the contribution of FWM can lead to equally spaced, phase-locked BFCs with deterministic spectral phases [12].

A schematic of the configuration used to generate and characterize chip-based BFCs is shown in Fig. 1(b). Polarized, quasi-continuous-wave (quasi-CW) pump light at λ=1551nm consisting of 300 ns long square pulses at 20 kHz repetition rate was used. A trace of one input pulse observed with an oscilloscope is shown in Fig. 1(b). The linewidth of the input light was estimated to be 3MHz determined by the temporal pulse length. The FP waveguide resonator used as a BFC resonator was a L=6.5cm long As2S3 chalcogenide rib waveguide [10,17,19] with cross-sectional dimensions of 3μm×850nm and an effective optical mode area of 1.725μm2. The waveguide was fabricated as described in [19] with the exception that the upper cladding was made out of polytetrafluoroethylene. The propagation loss of the waveguide was estimated to be about 0.3dB/cm [19]. A low-Q resonator with free spectral range (FSR) of 886 MHz was formed due to the refractive index step from As2S3 (n=2.4) to air. The waveguide facets provided a reflectivity of 17%. In As2S3, the Kerr nonlinearity and SBS are strong due to a large nonlinear index [14] n2=3.0×1018m2/W and a large Brillouin gain [16] gB=0.715×109m/W. The light was coupled in and out of the waveguide using lensed silica fibers.

A polarization controller before the chip was used to ensure the excitation of only one polarization mode of the waveguide. The output light was characterized in the spectral domain with an optical spectrum analyzer (OSA) and in the time domain with a photodiode connected to an oscilloscope, which allowed real-time analysis of the output signal.

The cascaded SBS process was additionally enhanced by a “Hill-type” Bragg grating written into the waveguide prior to the experiment [20,21]. The grating was located close to the input facet and had an estimated length of 6 mm. The pump wavelength was tuned such that the first- and second-order Stokes waves coincided with a band edge and a grating resonance, respectively. Higher-order Stokes, pump, and anti-Stokes waves did not experience feedback from the grating.

The spectrum of the input light shown in Fig. 2(a) consisted of a single line at the pump wavelength. The observed linewidth in Fig. 2(a) is determined by the resolution of the OSA. Figure 2(b) shows the normalized transmission spectrum of the Bragg grating. Figure 2(c) presents optical output spectra for 2W coupled peak power. The solid blue line shows the BFC obtained with the grating enhancement. It exhibits four orders of Stokes waves (1S–4S) at longer wavelengths and three orders of anti-Stokes waves at shorter wavelengths (1AS–3AS). The wavelength spacing between the waves is Δλ=60pm, which corresponds to a Brillouin frequency shift of νB=cΔλ/λ2=7.5GHz, where c is the vacuum speed of light. For comparison, the red dotted line in Fig. 2(c) shows the output spectrum observed for the same input power but without the Bragg grating. In this case, only weak first-order Stokes and first-order anti-Stokes waves were generated.

 

Fig. 2. Spectral measurements. (a) Input pump light (P) coupled into the resonator. (b) Normalized transmission spectrum of the Bragg grating. (c) Output spectra: with grating enhancement (solid blue line) revealing several Stokes waves (1S–4S) and anti-Stokes waves (1AS–3AS), and without grating enhancement (red dotted line). (a) and (c) were measured with an OSA (resolution 10pm), and (b) was measured with a swept wavelength system (resolution 1.3pm).

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The grating-enhanced BFC generated in the resonator was characterized by recording the traces of 110 consecutive quasi-CW output pulses in real time within a time interval of 5 ms. Figure 3(a) shows every tenth trace of this measurement. Each of the traces exhibited very similar temporal behavior: after about 20 ns, a rapidly oscillating interference signal was observed, which was not resolved in Fig. 3(a). This oscillation arises from the interference between the pump and the generated Stokes and anti-Stokes waves. After about 35 ns the dynamic interaction between the comb components seems to reach a steady state, resulting in an interference signal with a constant envelope. Figures 3(b)I and 3(b)II show 1 ns long zoomed-in sections of the interference at 70 and 280 ns, respectively. In Figs. 3(b)I and 3(b)II the traces of all 11 measurements presented in Fig. 3(a) are shown in the same plot in order to illustrate their similarity. We can see that the 11 independent measurements exhibit the same interference pattern, which is stable over the quasi-CW pulse length.

