Abstract

The bidirectional mode-locked oscillator is an emerging light source architecture suitable for dual-comb applications. Therein, bidirectional mode-locked fiber lasers (MLFLs) are particularly promising for their cost effectiveness, system compactness, and environmental robustness. However, the pulse energy has been limited to tens of picojoules, restricting practical dual-comb applications, especially in the nonlinear regime. In this paper, we break the pulse energy limit by devising the first bidirectional all-normal dispersion MLFL with an artificial saturable absorber (ASA). Bidirectional dissipative solitons are generated with ${\gt}{{5}}$-THz bandwidths and ${\gt}{{1}}$-nJ pulse energies. Free-running laser performance is extensively characterized, and the physical mechanism for bidirectional ASA mode-locking is studied. Last but not least, a proof-of-concept dual-comb spectroscopy measurement is demonstrated. Our work paves the way for a new class of bidirectional MLFLs benefiting dual-comb applications in both linear and nonlinear regimes.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

The bidirectional mode-locked oscillator is a novel light source that simultaneously generates two sets of pulse trains from counterpropagating directions in a single cavity. Its inherent cancellation of common-mode noises and passive stabilization of repetition rate difference enables diverse applications such as rotation sensing [1,2], asynchronous sampling [3], and particularly dual-comb spectroscopy [4], which provides fast data acquisition, fine spectral resolution, and high signal-to-noise ratio [5]. Consequently, research efforts have been devoted to realizing bidirectional mode-locked oscillators in various platforms [613]. Therein, bidirectional mode-locked fiber lasers (MLFLs) have attracted much attention thanks to their cost effectiveness, system compactness, and environmental robustness [813].

The dual-wavelength MLFL is another widely implemented technology with impressive dual-comb demonstrations [14,15]. However, external amplification and nonlinear spectral broadening are fundamentally required to create spectral overlap between the two combs, which increase the system complexity and degrade the stability. Moreover, the unidirectional intracavity pulse collision induces noticeable periodic perturbations [15,16]. In comparison, bidirectional MLFLs provide excellent spectral overlap and minimized cross talk simultaneously, and therefore are ideal for dual-comb applications.

However, until now, all bidirectional MLFLs have relied on real saturable absorbers (SAs). Compared to artificial saturable absorbers (ASAs) such as nonlinear polarization rotation (NPR) and nonlinear amplifying loop mirror (NALM), SAs have much slower time response and require soliton pulse shaping to achieve a larger bandwidth, which in turn restricts the attainable pulse energy to tens of picojoules [810]. Similarly, hybrid bidirectional MLFLs that include both SA and NPR have also been implemented recently [1113]. Overall, bidirectional MLFLs with high mutual coherence and relative stability have been demonstrated, but the maximum attainable pulse energy is still limited to 50 pJ [13]. Thus, external amplifiers are required for practical applications of bidirectional MLFLs.

Large pulse energy at the nanojoule-level, not achievable in state-of-the-art bidirectional MLFLs, is particularly important for various nonlinear dual-comb applications such as pump-probe spectroscopy [17], asynchronously pumped optical parametric oscillators [18], and coherent Raman spectroimaging [19]. Such pulse energy limit can be surpassed by devising a bidirectional MLFL mode-locked with an ASA in the dissipative soliton regime such as all-normal dispersion (ANDi) lasers that feature much higher pulse energy (tens of nanojoules), broader optical bandwidth, and flat-top spectral shape [2022]. Unfortunately, bidirectional operation has not yet been demonstrated in any ASA-based MLFLs. On the contrary, it has been suggested that bidirectional mode-locking is not feasible in ASA-based MLFLs, and they always operate unidirectionally, even without any intracavity isolator [23,24].

Here we experimentally demonstrate the first bidirectional ANDi laser based on NPR. Fundamental mode-locking was established in both directions with flat-top spectra spanning more than 20 nm at 1070 nm and output pulse energies greater than 1 nJ, more than an order of magnitude higher than state-of-the-art bidirectional MLFLs [813]. The fundamental repetition rate (${{f}_{\rm{rep}}}$) is 46 MHz, and the repetition rate difference ($\Delta\! {{f}_{\rm{rep}}}$) between the two directions is continuously tunable from 0.1 Hz to more than 100 Hz through adjustment of the pump power and the wave plates without losing or changing the mode-locked state, which brings significant flexibility to accommodate different applications. In addition, free-running frequency stability, common-mode noise cancellation, single-sideband (SSB) phase noise, and relative intensity noise (RIN) were comprehensively analyzed. Moreover, distinctly different spectral and power evolutions between the two directions were observed and studied, elucidating the indispensable role of cavity asymmetry in establishing the bidirectional NPR mode-locking. Finally, a proof-of-concept dual-comb spectroscopy measurement was demonstrated.

The experimental setup is shown in Fig. 1(a). A 2-m double-cladding ytterbium-doped fiber (DC-YDF, YB1200-6/125DC), pumped by a multimode 980-nm laser, was used as the gain medium. The pump was launched into the DC-YDF through a pump combiner that had 0.3-m double-cladding fiber (DCF, Coractive-DCF-UN-6/125-14) pigtails on both ends (blue). The rest of the fiber components consisted of a 0.7-m HI 1060 fiber on the left side and a 99/1 fiber coupler (with 0.6-m HI 1060 fiber pigtails on both ends) on the right side for monitoring the pulses in the clockwise (CW) direction. Therefore, a total of 0.7-m and 1.2-m passive fiber were deployed asymmetrically on the left and right side of the gain medium, respectively. A free-space beam sampler (3%) was used for monitoring the pulses in the counterclockwise (CCW) direction. Two quarter-wave plates (QWPs) and two half-wave plates (HWPs) were deployed for polarization control and two polarization beam splitters (PBSs) were used as output couplers. Between the two PBSs, a 10-nm bandwidth Gaussian shape spectral filter centered at 1070 nm (Thorlabs, FB1070-10) was used. Optical isolators (ISOs) were placed at both output ports to prevent any backreflections.

