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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published: December 15, 2021 doi: 10.3791/60689
* These authors contributed equally


Here, we present a protocol to generate soliton crystals in a butterfly-packaged micro-ring resonator using a thermal tuned method. Further, the repetition rate fluctuations of a soliton crystal with a single vacancy are measured using a delayed self-heterodyne method.


Temporal solitons have attracted great interest in the past decades for their behavior in a steady state, where the dispersion is balanced by the nonlinearity in a propagation Kerr medium. The development of dissipative Kerr solitons (DKSs) in high-Q microcavities drives a novel, compact, chip-scale soliton source. When DKSs serve as femtosecond pulses, the repetition rate fluctuation can be applied to ultrahigh precision metrology, high-speed optical sampling, and optical clocks, etc. In this paper, the rapid repetition rate fluctuation of soliton crystals (SCs), a special state of DKSs where particle-like solitons are tightly packed and fully occupy a resonator, is measured based on the well-known delayed self-heterodyne method. The SCs are generated using a thermal-controlled method. The pump is a frequency fixed laser with a linewidth of 100 Hz. The integral time in frequency fluctuation measurements is controlled by the length of the delay fiber. For a SC with a single vacancy, the repetition rate fluctuations are ~53.24 Hz within 10 µs and ~509.32 Hz within 125 µs, respectively.


The steady DKSs in microresonators, where the cavity dispersion is balanced by Kerr nonlinearity, as well as the Kerr gain and cavity dissipation1, have attracted great interest in the scientific research community for their ultra-high repetition rate, compact size, and low cost2. In the time domain, DKSs are stable pulse trains that have been used for high-speed ranging measurement3 and molecular spectroscopy4. In the frequency domain, DKSs have a series of frequency lines with equal frequency spacing that are suitable for wavelength-division-multiplex (WDM) communications systems5,6, optical frequency synthesis7,8, and ultra-low noise microwave generation9,10, etc. The phase noise or linewidth of comb lines directly affects the performance of these application systems. It has been proven that all the comb lines have a similar linewidth with the pump11. Therefore, using an ultra-narrow linewidth laser as a pump is an effective approach to improve the performance of DKSs. However, the pumps of most reported DKSs are frequency sweeping external cavity diode lasers (ECDLs), which suffer from relatively high noise and have a broad linewidth on the order of tens to hundreds of kHz. Compared with tunable lasers, fixed-frequency lasers have less noise, narrower linewidths and smaller volume. For example, Menlo systems can provide ultra-stable laser products with a linewidth of less than 1 Hz. Using such a frequency fixed laser as a pump can significantly reduce the noise of the generated DKSs. Recently, microheater or thermoelectric cooler (TEC)-based thermal tuning methods have been used for DKSs generation12,13,14.

Repetition rate stability is another important parameter of DKSs. Generally, frequency counters are used to characterize the frequency stability of DKSs within a gate time, which is generally on the order of a microsecond to a thousand seconds15,16. Limited by the bandwidth of the photodetector and frequency counter, electro-optic modulators or reference lasers are typically used to lower the detected frequency when the free-spectral-range (FSR) of the DKSs is over 100 GHz. This not only increases the complexity of test systems, but also produces additional measurement errors caused by the stability of RF sources or reference lasers.

In this paper, a micro-ring resonator (MRR) is butterfly packaged with a commercial TEC chip that is used to control the operation temperature. Using a frequency fixed laser with a linewidth of 100 Hz as a pump, soliton crystals (SCs) are stably generated by manually decreasing the operating temperature; these are special DKSs that can completely fill a resonator with collectively ordered ensembles of copropagating solitons17. To the best of our knowledge, this is the narrowest linewidth pump in DKSs generation experiments. The power spectral density (PSD) spectrum of every comb line is measured based on a delayed self-heterodyne interferometer (DSHI) method. Benefitting from the ultra-narrow linewidth of the comb lines, the repetition rate instability of soliton crystals (SCs) is derived from the central frequency drift of the PSD curves. For the SC with a single vacancy, we obtained a repetition rate instability of ~53.24 Hz within 10 µs and ~509.32 Hz within 125 µs.