 

Fig. 3. Temporal measurements of the BFC (sampling rate, 80GSa/s; bandwidth, 33 GHz). (a) Eleven output pulses generated by coupling eleven 300 ns input pump pulses into the waveguide with 0.5 ms delay. (b) 1 ns long zoomed-in section at 70 and 280 ns of all 11 traces shown in (a) (the traces have been shifted in time for better visibility).

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To understand the implications of this result we consider the spectral phase of the BFC. The complex electric fields of the individual comb components can be written in the form Ej(t)exp[i(ϕj(t)2πνjt)], where ϕj are phase offsets of the spectral components. The measured interference signal is independent of a constant offset of all phases ϕj. A linear change of the spectral phase corresponds to the shift in time [1,18]. The shape of the interference signal is determined by the phase dispersion ΔΔϕj(t)=ϕj1+ϕj+12ϕj.

A stable interference pattern in the time domain requires phase-locking of the spectral components, i.e.,

ddtΔΔϕj(t)=0.

The stable and deterministic interference signal of the BFC shown in Figs. 3(a) and 3(b) indicates that the pump, Stokes, and anti-Stokes waves attained the same phase-locked steady state with identical spectral phases (same values of ΔΔϕj) for all independent measurements. Coherent coupling of more than two adjacent comb components to a single acoustic wave is expected to be negligible since the corresponding interactions are not phase-matched and have coherence lengths <1cm [12]. We therefore believe that FWM of copropagating waves provides the phase-locking mechanism.

Recording the interference signal with real-time measurements allows the analysis of its RF spectrum via fast Fourier transform (FFT). Figure 4(a) shows the RF power spectrum (squared FFT magnitude) of one of the traces shown in Fig. 3(a). We can identify the beat notes of the comb components at multiple integer values of the Brillouin frequency shift nνB (n=14). A phase-locked frequency comb has narrow linewidth RF-beat notes that are equally spaced. The resolution bandwidth of the measurement in our case is limited by the length of the 300 ns pulses, i.e., 3MHz. Equally spaced RF-beat notes of 3MHz bandwidth would therefore be expected. However, we observed beat notes in the experiment [Fig. 4(a)] that were much broader. For example, the beat note at the frequency νB=7.5GHz has a linewidth of 40MHz.

 

Fig. 4. RF spectra of the BFC obtained via FFT of the temporal measurement shown Fig. 3. (a) RF spectrum of one entire quasi-CW output pulse. (b) Zoomed-in sections at νB and 2νB of RF spectra of 70 ns long intervals of one quasi-CW output pulse centered around 55 ns (black, squares), 125 ns (red, dots), 195 ns (blue triangles pointing up), and 265 ns (magenta, triangles pointing down), illustrating the increase of the comb repetition rate on a nanosecond time scale.

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To understand the origin of this broadening we performed a FFT of four consecutive, 70 ns long, time intervals of one 300 ns long pulse shown in Fig. 3(a). Figure 4(b) shows zoomed-in sections of the RF spectra around νB and 2νB. The four traces shown in both plots correspond to the RF spectra obtained for the consecutive 70 ns long time intervals centered around 55 ns, 125 ns, 195 ns, and 265 ns, respectively. Figure 4(b) explains why the phase-locked BFC exhibits broad beat notes in the RF spectrum [Fig. 4(a)]. The bandwidths of the beat notes within the consecutive intervals in Fig. 4(b) are resolution limited; however, the beat frequency at νB drifts within the 300 ns pulses by about 40 MHz towards higher frequency. At the same time the beat notes at nνB experience n times the frequency shift, which is shown for the RF frequency 2νB in Fig. 4(b). In other words, the RF-beat notes are narrow and equally spaced, but the repetition rate of the comb is chirped by about 130kHz/ns. The observation of a single beat at 7.5 GHz and the fact that the RF-beat notes at νB, 2νB, 3νB, and 4νB remain exactly equally spaced despite the chirp additionally demonstrate phase-locking of the comb, i.e., that Eq. (1) is fulfilled. We observed the same drift of the repetition rate for all 110 recorded traces with the same initial and final repetition rates of the comb.