 

Fig. 1. (a) Experimental setup of the bidirectional mode-locked ANDi laser. (b) Optical spectra and (c) oscilloscope trace of mode-locked pulses in CW (black) and CCW (red) direction.

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By increasing the pump power to 1.8 W, bidirectional mode-locking was achieved (Supplement 1, Section 1) as shown in Fig. 1(b). Benefiting from the dissipative soliton formation mechanism, the optical spectra for both directions were spectrally flat (${\lt}{{2}}\;{\rm{dB}}$ fluctuation) over 20 nm (5.3 THz). Such a broadband flat-top spectrum is highly desirable for dual-comb spectroscopy. At the pump power of 2 W, the output power of the CW and CCW directions were 50 mW and 72 mW, respectively, corresponding to pulse energies of more than 1 nJ for both directions. The efficiency can be further improved, thus reducing the pump power requirement, by minimizing the transmission loss of the Gaussian filter and utilizing large-core DC-YDFs with higher pump absorption. Time domain waveforms were measured using a 10-GHz photodetector and a 20-GHz real-time oscilloscope to confirm that both directions were fundamentally mode-locked, as shown in Fig. 1(c).

 

Fig. 2. Frequency stability of the bidirectional mode-locked ANDi laser. (a) $\Delta\! {{f}_{\rm{rep}}}$ between the two directions and its tunability by changing pump power (inset); (b) ${{f}_{\rm{rep}}}$ of the mode-locked pulses in CW direction (black) and CCW direction (red), and $\Delta\! {{f}_{\rm{rep}}}$ (blue) measured over a time span of 6000 s. Inset: zoom in of $\Delta\! {{f}_{\rm{rep}}}$ over the entire time span; (c) PSD of ${{f}_{\rm{rep}}}$ (black) and $\Delta\! {{f}_{\rm{rep}}}$ (blue), showing a common-mode noise cancellation of ${\gt}{{30}}\;{\rm{dB}}$ for slow fluctuations. The averaged traces are shown in green and pink. (d) Allan deviation of $\Delta\! {{f}_{\rm{rep}}}$, showing characteristic scaling of $\tau ^{-0.3}$ and $\tau ^{0.43}$ below and above the 100-s gate time.

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To observe the repetition rate difference ($\Delta\! {{f}_{\rm{rep}}}$), the outputs were combined through a 50/50 coupler and detected using a photodetector and an electrical spectral analyzer. As shown in Fig. 2(a), two RF tones with a small spacing of 140 Hz were observed. As shown in the inset of Fig. 2(a), by changing the pump power from 1.8 to 2.4 W, $\Delta\! {{f}_{\rm{rep}}}$ could be continuously tuned from 110 to 160 Hz without losing or changing the mode-locked state. More significantly, continuous $\Delta\! {{f}_{\rm{rep}}}$ tuning from 100 Hz all the way down to 0.1 Hz can be achieved by rotating the wave plates without lock-in effect and losing or changing the mode-locked state (Supplement 1, Section 2). Next, the free-running repetition rate was characterized by the simultaneous measurements of ${{f}_{\rm{rep}}}$ for both directions using two electronically synchronized frequency counters for 6000 s with a 1-s gate time. As shown in Fig. 2(b), ${{f}_{\rm{rep}}}$ of CW direction (black) and CCW direction (red) both drifted noticeably over time, showing a peak-to-peak deviation of 66 Hz. However, most of the ${{f}_{\rm{rep}}}$ drift is a common-mode noise, and thus it is not present in the $\Delta\! {{f}_{\rm{rep}}}$ (blue trace). As observed in the zoom-in view of the blue trace [inset of Fig. 2(b)], $\Delta\! {{f}_{\rm{rep}}}$ exhibited a much higher frequency stability and the corresponding peak-to-peak deviation was suppressed by 26 times to 2.5 Hz. To determine the common-mode noise cancellation, the measurement data were processed to obtain the power spectra density (PSD) of both ${{f}_{\rm{rep}}}$ and $\Delta\! {{f}_{\rm{rep}}}$, as shown in Fig. 2(c). ${\gt}{{30}}\;{\rm{dB}}$ common-mode noise cancellation is attainable for slow fluctuations below 0.1 Hz. At faster time scales, the measurement approaches the counter limit, and thus only an instrument-limited 10 dB noise suppression can be observed. To quantify the frequency stability of $\Delta\! {{f}_{\rm{rep}}}$, its Allan deviation was calculated and is shown in Fig. 2(d). For the gate time below 100 s, the free-running Allan deviation exhibits a characteristic roll-off as $\tau ^{-0.3}$, indicating that $\Delta\! {{f}_{\rm{rep}}}$ was dominated by white and flicker frequency noise in this time scale. The deviation reached its minimum of 110 mHz at 100-s gate time and started to increase with a scaling of $\tau ^{0.43}$ that is very close to the characteristic $\tau ^{0.5}$ scaling of random walk frequency noise. Thus, the long-term deviation can be attributed to the air disturbance and temperature fluctuation. Enclosing the bidirectional ANDi laser in a double-walled shielding box [25] will isolate it from environmental perturbations. In addition, as frequency drift features an Allan deviation linearly scaled with the gate time, we can conclude from the analysis that there is indeed no discernible drift in $\Delta\! {{f}_{\rm{rep}}}$.

