1. Introduction

A microresonator frequency comb (microcomb) is a compact optical frequency comb that is, in most cases, excited via the four-wave mixing seeded by a continuous wave (CW) light enhanced in a high-$Q$ microresonator [1]. It has attracted significant interests due to its distinct features from the conventional bulky optical frequency combs (OFCs), such as CMOS compatibility, small footprint, low power consumption, and a high repetition frequency. This new types of comb sources can potentially expand the applications of OFCs including optical clocks [2,3], optical communications [4], millimeter- and terahertz-wave generation [5–7], and precision distance measurement [8–10]. On the other hand, there are still several technical challenges for practical use, such as improving the power conversion efficiency and expanding a spectral bandwidth. In this regard, simple and quick characterization tools for microcombs are highly anticipated.

The combination of numerical and experimental research has so far advanced the development of microcomb technology. For instance, theoretical studies first predicted the existence of a low noise soliton state [11,12], which subsequently led to the experimental realization of a soliton microcomb [13,14]. On the other hand, experimental measurements of comb line phases and detuning to the cavity resonance revealed new comb states with discrete phase steps of $\pi$ or $\pi /2$ between different comb mode families. In addition, all the comb lines were found to be red-detuned in mode-locked states [15], which was unexpected from the thermal instability considerations. While a follow-up numerical simulation using the measured experimental parameters reproduced the overall spectral structures, some inconsistencies between the experiment and simulation still remains, suggesting the presence of the other mode-locking mechanisms that were not taken into account in that simulation.

Although accurate characterization of experimental parameters, such as dispersion, comb power distribution (i.e. envelope profile), phase, and comb-resonance detuning are crucial for precise numerical analysis, such measurements are generally not straightforward particularly in the frequency domain since it involves high resolution measurement over a broad spectral range. For instance, the previous study [15] performed two independent measurements to characterize comb-resonance detuning and comb line phases, respectively. While they successfully visualized these properties in a broadband frequency range, dedicated efforts were required for each measurement including spectral calibration of fine tuning and characterization of background dispersion. Given the limited stabilities of free-running microcomb states including some illusive ones, a fast measurement tool could be useful for tracing such states and capturing the experimental parameters relevant to the numerical simulations.

In this study, we propose to incorporate coherent heterodyne detection (CHD) in the comb-resonance detuning measurement using a broadly tunable external cavity laser. This greatly enhances the measurement sensitivity and thus allows us to obtain the quantitative measurement in a single sweep over a broad spectral range. Therefore, characterization of rather unstable comb states becomes possible. We also show that by using microcomb lines as spectral calibration markers, it is possible to evaluate the dispersive properties of a hot microring resonator, which was previously characterized by using a fiber comb Ref [16]. Since our method can also be extended to the relative phases measurement between comb lines, it potentially allows us to characterize most of the experimental parameters required for the numerical analysis of microcombs in a single experimental setup.

2. Principle of comb-resonance detuning measurement

Figure 1 schematically shows our experimental setup. The system is similar to the detuning measurement system in Ref. [15] but a CHD system is employed. We inject two CW lasers into a ring microresonator; one is a pump laser, and the other is a tunable probe laser (1520 1630 nm). The pump laser is amplified with erbium-doped fiber amplifiers (EDFAs) and used to generate a soliton microcomb by a fast frequency sweep with a single-sideband modulator (SSBM) [17]. The probe laser is split into two. One is coupled with the microresonator from the opposite direction to the pump for characterizing the microresonator transmission spectra. The probe power is attenuated to around −14 dBm with a variable optical attenuator (VOA) so that it does not affect the microcomb state. The other portion, whose power is about 4 dBm, is supplied to the CHD system as a local oscillator (LO). When the probe is frequency-swept, its frequency is effectively shifted from that of LO due to a controlled optical delay between them. Two 3-port optical circulators are used. Circulator 1 directs the pump light towards the microresonator while extracting the probe light and the back-scattered microcomb to the CHD system. Circulator 2 sends the probe to the microresonator and passes the generated microcomb to an optical spectrum analyzer (OSA) to monitor the microcomb spectra. We employ a commercial instrument (AP2683A, Apex Technologies) for the CHD including a tunable laser, indicated as the red-shaded region.

 

Fig. 1. Experimental setup. Inset shows a microresonator structure, whose diameter is about 150 µm.

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Suppose that the electric field $E_X (t)$ is given by,

Therefore, the output of the balanced detector $I_\mathrm {coherent}$ is expressed as follows,

Therefore, weak signals $E_\mathrm {comb}$ (or $E_\mathrm {probe}$) can be amplified by increasing the LO power without changing the probe power, as long as they are not overlapped with each other. Also, by sweeping the LO (probe) wavelength, the output provides both comb lines (as positive peaks) and resonator transmission spectra (as negative dips), simultaneously.