We believe that the increase of repetition rate is caused by a red-shift of the FP resonances, which leads to an increase in the Stokes wavelength due to frequency pulling [15]. A red-shift of the FP resonances is caused by an increase of the optical roundtrip path length (Δ(2nL)>0). We exclude the Kerr effect as the possible cause since the total power in the cavity is not increasing. The effect causing the shift seems to be accumulative within the 300 ns pulses and reversible within 50 μs, which is the time separation between consecutive pulses.

Local heating of the waveguide is one possible explanation for an increase of the optical path length. Neglecting heat dissipation, the heating of the waveguide by one quasi-CW pulse can be estimated with

ΔT=P(1eαL)ΔtVρcm=0.16K,
where P=2W is the coupled power, Δt=300ns is the pulse duration, and V is the volume of the waveguide. The parameters ρ=3.2g/cm3, cm=0.456J/(gK), and α=0.01cm1 are the density, the specific heat, and the bulk material absorption coefficient of As2S3, respectively [22]. This leads to a change of the accumulated roundtrip phase of
Δϕ=2πλ×2(nLT+LnT)ΔT=1.7π,
where L/T=LαL is the temperature-dependent expansion of the waveguide, αL=21.49×106K1 is the expansion coefficient, and n/T=9×106 is the refractive index change with temperature at 1550 nm [22,23]. A phase shift Δϕ of 2π corresponds to a shift of the FP resonances by one FSR. The calculated estimate of the phase shift Δϕ=1.7π shows that local heating could lead to a significant shift of the FP resonances and therefore the comb repetition rate. Another possible explanation for the frequency drift is a photosensitive refractive index change on a nanosecond time scale, which is reversed between the quasi-CW pulses [24].

In a previous experiment that demonstrated the generation of phase-locked BFCs in a 38 cm long FP chalcogenide fiber resonator, a change of the repetition rate within 500 ns long quasi-CW pulses was not observed [12]. In the fiber experiment, the effects of local heating are expected to be much smaller compared to the chip, and the maximum phase drift is estimated to be Δϕ=0.4π [using the parameters from [12] with Eqs. (2) and (3)]. The smaller FSR of the fiber cavity additionally reduces the frequency pulling [15]. Photosensitivity is also less pronounced in drawn chalcogenide fibers compared to thin films made with vapor deposition as used for the chips.

In summary, we temporally characterized a quasi-CW BFC generated by cascaded SBS. The BFC was generated in a FP waveguide resonator on a photonic chip. Real-time measurements demonstrate phase-locking of the comb components. In contrast to previous fiber-based work, the comb generation was enabled by an on-chip Bragg grating, which enhanced the nonlinear interactions between the comb components. Furthermore, we utilized the real-time measurements to study the RF spectrum of the BFC, which revealed a novel phenomenon for frequency combs generated by quasi-CW pumping: a chirp (130 kHz/ns) of the comb repetition rate without the loss of phase-locking.

In the future, we will investigate generation of BFCs in on-chip high-finesse resonators. In CW configurations the observed frequency drift is expected to stabilize. Besides being more compact than a fiber cavity [12], generating BFCs on chip has also proven to be much more robust to environmental fluctuations due to the much shorter resonator length. Photolithographic fabrication will allow construction of a large number of waveguides with precise control over the resonator length, which is crucial in the case of high-finesse resonators. Furthermore, by combining these nonlinear waveguide resonators with the rapidly developing technology of on-chip lasers [13], a gigahertz repetition rate source could be realized in a completely integrated package. Due to the transparency of chalcogenide glasses, this technology could also be used to generate high repetition rate optical frequency comb sources at mid-infrared wavelengths (3–10 μm) relevant for direct comb spectroscopy and sensing.

FUNDING INFORMATION

Australian Research Council (ARC) (CE110001018, DE130101033, FL120100029, FT110100853).