In order to obtain a deeper insight of the ${{f}_{\rm{rep}}}$ noise sources, SSB phase noises of both directions at 10-GHz carrier frequency were measured (Supplement 1, Section 3) and are shown in Fig. 3(a). Of note, the two SSB phase noise traces were indistinguishable, and they both exhibited significantly elevated phase noises for offset frequencies below 10 kHz. We attribute this excessive phase noise to the pump power fluctuation of the high-power multimode 980-nm laser. The phase noise has also been compared with the unidirectional mode-locked states, and no noticeable degradation was introduced by the bidirectional operation thanks to the minimized cross talk between the two directions (Supplement 1, Section 4). Similarly, the measured RINs of both directions were also indistinguishable, and thus only the RIN noise of the CW direction is shown in Fig. 3(b) for clarity. The integrated RIN noise from 1 kHz to 5 MHz was 0.8%, more than an order of magnitude higher than state-of-the-art ANDi lasers pumped by single-mode laser diodes [26]. As an ANDi laser features a large accumulated nonlinear phase, we expect the RIN-induced phase noise through self-steepening [27] to be one of the dominant noise sources. The contribution of such phase noise was estimated according to Eq. (45) in Ref. [27] and is shown as the blue trace in Fig. 3(a). Treating the nonlinear phase shift as the only free-fitting parameter, the calculated RIN-induced phase noise overlaps well with the measured phase noise when the nonlinear phase shift is 80 rad, close to the estimated value in our experiment. We conclude from the analysis that the SSB phase noise of the bidirectional ANDi laser is currently limited by the RIN-induced phase noise, which can be well compensated through active power stabilization [28]. The green dashed-dotted line in Fig. 3(a) plots the calculated RIN-induced phase noise by assuming the RIN noise from 10 Hz to 10 kHz are all actively suppressed to the $ - 115\;{\rm dB}$ level [28]. An improvement of more than 40 dB can be achieved, and the resulting SSB phase noise will reach the same level of other free-running MLFLs used as ultrastable master oscillators [29]. In addition, the Gordon–Haus jitter [30] was calculated and is shown as the pink dashed line in Fig. 3(a). As ANDi lasers feature large cavity dispersions, the SSB phase noise is ultimately going to be limited by the Gordon–Haus jitter, which is still 30 dB below the suppressed RIN-induced phase noise in our current cavity design. Therefore, longer cavity length and larger cavity dispersion can be utilized together with large-mode-area fiber to further scale the pulse energy up to 100 nJ [31,32] before the Gordon–Haus jitter starts to limit the laser performance.

 

Fig. 3. (a) Measured SSB phase noises at 10 GHz carrier for CW (black) and CCW (red) directions, showing that the bidirectional mode-locked ANDi laser is currently limited by the RIN-induced phase noise (blue) rather than the Gordon–Haus jitter (pink); (b) PSD of the RIN noise.

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To shed light on the physical mechanism behind the bidirectional NPR mode-locking in ANDi lasers, we varied the pump power and recorded the distinctly different evolutions of optical spectra, output power, and intracavity power from the two directions. The optical spectra from CW and CCW output ports are shown in Figs. 4(a) and 4(b), respectively, as the pump power was tuned from 1.9 to 2.5 W at a step of 100 mW. While the CW output spectrum broadened monolithically with the increase of the pump power, the CCW output spectrum only showed negligible changes. Such a phenomenon is universal for all the identified mode-locking states. The output power and intracavity power from both directions were measured from output ports and estimated from monitor ports, respectively. Then, the transmitted power and coupling ratio were calculated and are shown in Figs. 4(c) and 4(d). While the transmitted power in the CW direction increased by 42%, that in the CCW direction only increased by 5%, explaining the distinct spectral evolution. The different transmitted power evolution was a direct consequence of the opposite coupling ratio evolution, as shown in Fig. 4(d). When the intracavity power increased with higher pump power, the coupling ratio of the CCW direction also increased, thus resulting in a nearly constant transmitted power. The distinct evolutions of output coupling ratio for the two directions are attributed to the different accumulated nonlinearity resulting from the cavity asymmetry. More importantly, the nearly constant transmitted power and increased coupling ratio (decreased transmission) for the CCW direction indicate that it is mode-locked around the critical saturation power (CSP) [33], where the effect of saturable absorption is saturated and turning into reverse saturable absorption. It has been shown that the peak power clamping effect around the CSP would facilitate the amplification of background noise, inducing noise-like-pulse in unidirectional MLFLs [33]. In our case, the mode-locking around the CSP could mitigate the gain competition between the counterpropagating directions, thus leading to the bidirectional mode-locking. In addition, numerical simulation is performed, and similar phenomena have been successfully reproduced (Supplement 1, Section 5), which further confirms the experimental observation.

 

Fig. 4. (a), (b) Measured evolutions of the optical spectra; (c) the transmitted power and (d) output coupling ratio as functions of the pump power.