The protocol consists of several main stages: First, the MRR is coupled with a fiber array (FA) using a six-axis coupling stage. The MRR is fabricated by a high-index doped silica glass platform18,19. Then, the MRR is packaged into a 14-pin butterfly package, which increases the stability for the experiments. SCs are generated using a thermal-controlled method. Finally, the repetition rate fluctuations of SCs are measured by a DSHI method.

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1. Optical coupling

  1. Polish the end-face of the MRR on a grinding plate using 1.5 μm abrasive powders (aluminum oxide) mixed with water for 5 min.
  2. Fix the MRR with a chip fixture and place an eight-channel FA on a six-axis coupling stage, which includes three linear stages with a resolution of 50 nm and three angle stages with a resolution of 0.003°. The patches of the MRR and FA are 250 μm.
  3. Use a 1,550 nm laser as an optical source for real-time monitoring of the coupling efficiency. Carefully adjust the position of the FA until the inset loss reaches the minimum value, typically less than 6 dB, corresponding to a coupling loss of less than 3 dB per facet.
  4. Use an ultraviolet (UV) curved adhesive (Table of Materials) to glue the MRR and FA. Place the adhesive on the side edge of the contact surface, which ensures that there is no glue on the optical path.
  5. Expose the UV-curved adhesive to a UV lamp for 150 s and bake in a chamber at 120 °C for more than 1 h.

2. Device packaging

  1. Conglutinate a 10.2 mm x 6.05 mm TEC chip with a maximum power of 3.9 W to the baseplate of a standard 14-pin butterfly package using silver glue. Solder the two electrodes of the TEC chip to two pins of the butterfly package.
  2. Paste a 5 mm × 5 mm × 1 mm tungsten plate to the surface of the TEC chip using silver glue. Use the tungsten plate as a heat sink to fill the gap between the TEC and MRR.
  3. Paste the MRR device to the top of the tungsten plate using silver glue and fix the pigtail of the FA to the output port of the butterfly package.
  4. Paste a thermistor chip to the surface of the TEC chip using silver glue. Connect one electrode of the thermistor to the top surface of TEC chip. Wire bond the other electrode of the thermistor and the top surface of TEC chip to two pins of the butterfly package using gold thread.
  5. Bake the packaged device at 100 °C for 1 h to solidify the silver glue.
  6. Seal the butterfly package. Figure 1 shows the packaged device.

3. SCs generation

  1. Figure 2 shows the set-up of the experiments. Use an erbium-doped fiber amplifier (EDFA) to boost the pump for micro-comb generation. Control the polarization state of the pump using a fiber polarization controller (FPC). Connect all the devices using single mode fibers (SMF).
  2. Fix the wavelength of the pump laser at 1,556.3 nm. Manually tune the operation temperature through an external commercial TEC controller.
  3. Monitor the output optical spectrum with an optical spectrum analyzer. Detect the output power trace with a 3 GHz photodetector and record with an oscilloscope.
  4. Set the output of the EDFA to 34 dBm, corresponding to an on-chip power of 30.5 dBm (considering the coupling loss of the MRR and FA, insert loss of the FPC), which ensures that there is enough power coupled into the MRR for micro-comb generation.
  5. Set the thermistor to 2 kΩ, corresponding to an operating temperature of 66 °C. Then slowly decrease the operating temperature by changing the set value of the thermistor. In these experiments, when the thermistor was set to 5.8 kΩ, corresponding to 38 °C, one resonance of the MRR passed through the pump and a triangular shape power trace was recorded.
  6. Tune the polarization of the pump by the FPC until an SC step is observed at the falling edge of the triangular transmission power trace. Figure 3 shows a typical optical transmission power trace.
  7. Slowly decrease the operation temperature from ~66 °C and stop when a palm-like optical spectrum is observed on the optical spectrum analyzer. The value of the thermistor was around 5.6 kΩ in these experiments. Figure 4A and Figure 5B show the optical spectra of perfect SCs and SCs with a single vacancy, respectively.