References

1. F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (2011). [CrossRef]  

2. S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007). [CrossRef]  

3. S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003). [CrossRef]  

4. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007). [CrossRef]  

5. E. P. Ippen and R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972). [CrossRef]  

6. K. O. Hill, D. C. Johnson, and B. S. Kawasaki, Appl. Phys. Lett. 29, 185 (1976). [CrossRef]  

7. M. Tomes and T. Carmon, Phys. Rev. Lett. 102, 113601 (2009). [CrossRef]  

8. I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009). [CrossRef]  

9. D. Braje, L. Hollberg, and S. Diddams, Phys. Rev. Lett. 102, 193902 (2009). [CrossRef]  

10. R. Pant, E. Li, D.-Y. Choi, C. G. Poulton, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, Opt. Lett. 36, 3687 (2011). [CrossRef]  

11. J. Li, H. Lee, T. Chen, and K. J. Vahala, Opt. Express 20, 369 (2012).

12. T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, and B. J. Eggleton, Sci. Rep. 4, 1 (2014). [CrossRef]  

13. D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, and L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010). [CrossRef]  

14. B. J. Eggleton, B. Luther-Davies, and K. Richardson, Nat. Photonics 5, 141 (2011).

15. V. Lecoeuche, S. Randoux, B. Ségard, and J. Zemmouri, Quantum Semiclassical Opt. 8, 1109 (1996).

16. R. Pant, C. G. Poulton, D.-Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, Opt. Express 19, 8285 (2011). [CrossRef]  

17. I. V. Kabakova, R. Pant, D.-Y. Choi, S. Debbarma, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, Opt. Lett. 38, 3208 (2013). [CrossRef]  

18. P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014). [CrossRef]  

19. T. Han, S. Madden, D. Bulla, and B. Luther-Davies, Opt. Express 18, 19286 (2010). [CrossRef]  

20. K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978). [CrossRef]  

21. T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, E. Li, and B. J. Eggleton, Opt. Express 20, 26434 (2012). [CrossRef]  

22. Amorphous Materials, Inc., “AMTIR-6 (As2S3),” http://www.amorphousmaterials.com/app/download/6552919404/AMTIR-6+Information.pdf.

23. W. S. Rodney, I. H. Malitson, and T. A. King, J. Opt. Soc. Am. 48, 633 (1958). [CrossRef]  

24. Y. Sakaguchi and K. Tamura, J. Phys. Condens. Matter 18, L331 (2006). [CrossRef]  

References

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  1. F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
    [Crossref]
  2. S. A. Diddams, L. Hollberg, V. Mbele, Nature 445, 627 (2007).
    [Crossref]
  3. S. T. Cundiff, J. Ye, Rev. Mod. Phys. 75, 325 (2003).
    [Crossref]
  4. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, Nature 450, 1214 (2007).
    [Crossref]
  5. E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
    [Crossref]
  6. K. O. Hill, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 29, 185 (1976).
    [Crossref]
  7. M. Tomes, T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
    [Crossref]
  8. I. S. Grudinin, A. B. Matsko, L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
    [Crossref]
  9. D. Braje, L. Hollberg, S. Diddams, Phys. Rev. Lett. 102, 193902 (2009).
    [Crossref]
  10. R. Pant, E. Li, D.-Y. Choi, C. G. Poulton, S. J. Madden, B. Luther-Davies, B. J. Eggleton, Opt. Lett. 36, 3687 (2011).
    [Crossref]
  11. J. Li, H. Lee, T. Chen, K. J. Vahala, Opt. Express 20, 369 (2012).
  12. T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, B. J. Eggleton, Sci. Rep. 4, 1 (2014).
    [Crossref]
  13. D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
    [Crossref]
  14. B. J. Eggleton, B. Luther-Davies, K. Richardson, Nat. Photonics 5, 141 (2011).
  15. V. Lecoeuche, S. Randoux, B. Ségard, J. Zemmouri, Quantum Semiclassical Opt. 8, 1109 (1996).
  16. R. Pant, C. G. Poulton, D.-Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, B. J. Eggleton, Opt. Express 19, 8285 (2011).
    [Crossref]
  17. I. V. Kabakova, R. Pant, D.-Y. Choi, S. Debbarma, B. Luther-Davies, S. J. Madden, B. J. Eggleton, Opt. Lett. 38, 3208 (2013).
    [Crossref]
  18. P. Del’Haye, K. Beha, S. B. Papp, S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
    [Crossref]
  19. T. Han, S. Madden, D. Bulla, B. Luther-Davies, Opt. Express 18, 19286 (2010).
    [Crossref]
  20. K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
    [Crossref]
  21. T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, E. Li, B. J. Eggleton, Opt. Express 20, 26434 (2012).
    [Crossref]
  22. Amorphous Materials, Inc., “AMTIR-6 (As2S3),” http://www.amorphousmaterials.com/app/download/6552919404/AMTIR-6+Information.pdf .
  23. W. S. Rodney, I. H. Malitson, T. A. King, J. Opt. Soc. Am. 48, 633 (1958).
    [Crossref]
  24. Y. Sakaguchi, K. Tamura, J. Phys. Condens. Matter 18, L331 (2006).
    [Crossref]