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Last but not least, dual-comb spectroscopy measurement was performed on a homemade optical band-stop filter (OBSF), mimicking a sample with several absorption lines (Supplement 1, Section 6). As shown in Fig. 5(a), the interferogram represents a $\Delta\! {{f}_{\rm{rep}}}$ of 83 Hz, which was chosen to obtain the maximal nonaliasing bandwidth. The zoom-in of a single-shot interferogram is shown in Fig. 5(b), which is later Fourier-transformed to obtain the spectrum in the RF domain, shown in Fig. 5(c). Thanks to the perfect comb spectral overlap, the whole spectrum is converted to the RF domain and the OBSF feature is clearly observed. The extracted OBSF transmission matches well with that measured by an optical spectrum analyzer (OSA) [Fig. 5(d)]. The minor mismatches at low signal level are attributed to the residual RIN noise, which can be mitigated after further pump stabilization in the future.

 

Fig. 5. (a) Multiperiod interferogram; (b) zoom-in of a single interferogram, which is Fourier-transformed to obtain the (c) RF domain spectrum; (d) comparison between the transmission spectra measured by the dual-comb spectroscopy (red dotted line) and the OSA (black solid line).

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In summary, we have demonstrated the first bidirectional NPR mode-locked ANDi laser with flat-top spectra spanning more than 5 THz and output pulse energies greater than 1 nJ. Free-running frequency stability, common-mode noise cancellation, SSB phase noise, and RIN have been comprehensively analyzed to facilitate understanding of performance limits and provide guidance to further improvements. The critical role of asymmetric nonlinearity in establishing bidirectional NPR mode-locking is revealed by both experimental and numerical studies. Moreover, a proof-of-concept dual-comb spectroscopy measurement was demonstrated on a homemade OBSF, mimicking a sample with several absorption lines. The bidirectional mode-locking principle can be further extended to other ASA-based MLFL platforms such as low-phase-noise dispersion-managed MLFL [34] and environmentally stable polarization-maintaining NALM MLFL [35]. Our work paves the way for a new class of bidirectional MLFLs that will benefit precision optical metrologies, including dual-comb applications in both linear and nonlinear regimes.

Disclosures

The authors declare no conflicts of interest.

 

See Supplement 1 for supporting content.

REFERENCES

1. Y. Liu, L. Sun, H. Qiu, Y. Wang, Q. Tian, and X. Ma, Laser Phys. Lett. 4, 187 (2007). [CrossRef]  

2. M. Chernysheva, S. Sugavanam, and S. Turitsyn, APL Photon. 5, 016104 (2020). [CrossRef]  

3. R. D. Baker, N. T. Yardimci, Y. H. Ou, K. Kieu, and M. Jarrahi, Sci. Rep. 8, 1 (2018). [CrossRef]  

4. S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, Appl. Phys. Lett. 108, 231104 (2016). [CrossRef]  

5. I. Coddington, N. Newbury, and W. Swann, Optica 3, 414 (2016). [CrossRef]  

6. Q. F. Yang, X. Yi, K. Y. Yang, and K. J. Vahala, Nat. Photon. 11, 560 (2017). [CrossRef]  

7. T. Ideguchi, T. Nakamura, Y. Kobayashi, and K. Goda, Optica 3, 748 (2016). [CrossRef]  

8. K. Kieu and M. Mansuripur, Opt. Lett. 33, 64 (2008). [CrossRef]  

9. X. Yao, Appl. Opt. 53, 27 (2014). [CrossRef]  

10. C. Zeng, X. Liu, and L. Yun, Opt. Express 21, 18937 (2013). [CrossRef]  

11. A. A. Krylov, D. S. Chernykh, N. R. Arutyunyan, V. V. Grebenyukov, A. S. Pozharov, and E. D. Obraztsova, Appl. Opt. 55, 4201 (2016). [CrossRef]  

12. M. Chernysheva, M. Al Araimi, H. Kbashi, R. Arif, S. V. Sergeyev, and A. Rozhin, Opt. Express 24, 15721 (2016). [CrossRef]  

13. Y. Nakajima, Y. Hata, and K. Minoshima, Opt. Express 27, 5931 (2019). [CrossRef]  

14. X. Zhao, G. Hu, B. Zhao, C. Li, Y. Pan, Y. Liu, and Z. Zheng, Opt. Express 24, 21833 (2016). [CrossRef]  

15. F. J. Ellinger, A. S. Mayer, G. Winkler, G. W. Rosinger, G. W. Truong, S. Droste, C. Li, C. M. Heyl, I. Hartl, and O. H. Heckl, Opt. Express 27, 28062 (2019). [CrossRef]  

16. Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, Appl. Phys. Lett. 112, 081104 (2018). [CrossRef]  