4. Repetition rate fluctuation measurement

  1. Connect the generated SCs to a tunable bandpass filter (TBPF) to extract an individual comb line. Set the passband of the TBPF to 0.1 nm. Its central wavelength can be tuned over the full C and L band. The filter slope is 400 dB/nm.
  2. Couple the selected comb line to an asymmetric Mach-Zehnder interferometer (AMZI). The optical frequency in one arm of the AMZI is shifted by 200 MHz using an acousto-optic modulator (AOM). The optical field in the other arm is delayed by a segment of optical fiber. Delay fibers of 2 km and 25 km are used in these experiments.
  3. Detect the output optical signal with a photodiode and analyze the PSD spectrum using an electrical spectrum analyzer.
  4. Tune the central wavelength of the TBPF. Measure the PSDs of every comb line using the described method. Figure 4B,C shows the PSD spectra for comb lines S1 and S2 of perfect SCs with the 2 km and 25 km delay optical fibers, respectively.
  5. Using the same method, measure the PSD curves of SCs with a vacancy. Record the 3 dB bandwidth of the PSD curve and linearly fit it piecewise as shown in Figure 5B,C. Repetition rate fluctuations of ~53.24 Hz within 10 µs and ~509.32 Hz within 125 µs were derived.

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Representative Results

Figure 3 shows the transmission power trace while a resonance thermal was tuned across the pump. There was an obvious power step that indicated the generation of SCs. The step had similar power compared with its precursor, the modulational instability comb. Therefore, the generation of SCs was not tuning speed dependent. The SCs exhibited a great variety of states, including vacancies (Schottky defects), Frenkel defects, and superstructure12,17. As examples, Figure 4A shows a perfect SC with 27 solitons and Figure 5A is a SC with a single vacancy.

The frequency of the µth comb line equals to

Equation 1

and the frequency fluctuation of the µth comb line can be expressed as:

Equation 2

where µ is the mode number away from the pump, frep is the repetition rate of the SCs, and Δfpump and Δfrep are the frequency fluctuations of the pump laser and the repetition rate of the SCs, respectively. Therefore, the repetition rate fluctuation of the SCs was almost amplified µ times at the µth frequency line.

For perfect SCs, Figure 4B,C shows the measured PSD spectra for the pump, S1 and S2, based on a 2 km and a 25 km delay fiber, respectively. The most notable features of the PSD curves were the flat tops, which were caused by the frequency fluctuation within the delay time. When the delay time was 10 µs, the frequency fluctuations of S1 and S2 were 2.08 kHz and 3.54 kHz, respectively. When the delay fiber was 25 km, the measured frequency fluctuations of S1 and S2 were 14.31 kHz and 28.02 kHz, respectively.

Figure 5A shows the typical optical spectrum of SC with a single vacancy. There were 27 solitons circulating in the MRR. The measured frequency fluctuations of each comb line were plotted and are shown in Figure 5B,C. The piecewise linear fitting lines are plotted in blue lines which can be expressed as

Equation 3
Equation 4

The average slopes of the fitting lines were about 53.24 Hz/FSR and 509.32 Hz/FSR, which represent the repetition rate fluctuations of the SC within the responding delay times of 10 µs and 125 µs, respectively. The residual frequency fluctuations were regarded as the frequency fluctuation of the pump laser together with the frequency fluctuation of the driven radio signal of the AOM.

Figure 1
Figure 1. Butterfly Packaged MRR. (A) Model and (B) picture of the butterfly packaged MRR. Please click here to view a larger version of this figure.

Figure 2
Figure 2. The experimental setup of Kerr OFCs generation and repetition rate fluctuation measurement. The inset shows the optical spectrum of one typical SC with a single vacancy. A frequency fixed CW laser with a linewidth of 100 Hz was used as the pump. An EDFA was used to boost the pump up to 34 dBm. The frequency fluctuation was measured by the delayed self-heterodyne interferometer method. CW = continuous wave; EDFA = erbium-doped fiber amplifier; FPC = fiber polarization controller; TEC = thermoelectric cooler; MRR = micro-ring resonator; BPF = bandpass filter; AOM = acousto-optic modulator; PD = photodiode; ESA = electrical spectrum analyzer. Please click here to view a larger version of this figure.