2014 (2)

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, B. J. Eggleton, Sci. Rep. 4, 1 (2014).
[Crossref]

P. Del’Haye, K. Beha, S. B. Papp, S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[Crossref]

2013 (1)

2012 (2)

2011 (4)

R. Pant, C. G. Poulton, D.-Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, B. J. Eggleton, Opt. Express 19, 8285 (2011).
[Crossref]

B. J. Eggleton, B. Luther-Davies, K. Richardson, Nat. Photonics 5, 141 (2011).

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
[Crossref]

R. Pant, E. Li, D.-Y. Choi, C. G. Poulton, S. J. Madden, B. Luther-Davies, B. J. Eggleton, Opt. Lett. 36, 3687 (2011).
[Crossref]

2010 (2)

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

T. Han, S. Madden, D. Bulla, B. Luther-Davies, Opt. Express 18, 19286 (2010).
[Crossref]

2009 (3)

M. Tomes, T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
[Crossref]

I. S. Grudinin, A. B. Matsko, L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

D. Braje, L. Hollberg, S. Diddams, Phys. Rev. Lett. 102, 193902 (2009).
[Crossref]

2007 (2)

S. A. Diddams, L. Hollberg, V. Mbele, Nature 445, 627 (2007).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

2006 (1)

Y. Sakaguchi, K. Tamura, J. Phys. Condens. Matter 18, L331 (2006).
[Crossref]

2003 (1)

S. T. Cundiff, J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[Crossref]

1996 (1)

V. Lecoeuche, S. Randoux, B. Ségard, J. Zemmouri, Quantum Semiclassical Opt. 8, 1109 (1996).

1978 (1)

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[Crossref]

1976 (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 29, 185 (1976).
[Crossref]

1972 (1)

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

1958 (1)

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Beha, K.

P. Del’Haye, K. Beha, S. B. Papp, S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[Crossref]

Braje, D.

D. Braje, L. Hollberg, S. Diddams, Phys. Rev. Lett. 102, 193902 (2009).
[Crossref]

Bulla, D.

Büttner, T. F. S.

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, B. J. Eggleton, Sci. Rep. 4, 1 (2014).
[Crossref]

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, E. Li, B. J. Eggleton, Opt. Express 20, 26434 (2012).
[Crossref]

Carmon, T.

M. Tomes, T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
[Crossref]

Chen, L.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
[Crossref]

Chen, T.

J. Li, H. Lee, T. Chen, K. J. Vahala, Opt. Express 20, 369 (2012).

Choi, D.-Y.

Cundiff, S. T.

S. T. Cundiff, J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[Crossref]

Debbarma, S.

Del’Haye, P.

P. Del’Haye, K. Beha, S. B. Papp, S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Diddams, S.

D. Braje, L. Hollberg, S. Diddams, Phys. Rev. Lett. 102, 193902 (2009).
[Crossref]

Diddams, S. A.