17. M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, Rev. Sci. Instrum. 87, 031101 (2016). [CrossRef]  

18. Z. Zhang, C. Gu, J. Sun, C. Wang, T. Gardiner, and D. T. Reid, Opt. Lett. 37, 187 (2012). [CrossRef]  

19. T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, Nature 502, 355 (2013). [CrossRef]  

20. A. Chong, W. H. Renninger, and F. W. Wise, Opt. Lett. 32, 2408 (2007). [CrossRef]  

21. A. Chong, W. H. Renninger, and F. W. Wise, J. Opt. Soc. Am. B 25, 140 (2008). [CrossRef]  

22. K. Kieu and F. W. Wise, Opt. Express 16, 11453 (2008). [CrossRef]  

23. L. M. Zhao, D. Y. Tang, T. H. Cheng, and C. Lu, J. Opt. A 9, 477 (2007). [CrossRef]  

24. D. Li, D. Shen, L. Li, H. Chen, D. Tang, and L. Zhao, Appl. Opt. 54, 7912 (2015). [CrossRef]  

25. K. Jung and J. Kim, Sci. Rep. 5, 1 (2015). [CrossRef]  

26. P. Qin, Y. Song, H. Kim, J. Shin, D. Kwon, M. Hu, and J. Kim, Opt. Express 22, 28276 (2014). [CrossRef]  

27. R. Paschotta, Appl. Phys. B 79, 163 (2004). [CrossRef]  

28. J. Kim and Y. Song, Adv. Opt. Photon. 8, 465 (2016). [CrossRef]  

29. A. Winter, P. Schmuser, H. Schlarb, F. O. Ilday, J. W. Kim, and F. X. Kätner, in Particle Accelerator Conference (2005).

30. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986). [CrossRef]  

31. S. Lefrançois, K. Kieu, Y. Deng, J. D. Kafka, and F. W. Wise, Opt. Lett. 35, 1569 (2010). [CrossRef]  

32. M. Baumgartl, F. Jansen, F. Stutzki, C. Jauregui, B. Ortaç, J. Limpert, and A. Tünnermann, Opt. Lett. 36, 244 (2011). [CrossRef]  

33. Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, and Y. Kwon, Opt. Fiber Technol. 20, 575 (2014). [CrossRef]  

34. C. Kim, S. Bae, K. Kieu, and J. Kim, Opt. Express 21, 26533 (2013). [CrossRef]  

35. Y. Nakajima, Y. Hata, and K. Minoshima, Opt. Express 27, 14648 (2019). [CrossRef]  

References

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  • |

  1. Y. Liu, L. Sun, H. Qiu, Y. Wang, Q. Tian, and X. Ma, Laser Phys. Lett. 4, 187 (2007).
    [Crossref]
  2. M. Chernysheva, S. Sugavanam, and S. Turitsyn, APL Photon. 5, 016104 (2020).
    [Crossref]
  3. R. D. Baker, N. T. Yardimci, Y. H. Ou, K. Kieu, and M. Jarrahi, Sci. Rep. 8, 1 (2018).
    [Crossref]
  4. S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, Appl. Phys. Lett. 108, 231104 (2016).
    [Crossref]
  5. I. Coddington, N. Newbury, and W. Swann, Optica 3, 414 (2016).
    [Crossref]
  6. Q. F. Yang, X. Yi, K. Y. Yang, and K. J. Vahala, Nat. Photon. 11, 560 (2017).
    [Crossref]
  7. T. Ideguchi, T. Nakamura, Y. Kobayashi, and K. Goda, Optica 3, 748 (2016).
    [Crossref]
  8. K. Kieu and M. Mansuripur, Opt. Lett. 33, 64 (2008).
    [Crossref]
  9. X. Yao, Appl. Opt. 53, 27 (2014).
    [Crossref]
  10. C. Zeng, X. Liu, and L. Yun, Opt. Express 21, 18937 (2013).
    [Crossref]
  11. A. A. Krylov, D. S. Chernykh, N. R. Arutyunyan, V. V. Grebenyukov, A. S. Pozharov, and E. D. Obraztsova, Appl. Opt. 55, 4201 (2016).
    [Crossref]
  12. M. Chernysheva, M. Al Araimi, H. Kbashi, R. Arif, S. V. Sergeyev, and A. Rozhin, Opt. Express 24, 15721 (2016).
    [Crossref]
  13. Y. Nakajima, Y. Hata, and K. Minoshima, Opt. Express 27, 5931 (2019).
    [Crossref]
  14. X. Zhao, G. Hu, B. Zhao, C. Li, Y. Pan, Y. Liu, and Z. Zheng, Opt. Express 24, 21833 (2016).
    [Crossref]
  15. F. J. Ellinger, A. S. Mayer, G. Winkler, G. W. Rosinger, G. W. Truong, S. Droste, C. Li, C. M. Heyl, I. Hartl, and O. H. Heckl, Opt. Express 27, 28062 (2019).
    [Crossref]
  16. Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, Appl. Phys. Lett. 112, 081104 (2018).
    [Crossref]
  17. M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, Rev. Sci. Instrum. 87, 031101 (2016).
    [Crossref]
  18. Z. Zhang, C. Gu, J. Sun, C. Wang, T. Gardiner, and D. T. Reid, Opt. Lett. 37, 187 (2012).
    [Crossref]
  19. T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, Nature 502, 355 (2013).
    [Crossref]
  20. A. Chong, W. H. Renninger, and F. W. Wise, Opt. Lett. 32, 2408 (2007).
    [Crossref]
  21. A. Chong, W. H. Renninger, and F. W. Wise, J. Opt. Soc. Am. B 25, 140 (2008).
    [Crossref]
  22. K. Kieu and F. W. Wise, Opt. Express 16, 11453 (2008).
    [Crossref]
  23. L. M. Zhao, D. Y. Tang, T. H. Cheng, and C. Lu, J. Opt. A 9, 477 (2007).
    [Crossref]
  24. D. Li, D. Shen, L. Li, H. Chen, D. Tang, and L. Zhao, Appl. Opt. 54, 7912 (2015).
    [Crossref]
  25. K. Jung and J. Kim, Sci. Rep. 5, 1 (2015).
    [Crossref]
  26. P. Qin, Y. Song, H. Kim, J. Shin, D. Kwon, M. Hu, and J. Kim, Opt. Express 22, 28276 (2014).
    [Crossref]
  27. R. Paschotta, Appl. Phys. B 79, 163 (2004).
    [Crossref]
  28. J. Kim and Y. Song, Adv. Opt. Photon. 8, 465 (2016).
    [Crossref]
  29. A. Winter, P. Schmuser, H. Schlarb, F. O. Ilday, J. W. Kim, and F. X. Kätner, in Particle Accelerator Conference (2005).
  30. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [Crossref]
  31. S. Lefrançois, K. Kieu, Y. Deng, J. D. Kafka, and F. W. Wise, Opt. Lett. 35, 1569 (2010).
    [Crossref]
  32. M. Baumgartl, F. Jansen, F. Stutzki, C. Jauregui, B. Ortaç, J. Limpert, and A. Tünnermann, Opt. Lett. 36, 244 (2011).
    [Crossref]
  33. Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, and Y. Kwon, Opt. Fiber Technol. 20, 575 (2014).
    [Crossref]
  34. C. Kim, S. Bae, K. Kieu, and J. Kim, Opt. Express 21, 26533 (2013).
    [Crossref]
  35. Y. Nakajima, Y. Hata, and K. Minoshima, Opt. Express 27, 14648 (2019).
    [Crossref]

