Wideband mode-locked optical frequency combs
Optical frequency combs have been one of the most exciting achievements in the optics field from the past few decades. These tools can be used to make very precise measurements of different colors and are used in several applications (e.g., in atomic clocks and coherent communications).1 These systems, however, are based on mode-locked lasers that generally have high complexity and large volumes. Microresonator-based Kerr frequency comb (microcomb) generation is thus an emerging technique. In this approach, high-quality-factor microresonators are used to convert a single frequency pump to a broadband comb.2 Microcombs offer the potential of chip-level integration and low power consumption. Both these properties are vital if frequency comb applications are to be extended beyond specialized research laboratories.
In typical microresonators, coupling between transverse modes can shift some resonances away from their natural frequencies. Such resonance shifts introduce an equivalent localized anomalous dispersion in waveguides that have global normal dispersion, which thereby enables hyperparametric oscillation.3 Microresonator group velocity dispersion plays an important role in comb formation dynamics.4 Moreover, it is relatively easy to access hyperparametric oscillation information—required for spontaneous comb initiation—in the anomalous dispersion regime. As such, microresonator geometry generally needs to be tailored so that proper waveguide dispersion can be achieved. The waveguide dispersion can then be used in combination with the material dispersion to produce the overall anomalous dispersion. Tailoring the waveguide dispersion, however, is not always a simple task. Furthermore, in the visible and near-IR wavelength range, material dispersion is strongly normal, which makes tailoring of dispersion even more challenging.
In our work we have addressed the problems associated with tailoring the waveguide dispersion. We have developed a mode-coupling scheme with which we can generate normal-dispersion frequency combs. To do this, we exploit mode coupling to achieve comb generation in silicon nitride (SiN) microrings that have large global normal dispersion in the fiber telecom S, C, and L bands (i.e., 1460–1625nm).5–7
The measured free spectral range (FSR) at different wavelengths for two coupled transverse modes in one of our SiN microrings (with a FSR of about 25GHz) is shown in Figure 1(a).5 Both modes display an overall increasing trend in FSR with wavelength, which corresponds to a global normal dispersion of about −160ps/nm/km. The FSR slope drastically changes, however, in the mode-crossing region. This is caused by mode coupling, which produces significant changes in the local dispersion, as shown in Figure 1(b). We find that the level of dispersion can increase by more than an order of magnitude and that the sign can change from normal to anomalous. We have successfully generated our frequency combs by pumping the mode, which has local anomalous dispersion, in the mode-crossing region. Our results show that one of the comb sidebands was always pinned at a similar mode-crossing wavelength (i.e., a signature of mode-coupling-assisted comb generation).
We have also observed transitions from high-noise combs to low-noise, mode-locked states, which is related to the formation of temporal dark pulses.6 Mode-locked microcombs—related to the formation of bright soliton pulses—have previously been demonstrated in the anomalous dispersion regime.8 Their counterpart dark pulses in the normal dispersion regime, however, had not been clearly observed in the time domain prior to our work. We have used spectral line-by-line shaping to characterize the dark-pulse comb.9 We used the experimental setup shown in Figure 2(a) to pump a SiN microring (with a FSR of about 231GHz) and thus generate the comb. We then used a pulse shaper to compress the comb into transform-limited pulses and thereby retrieve the spectral phase of the comb. We could subsequently reconstruct the time-domain waveform from the amplitude and phase information of the comb. We have thus been able to experimentally reveal dark pulses with complex frequency chirp structures for the first time, as illustrated in Figure 2(b). Furthermore, we have found that mode coupling is required to initiate the dark pulse comb, but it is not essential for maintaining the comb. The cavity dark pulses are localized structures that are balanced by normal dispersion and Kerr nonlinearity, but they are distinct from the dark solitons previously observed in fibers.10 We also applied a thermo-optic heater control to the SiN microring. This, for the first time, allowed substantial tuning of the comb frequencies while mode-locked behavior was maintained. This illustrates—see Figure 2(c)—the robustness of the operating regime that we have discovered.
Mode coupling between different transverse modes depends on accidental degeneracies that are very difficult to control. To solve this issue, we have introduced a new scheme in which we incorporate dual-coupled microrings. We can tune the microrings into degeneracy with the use of thermo-optic control, as shown in Figure 3(a) and (b).7 We have been able to achieve reliable initiation of normal-dispersion microcombs. We have thus generated—see Figure 3(c)—broadband mode-locked frequency combs that we compressed (through line-by-line shaping) to ultra-short transform-limited pulses.
We have developed a new mode-coupling scheme to generate normal-dispersion frequency combs. With our approach, we can achieve comb generation at wavelength ranges where this has previously been prevented (because of the difficulty of achieving wideband anomalous dispersion). Furthermore, in contrast to anomalous-dispersion bright soliton combs, which display stochastic transition behavior,8 we find that normal-dispersion dark pulse combs offer a more deterministic route to mode locking6 and a greater potential for power efficiency.11 In our future work we will investigate comb generation in the visible and near-IR wavelength range, i.e., where material dispersion is strongly normal. We will tailor the dispersion so that it is close to zero, and we will optimize the higher-order dispersion. It may be possible, therefore, to generate ultra-wideband frequency combs that would potentially span more than one octave. This would be valuable for the ‘frequency–2×frequency’ comb self-referencing technique.
Xiaoxiao Xue received his PhD from Tsinghua University, China, in 2012. He is currently a postdoctoral research associate working with Andrew M. Weiner in the Ultrafast Optics and Optics Fiber Communications Laboratory. His research interests include on-chip optical frequency comb generation and microwave photonic signal processing.