P. Del’Haye, K. Beha, S. B. Papp, S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[Crossref]

S. A. Diddams, L. Hollberg, V. Mbele, Nature 445, 627 (2007).
[Crossref]

Eggleton, B. J.

Ferdous, F.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
[Crossref]

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[Crossref]

Grenouillet, L.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Grudinin, I. S.

I. S. Grudinin, A. B. Matsko, L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

Han, T.

Hile, S.

Hill, K. O.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[Crossref]

K. O. Hill, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 29, 185 (1976).
[Crossref]

Hollberg, L.

D. Braje, L. Hollberg, S. Diddams, Phys. Rev. Lett. 102, 193902 (2009).
[Crossref]

S. A. Diddams, L. Hollberg, V. Mbele, Nature 445, 627 (2007).
[Crossref]

Holzwarth, R.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Hudson, D. D.

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, B. J. Eggleton, Sci. Rep. 4, 1 (2014).
[Crossref]

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, E. Li, B. J. Eggleton, Opt. Express 20, 26434 (2012).
[Crossref]

Ippen, E. P.

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

Johnson, D. C.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[Crossref]

K. O. Hill, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 29, 185 (1976).
[Crossref]

Judge, A. C.

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, B. J. Eggleton, Sci. Rep. 4, 1 (2014).
[Crossref]

Kabakova, I. V.

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[Crossref]

K. O. Hill, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 29, 185 (1976).
[Crossref]

King, T. A.

Kippenberg, T. J.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Kopp, C.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Kumar, R.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Kumar, S.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Leaird, D. E.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
[Crossref]

Lecoeuche, V.

V. Lecoeuche, S. Randoux, B. Ségard, J. Zemmouri, Quantum Semiclassical Opt. 8, 1109 (1996).

Lee, H.

J. Li, H. Lee, T. Chen, K. J. Vahala, Opt. Express 20, 369 (2012).

Li, E.

Li, J.

J. Li, H. Lee, T. Chen, K. J. Vahala, Opt. Express 20, 369 (2012).

Liu, L.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Luther-Davies, B.

Madden, S.

Madden, S. J.

Maleki, L.

I. S. Grudinin, A. B. Matsko, L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

Malitson, I. H.

Mandorlo, F.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Matsko, A. B.

I. S. Grudinin, A. B. Matsko, L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

Mbele, V.

S. A. Diddams, L. Hollberg, V. Mbele, Nature 445, 627 (2007).
[Crossref]

Mcfarlane, H.

Member, S.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Miao, H.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
[Crossref]

Morthier, G.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Pant, R.

Papp, S. B.

P. Del’Haye, K. Beha, S. B. Papp, S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[Crossref]

Poulton, C. G.

Randoux, S.

V. Lecoeuche, S. Randoux, B. Ségard, J. Zemmouri, Quantum Semiclassical Opt. 8, 1109 (1996).

Raz, O.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Regreny, P.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Richardson, K.

B. J. Eggleton, B. Luther-Davies, K. Richardson, Nat. Photonics 5, 141 (2011).

Rodney, W. S.

Rojo-Romeo, P.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Sakaguchi, Y.

Y. Sakaguchi, K. Tamura, J. Phys. Condens. Matter 18, L331 (2006).
[Crossref]

Schliesser, A.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Ségard, B.

V. Lecoeuche, S. Randoux, B. Ségard, J. Zemmouri, Quantum Semiclassical Opt. 8, 1109 (1996).

Spuesens, T.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Srinivasan, K.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
[Crossref]

Stolen, R. H.

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

Tamura, K.

Y. Sakaguchi, K. Tamura, J. Phys. Condens. Matter 18, L331 (2006).
[Crossref]

Thevenaz, L.

Tomes, M.

M. Tomes, T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
[Crossref]

Vahala, K. J.

J. Li, H. Lee, T. Chen, K. J. Vahala, Opt. Express 20, 369 (2012).

Van Thourhout, D.

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

Varghese, L. T.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
[Crossref]

Wang, J.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
[Crossref]

Weiner, A. M.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
[Crossref]

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Ye, J.

S. T. Cundiff, J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[Crossref]

Zemmouri, J.