2020 (1)

M. Chernysheva, S. Sugavanam, and S. Turitsyn, APL Photon. 5, 016104 (2020).
[Crossref]

2019 (3)

2018 (2)

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, Appl. Phys. Lett. 112, 081104 (2018).
[Crossref]

R. D. Baker, N. T. Yardimci, Y. H. Ou, K. Kieu, and M. Jarrahi, Sci. Rep. 8, 1 (2018).
[Crossref]

2017 (1)

Q. F. Yang, X. Yi, K. Y. Yang, and K. J. Vahala, Nat. Photon. 11, 560 (2017).
[Crossref]

2016 (8)

2015 (2)

2014 (3)

2013 (3)

C. Zeng, X. Liu, and L. Yun, Opt. Express 21, 18937 (2013).
[Crossref]

C. Kim, S. Bae, K. Kieu, and J. Kim, Opt. Express 21, 26533 (2013).
[Crossref]

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, Nature 502, 355 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (1)

2008 (3)

2007 (3)

L. M. Zhao, D. Y. Tang, T. H. Cheng, and C. Lu, J. Opt. A 9, 477 (2007).
[Crossref]

A. Chong, W. H. Renninger, and F. W. Wise, Opt. Lett. 32, 2408 (2007).
[Crossref]

Y. Liu, L. Sun, H. Qiu, Y. Wang, Q. Tian, and X. Ma, Laser Phys. Lett. 4, 187 (2007).
[Crossref]

2004 (1)

R. Paschotta, Appl. Phys. B 79, 163 (2004).
[Crossref]

1986 (1)

Al Araimi, M.

Arif, R.

Arutyunyan, N. R.

Bae, S.

Baker, R. D.

R. D. Baker, N. T. Yardimci, Y. H. Ou, K. Kieu, and M. Jarrahi, Sci. Rep. 8, 1 (2018).
[Crossref]

Baumgartl, M.

Bernhardt, B.

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, Nature 502, 355 (2013).
[Crossref]

Chen, H.

Cheng, T. H.

L. M. Zhao, D. Y. Tang, T. H. Cheng, and C. Lu, J. Opt. A 9, 477 (2007).
[Crossref]

Chernykh, D. S.

Chernysheva, M.

Chong, A.

Coddington, I.

Deng, Y.

Droste, S.

Ellinger, F. J.

Fischer, M. C.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, Rev. Sci. Instrum. 87, 031101 (2016).
[Crossref]

Gardiner, T.

Goda, K.

Gordon, J. P.

Grebenyukov, V. V.

Gu, C.

Guelachvili, G.

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, Nature 502, 355 (2013).
[Crossref]

Hänsch, T. W.

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, Nature 502, 355 (2013).
[Crossref]

Hartl, I.

Hata, Y.

Haus, H. A.

Heckl, O. H.

Heyl, C. M.

Holzner, S.

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, Nature 502, 355 (2013).
[Crossref]

Hu, G.

Hu, M.

Ideguchi, T.

T. Ideguchi, T. Nakamura, Y. Kobayashi, and K. Goda, Optica 3, 748 (2016).
[Crossref]

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, Nature 502, 355 (2013).
[Crossref]

Ilday, F. O.

A. Winter, P. Schmuser, H. Schlarb, F. O. Ilday, J. W. Kim, and F. X. Kätner, in Particle Accelerator Conference (2005).

Jansen, F.

Jarrahi, M.

R. D. Baker, N. T. Yardimci, Y. H. Ou, K. Kieu, and M. Jarrahi, Sci. Rep. 8, 1 (2018).
[Crossref]

Jauregui, C.

Jeong, Y.

Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, and Y. Kwon, Opt. Fiber Technol. 20, 575 (2014).
[Crossref]

Jung, K.

K. Jung and J. Kim, Sci. Rep. 5, 1 (2015).
[Crossref]

Kafka, J. D.

Kätner, F. X.

A. Winter, P. Schmuser, H. Schlarb, F. O. Ilday, J. W. Kim, and F. X. Kätner, in Particle Accelerator Conference (2005).

Kbashi, H.