The output signal $I_\mathrm {coherent}$ is subsequently filtered by an RF bandpass filter (BPF) prior to digital data acquisition. Note that by the virtue of CHD, no optical filters, as well as the synchronous scanning of a laser and a filter, are required to improve the signal-to-noise ratio, as used in Ref. [15]. Under the experimental conditions, the frequency sweep rate can be made as fast as 4.4 THz/s while the spectral resolution was fixed at 5 MHz. The former is limited by the mechanical motor control for the laser scanning. The latter was determined by the bandwidth of the BPF, but could further be decreased to the limit set by the linewidth of the probe laser ($\sim$ 100 kHz). A critical limitation for the amount of acquired data in unit time is the acquisition time of the analog-to-digital converter in the system. In addition, relative phase measurements of comb lines should be feasible in this configuration by subtracting the background dispersion or by RF signal processing at later stages [19], provided that the comb lines are located far from the resonance. The measurement scheme can simplify the broadband and simultaneous characterization of multiple optical properties of a microcomb.

To demonstrate the system, we characterize various microcomb states for different detuning in the SiN ring resonator ($Q=2\times 10^{6}$, FSR of $\sim$ 300 GHz), fabricated by Ligentec. Figure 2 compares the optical spectra obtained by the conventional OSA and magnified spectra (indicated by the red arrows in the corresponding regions) taken in our system. When we gradually scan the pump light into the resonance from the higher to lower frequencies, the primary comb lines emerge (Fig. 2(a)). We clearly observe single sharp optical lines at the blue side of each resonance (Fig. 2(b)). As we build up the intracavity power by further approaching the pump frequency to the resonance, the comb enters a chaotic state, where interferences between multiple subcombs results in fast fluctuations of their frequencies. In the conventional OSA, these fluctuations are not noticeable and fully populated combs are observed (Fig. 2(c)). On the other hand, it can be clearly seen that the comb line overlaps with the resonance, resulting in a characteristic Fano-shape profile in the CHD system. Besides, the width of the comb line is also broadened, indicative of the fast frequency fluctuations (Fig. 2(d)). When we perform a fast sweep from the primary comb state, we are able to obtain a soliton microcomb (Fig. 2(e)). In this case, we have single sharp comb lines in the red sides of each resonances (Fig. 2(f)). We also plot the measured detuning between the comb lines and the resonance dips Fig. 2(a) and (e), where the curve trends are reminiscent of the parabolic dispersion profile of the resonator, as expected. These results illustrate that our method allows us to readily identify which side of the resonances the comb lines lie, that is difficult to recognize using a standard OSA alone, and that it is also possible to quantify the comb-resonance detuning despite the fast and broad frequency sweep.

 

Fig. 2. Optical spectra (left half) and enlarged views of comb lines and resonances measured with the coherent detection system (right half)

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2.1 Dispersion characterization based on detuning measurement

Here, we show that the broadband detuning measurement is useful for estimating the resonator dispersion, a key parameter that determines microcomb properties. The resonator dispersion is often expressed by the following equation as a function of the relative mode number $\mu$ to the pump mode,

Here, $\omega _{0}$, $D_{i}$ ($i$ is a natural number), and $D_{\rm int}(\mu )$ are the angular frequency of the pump mode, the $i$-th order dispersion coefficient, and the integrated higher-order mode dispersion. Each dispersion coefficient is generally obtained by polynomial fitting to the measured resonant frequencies extracted from transmission spectra. However, precise transmission spectrum measurement requires consistent tracking of scanned frequencies with high-resolution over a broad frequency range ($>10$ THz), resulting in significant data volume and high computation cost for data procressing [20].

On the other hand, we can describe the resonant frequencies by using the comb mode frequencies and the comb-resonance detuning $\delta (\mu )$,

A comparison between Eqs. (6) and (7) tells us that the profile of the detuning frequencies itself reflects the higher-order integrated dispersion, provided that $\omega _{\rm rep} \sim D_{1}$. In microcombs, $\omega _{\rm rep}$ can be regarded as a constant for a short period of time and therefore the comb lines can conveniently used as sparse frequency markers, eliminating the need of fringe or peak counting. Although $\omega _{\rm rep}$ needs to be evaluated separately, it is not necessary to estimate $D_{\rm int}(\mu )$. Given that a typical drift value of $\omega _{\rm rep}$ in a free-running soliton comb is 100 kHz$/$sec [21], the detuning errors originated from the drift of $\omega _{\rm rep}$ due to a finite sweep time would amount to a few hundred of kHz, which is an order of magnitude smaller than the current spectral resolution set by the BPF ($\sim$ 5 MHz).