V. Lecoeuche, S. Randoux, B. Ségard, J. Zemmouri, Quantum Semiclassical Opt. 8, 1109 (1996).

Appl. Phys. Lett. (3)

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

K. O. Hill, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 29, 185 (1976).
[Crossref]

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

D. Van Thourhout, T. Spuesens, S. Kumar, S. Member, L. Liu, R. Kumar, G. Morthier, S. Member, P. Rojo-Romeo, F. Mandorlo, P. Regreny, O. Raz, C. Kopp, L. Grenouillet, IEEE J. Sel. Top. Quantum Electron. 16, 1363 (2010).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. Condens. Matter (1)

Y. Sakaguchi, K. Tamura, J. Phys. Condens. Matter 18, L331 (2006).
[Crossref]

Nat. Photonics (2)

B. J. Eggleton, B. Luther-Davies, K. Richardson, Nat. Photonics 5, 141 (2011).

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, A. M. Weiner, Nat. Photonics 5, 770 (2011).
[Crossref]

Nature (2)

S. A. Diddams, L. Hollberg, V. Mbele, Nature 445, 627 (2007).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, Nature 450, 1214 (2007).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. Lett. (4)

M. Tomes, T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
[Crossref]

I. S. Grudinin, A. B. Matsko, L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

D. Braje, L. Hollberg, S. Diddams, Phys. Rev. Lett. 102, 193902 (2009).
[Crossref]

P. Del’Haye, K. Beha, S. B. Papp, S. A. Diddams, Phys. Rev. Lett. 112, 043905 (2014).
[Crossref]

Quantum Semiclassical Opt. (1)

V. Lecoeuche, S. Randoux, B. Ségard, J. Zemmouri, Quantum Semiclassical Opt. 8, 1109 (1996).

Rev. Mod. Phys. (1)

S. T. Cundiff, J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[Crossref]

Sci. Rep. (1)

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, B. J. Eggleton, Sci. Rep. 4, 1 (2014).
[Crossref]

Other (1)

Amorphous Materials, Inc., “AMTIR-6 (As2S3),” http://www.amorphousmaterials.com/app/download/6552919404/AMTIR-6+Information.pdf .

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Figures (4)

Fig. 1.
Fig. 1. (a) Illustration of BFC generation via the interplay of SBS and Kerr-nonlinear FWM (P, pump laser). (b) Schematic of the experiment. OSA, optical spectrum analyzer; PD, photodiode; RT-Scope, real-time oscilloscope.
Fig. 2.
Fig. 2. Spectral measurements. (a) Input pump light (P) coupled into the resonator. (b) Normalized transmission spectrum of the Bragg grating. (c) Output spectra: with grating enhancement (solid blue line) revealing several Stokes waves (1S–4S) and anti-Stokes waves (1AS–3AS), and without grating enhancement (red dotted line). (a) and (c) were measured with an OSA (resolution 10pm), and (b) was measured with a swept wavelength system (resolution 1.3pm).
Fig. 3.
Fig. 3. Temporal measurements of the BFC (sampling rate, 80GSa/s; bandwidth, 33 GHz). (a) Eleven output pulses generated by coupling eleven 300 ns input pump pulses into the waveguide with 0.5 ms delay. (b) 1 ns long zoomed-in section at 70 and 280 ns of all 11 traces shown in (a) (the traces have been shifted in time for better visibility).
Fig. 4.
Fig. 4. RF spectra of the BFC obtained via FFT of the temporal measurement shown Fig. 3. (a) RF spectrum of one entire quasi-CW output pulse. (b) Zoomed-in sections at νB and 2νB of RF spectra of 70 ns long intervals of one quasi-CW output pulse centered around 55 ns (black, squares), 125 ns (red, dots), 195 ns (blue triangles pointing up), and 265 ns (magenta, triangles pointing down), illustrating the increase of the comb repetition rate on a nanosecond time scale.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

ddtΔΔϕj(t)=0.
ΔT=P(1eαL)ΔtVρcm=0.16K,
Δϕ=2πλ×2(nLT+LnT)ΔT=1.7π,

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