Kieu, K.

Kim, C.

Kim, H.

Kim, J.

Kim, J. W.

A. Winter, P. Schmuser, H. Schlarb, F. O. Ilday, J. W. Kim, and F. X. Kätner, in Particle Accelerator Conference (2005).

Kobayashi, Y.

Krylov, A. A.

Kwon, D.

Kwon, Y.

Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, and Y. Kwon, Opt. Fiber Technol. 20, 575 (2014).
[Crossref]

Lee, S.

Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, and Y. Kwon, Opt. Fiber Technol. 20, 575 (2014).
[Crossref]

Lefrançois, S.

Li, B.

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, Appl. Phys. Lett. 112, 081104 (2018).
[Crossref]

Li, C.

Li, D.

Li, L.

Limpert, J.

Liu, X.

Liu, Y.

X. Zhao, G. Hu, B. Zhao, C. Li, Y. Pan, Y. Liu, and Z. Zheng, Opt. Express 24, 21833 (2016).
[Crossref]

Y. Liu, L. Sun, H. Qiu, Y. Wang, Q. Tian, and X. Ma, Laser Phys. Lett. 4, 187 (2007).
[Crossref]

Lu, C.

L. M. Zhao, D. Y. Tang, T. H. Cheng, and C. Lu, J. Opt. A 9, 477 (2007).
[Crossref]

Ma, X.

Y. Liu, L. Sun, H. Qiu, Y. Wang, Q. Tian, and X. Ma, Laser Phys. Lett. 4, 187 (2007).
[Crossref]

Mansuripur, M.

Mayer, A. S.

Mehravar, S.

S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, Appl. Phys. Lett. 108, 231104 (2016).
[Crossref]

Minoshima, K.

Nakajima, Y.

Nakamura, T.

Newbury, N.

Norwood, R. A.

S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, Appl. Phys. Lett. 108, 231104 (2016).
[Crossref]

Obraztsova, E. D.

Ortaç, B.

Ou, Y. H.

R. D. Baker, N. T. Yardimci, Y. H. Ou, K. Kieu, and M. Jarrahi, Sci. Rep. 8, 1 (2018).
[Crossref]

Pan, Y.

Paschotta, R.

R. Paschotta, Appl. Phys. B 79, 163 (2004).
[Crossref]

Peyghambarian, N.

S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, Appl. Phys. Lett. 108, 231104 (2016).
[Crossref]

Picqué, N.

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, Nature 502, 355 (2013).
[Crossref]

Pozharov, A. S.

Qin, P.

Qiu, H.

Y. Liu, L. Sun, H. Qiu, Y. Wang, Q. Tian, and X. Ma, Laser Phys. Lett. 4, 187 (2007).
[Crossref]

Reid, D. T.

Renninger, W. H.

Robles, F. E.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, Rev. Sci. Instrum. 87, 031101 (2016).
[Crossref]

Rosinger, G. W.

Rozhin, A.

Schlarb, H.

A. Winter, P. Schmuser, H. Schlarb, F. O. Ilday, J. W. Kim, and F. X. Kätner, in Particle Accelerator Conference (2005).

Schmuser, P.

A. Winter, P. Schmuser, H. Schlarb, F. O. Ilday, J. W. Kim, and F. X. Kätner, in Particle Accelerator Conference (2005).

Sergeyev, S. V.

Shen, D.

Shin, J.

Song, Y.

Stutzki, F.

Sugavanam, S.

M. Chernysheva, S. Sugavanam, and S. Turitsyn, APL Photon. 5, 016104 (2020).
[Crossref]

Sun, J.

Sun, L.

Y. Liu, L. Sun, H. Qiu, Y. Wang, Q. Tian, and X. Ma, Laser Phys. Lett. 4, 187 (2007).
[Crossref]

Swann, W.

Tang, D.

Tang, D. Y.

L. M. Zhao, D. Y. Tang, T. H. Cheng, and C. Lu, J. Opt. A 9, 477 (2007).
[Crossref]

Tian, Q.

Y. Liu, L. Sun, H. Qiu, Y. Wang, Q. Tian, and X. Ma, Laser Phys. Lett. 4, 187 (2007).
[Crossref]

Truong, G. W.

Tünnermann, A.

Turitsyn, S.

M. Chernysheva, S. Sugavanam, and S. Turitsyn, APL Photon. 5, 016104 (2020).
[Crossref]

Vahala, K. J.

Q. F. Yang, X. Yi, K. Y. Yang, and K. J. Vahala, Nat. Photon. 11, 560 (2017).
[Crossref]

Vazquez-Zuniga, L. A.

Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, and Y. Kwon, Opt. Fiber Technol. 20, 575 (2014).
[Crossref]

Wang, C.

Wang, Y.

Y. Liu, L. Sun, H. Qiu, Y. Wang, Q. Tian, and X. Ma, Laser Phys. Lett. 4, 187 (2007).
[Crossref]

Warren, W. S.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, Rev. Sci. Instrum. 87, 031101 (2016).
[Crossref]

Wei, X.

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, Appl. Phys. Lett. 112, 081104 (2018).
[Crossref]

Wei, Y.

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, Appl. Phys. Lett. 112, 081104 (2018).
[Crossref]

Wilson, J. W.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, Rev. Sci. Instrum. 87, 031101 (2016).
[Crossref]

Winkler, G.

Winter, A.