To exemplify the above concept, we performed the dispersion measurements for soliton microcombs in two different types of microresonators: ring and race-track resonators. Each comb spectrum is shown in Fig. 2(e) and Fig. 3(a), respectively.

 

Fig. 3. (a) Optical spectrum of a microcomb generated from the racetrack resonator. (b-1)(b-2)(b-3) Enlarged views of optical peaks at around THz, respectively.

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It is intriguing that a few comb lines are observed around the resonances in the race-track-type resonator spectra (Fig. 3(b-1), (b-2), (b-3)). The presence of these multiple comb lines suggests either a multiple soliton state, a breather state or both [22]. Although we did not perform any backward tuning to deliberately generate breather solitons, this resonator favors to operate in this state since the result was reproducible. Given the fact that the typical spacing between these lines is $\sim 250$ MHz or its multiple and that there are more than two lines, it is likely the breather state with a recurrence period of $\sim 4$ nsec while the envelope profile was not a triangular shape, a characteristic of a breather soliton, as previously reported [22]. Although detailed identification of the observed state is beyond the scope of this study, the ability to spectrally resolve each comb line peak highlights interesting opportunities for thorough understanding of complex soliton dynamics using our measurement, combined with the other characterization techniques [22,23]. For dispersion analysis, we manually pick up the relevant peaks for polynomial fit as described below (other peaks are displayed as grey dots in Fig. 4(b)).

 

Fig. 4. Dispersion measurement results for (a) ring-type and (b) race-track type resonators. IF: interferometer. Insets depict the ring resonator structure with a radius of about 75 µm and the racetrack resonator structure with a radius of curvature of about 45 µm and a straight part length of about 90 µm, respectively. Grey dots in (b) show the detuning of peaks observed in the experiment, from which blue dots were selected with the aid of the numerical simulation. (c) Enlarged view of the transmission spectrum of a split resonance due to mode coupling (mode number 14 in (b)).

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Figure 4(a) and (b) present the obtained integrated higher-order dispersion for the two types of resonators. We compare the results with those for cold resonators obtained in the transmission measurements, where a fiber interferometer was used for frequency calibration (denoted as IF) [20]. The black dashed curves present the integrated higher-order dispersion calculated from the dispersion parameters for a straight waveguide modelled by using the finite difference eigenmode solver (MODE, Lumerical Inc.). The data points for the race-track resonator were chosen by using a numerical calculations as a guide. Overall trends are in reasonable agreement in both cases while the plots for the race-track resonator deviates more from the calculation, particularly in the conventional measurements. This can be attributed to the mode splitting that is frequently observed in the race-track resonator. Since no special precautions were taken between the curved and straight waveguide sections in its layout design, a finite amount of transition losses could occur at these points within the race-track resonator. Because the resonator consists of a multi-moded waveguide, combined with the high quality factor, this type of subtle losses in turn may promote the modal coupling to higher order modes that eventually leads to mode splitting when the resonances are overlapped with each other [24]. Besides, we also identified several difficulties that prevent precise detuning measurement. For example, when the comb line frequency overlaps with the resonance (e.g., Fig. 3(b-2)) the resonance dip structure is obscured, making the determination of resonance frequency less accurate. Also, a Fano-shape resonance is sometimes observed as shown in Fig. 3(b-3), which is probably induced by an accidental weak coupling to a Fabry-Perot resonance in the peripheral fiber-optics components.

Despite these issues, the errors are not accumulated in our measurement, as opposed to the conventional one, since the comb lines are used as reference markers. This means that our method is more tolerant to the modal interactions in estimating the dispersion values. We obtained the dispersion parameters $D_{2}/ 2\pi$ and $D_{3}/ 2\pi$ of 8.3 MHz and 1.1 kHz (5.8 MHz and −1.6 MHz) for the ring resonator (race-track resonator) through the detuning measurement, respectively. These values are in good agreement to the numerically predicted values of 8.1 MHz and 5.6 kHz, respectively, while how the above issues affect the measurement in the latter.

3. Conclusion

We develop an experimental system based on coherent detection to measure the microcomb’s comb-resonance detuning over a broad frequency range in a single sweep. The system clearly resolves the comb lines and resonance dips. We also apply this method to estimate the resonator dispersion and obtain dispersion parameters consistent with those measured in a conventional technique and numerical calculations. Since our approach is based on coherent detection using a tunable laser, this method is, in principle, compatible with the relative phase measurement between the microcomb lines. Our system is capable of characterizing important parameters of microcombs in situ, including comb power, detuning, resonator dispersion, and potentially relative phases between comb lines simultaneously in a single setup that can be assembled with less expensive components and system control compared to previous studies, and which we believe to be useful in experimental characterization of microcombs.