A. Winter, P. Schmuser, H. Schlarb, F. O. Ilday, J. W. Kim, and F. X. Kätner, in Particle Accelerator Conference (2005).

Wise, F. W.

Wong, K. K. Y.

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, Appl. Phys. Lett. 112, 081104 (2018).
[Crossref]

Yang, K. Y.

Q. F. Yang, X. Yi, K. Y. Yang, and K. J. Vahala, Nat. Photon. 11, 560 (2017).
[Crossref]

Yang, Q. F.

Q. F. Yang, X. Yi, K. Y. Yang, and K. J. Vahala, Nat. Photon. 11, 560 (2017).
[Crossref]

Yao, X.

Yardimci, N. T.

R. D. Baker, N. T. Yardimci, Y. H. Ou, K. Kieu, and M. Jarrahi, Sci. Rep. 8, 1 (2018).
[Crossref]

Yi, X.

Q. F. Yang, X. Yi, K. Y. Yang, and K. J. Vahala, Nat. Photon. 11, 560 (2017).
[Crossref]

Yu, Y.

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, Appl. Phys. Lett. 112, 081104 (2018).
[Crossref]

Yun, L.

Zeng, C.

Zhang, Z.

Zhao, B.

Zhao, L.

Zhao, L. M.

L. M. Zhao, D. Y. Tang, T. H. Cheng, and C. Lu, J. Opt. A 9, 477 (2007).
[Crossref]

Zhao, X.

Zheng, Z.

Adv. Opt. Photon. (1)

APL Photon. (1)

M. Chernysheva, S. Sugavanam, and S. Turitsyn, APL Photon. 5, 016104 (2020).
[Crossref]

Appl. Opt. (3)

Appl. Phys. B (1)

R. Paschotta, Appl. Phys. B 79, 163 (2004).
[Crossref]

Appl. Phys. Lett. (2)

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, Appl. Phys. Lett. 112, 081104 (2018).
[Crossref]

S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, Appl. Phys. Lett. 108, 231104 (2016).
[Crossref]

J. Opt. A (1)

L. M. Zhao, D. Y. Tang, T. H. Cheng, and C. Lu, J. Opt. A 9, 477 (2007).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Phys. Lett. (1)

Y. Liu, L. Sun, H. Qiu, Y. Wang, Q. Tian, and X. Ma, Laser Phys. Lett. 4, 187 (2007).
[Crossref]

Nat. Photon. (1)

Q. F. Yang, X. Yi, K. Y. Yang, and K. J. Vahala, Nat. Photon. 11, 560 (2017).
[Crossref]

Nature (1)

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, Nature 502, 355 (2013).
[Crossref]

Opt. Express (9)

Opt. Fiber Technol. (1)

Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, and Y. Kwon, Opt. Fiber Technol. 20, 575 (2014).
[Crossref]

Opt. Lett. (6)

Optica (2)

Rev. Sci. Instrum. (1)

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, Rev. Sci. Instrum. 87, 031101 (2016).
[Crossref]

Sci. Rep. (2)

R. D. Baker, N. T. Yardimci, Y. H. Ou, K. Kieu, and M. Jarrahi, Sci. Rep. 8, 1 (2018).
[Crossref]

K. Jung and J. Kim, Sci. Rep. 5, 1 (2015).
[Crossref]

Other (1)

A. Winter, P. Schmuser, H. Schlarb, F. O. Ilday, J. W. Kim, and F. X. Kätner, in Particle Accelerator Conference (2005).

Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. (a) Experimental setup of the bidirectional mode-locked ANDi laser. (b) Optical spectra and (c) oscilloscope trace of mode-locked pulses in CW (black) and CCW (red) direction.
Fig. 2.
Fig. 2. Frequency stability of the bidirectional mode-locked ANDi laser. (a) $\Delta\! {{f}_{\rm{rep}}}$ between the two directions and its tunability by changing pump power (inset); (b) ${{f}_{\rm{rep}}}$ of the mode-locked pulses in CW direction (black) and CCW direction (red), and $\Delta\! {{f}_{\rm{rep}}}$ (blue) measured over a time span of 6000 s. Inset: zoom in of $\Delta\! {{f}_{\rm{rep}}}$ over the entire time span; (c) PSD of ${{f}_{\rm{rep}}}$ (black) and $\Delta\! {{f}_{\rm{rep}}}$ (blue), showing a common-mode noise cancellation of ${\gt}{{30}}\;{\rm{dB}}$ for slow fluctuations. The averaged traces are shown in green and pink. (d) Allan deviation of $\Delta\! {{f}_{\rm{rep}}}$, showing characteristic scaling of $\tau ^{-0.3}$ and $\tau ^{0.43}$ below and above the 100-s gate time.
Fig. 3.
Fig. 3. (a) Measured SSB phase noises at 10 GHz carrier for CW (black) and CCW (red) directions, showing that the bidirectional mode-locked ANDi laser is currently limited by the RIN-induced phase noise (blue) rather than the Gordon–Haus jitter (pink); (b) PSD of the RIN noise.
Fig. 4.
Fig. 4. (a), (b) Measured evolutions of the optical spectra; (c) the transmitted power and (d) output coupling ratio as functions of the pump power.
Fig. 5.
Fig. 5. (a) Multiperiod interferogram; (b) zoom-in of a single interferogram, which is Fourier-transformed to obtain the (c) RF domain spectrum; (d) comparison between the transmission spectra measured by the dual-comb spectroscopy (red dotted line) and the OSA (black solid line).

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