Figure 3
Figure 3. Optical transmission power trace at the drop port. A SC step that had similar power to its precursor is clearly obtained. Please click here to view a larger version of this figure.

Figure 4
Figure 4. Perfect SC. (A) Measured optical spectrum of a perfect SC. The inset shows the uniformly distributed 27 solitons in the MRR. (B) Measured PSD curves of the pump, S1 and S2, with the 2 km delay fiber. (C) Measured PSD curves of the pump, S1 and S2, with the 25 km delay fiber. The flat-top PSD curve was caused by the rapid frequency fluctuation of the comb lines. Please click here to view a larger version of this figure.

Figure 5
Figure 5. SC with a single vacancy. (A) Optical spectrum of SC with a single vacancy. The inset shows the soliton distribution in the MRR. (B) Frequency fluctuations with the 2 km delay fiber. The repetition rate fluctuation was about 53.24 Hz within 10 µs. The frequency fluctuation introduced by the pump laser and measurement system was about 500 Hz. (C) The repetition rate fluctuation with a 25 km delay fiber was about 626 Hz within 125 µs. The frequency fluctuation introduced by the pump laser and measurement system was about 1 kHz. Please click here to view a larger version of this figure.

Figure 6
Figure 6. Theorical PSD of the photocurrent when the optical coherent length is larger than the relative delay time. The red line shows no central frequency fluctuation. The blue line presents the PSD with linear central frequency fluctuation. Please click here to view a larger version of this figure.

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On-chip DKSs provide novel compact coherent optical sources and exhibit excellent application prospects in optical metrology, molecular spectroscopy, and other functions. For commercial applications, compact packaged micro-comb sources are essential. This protocol provides a practical approach to make a packaged micro-comb that benefits from the reliable, low coupling loss connection between the MRR and FA, as well as a robust thermal-controlled DKS generation method. Therefore, our experiments are no longer coupling stage dependent and exhibit excellent environmental adaptation. Meanwhile, the pump is a wavelength fixed laser that can be operated with narrower linewidths, produces significantly less noise, and is much smaller compared to tunable lasers. Therefore, the protocol is a promising approach to potential commercial applications of integrated high-performance on-chip DKSs sources.

The main limitation to obtaining a fully integrated SCs source is the high pump power, which needs an EDFA. Recently, DKSs have been realized on SiN MRR with very low pump power. Therefore, we believe that practical fully integrated DKS sources will be made in the near future.

The stability of the repetition rate is one of the most important parameters to evaluate the performance of OFCs. Generally, the repetition rate stability is measured using a frequency counter. However, the repetition rates of micro-combs are typically on the order of tens of GHz to THz, which is out of the bandwidth of frequency counters and photodetectors. Therefore, indirect methods, such as a reference laser source or a modulator, are usually used for repetition rate stability measurement, which increases the complexity of the measurement system. Our protocol provides a DSHI based repetition rate fluctuation measurement scheme, where high frequency components and ultra-stable reference sources are unnecessary. The system does not have an upper repetition rate limitation. Our system measures the accumulated frequency fluctuation during the delay time, while the frequency counter-based method tests the average value in a gate time. Therefore, our scheme is complementary to frequency counter-based repetition rate stability measurement systems.

The linewidth of the pump laser is essential for a DSHI based repetition rate fluctuation measurement scheme. When an optical field

Equation 5

is measured by a DSHI scheme, the PSD spectrum of the photocurrent can be expressed as:

Equation 6

where E0 and ω0 are the amplitude and angular frequency, respectively; φ(t) is the initial phase of the optical field; α is the power ratio of the two interference arms; I0 is the input optical intensity; τd and τc are the relative delay time and the coherent time of the optical field, respectively; and Ω is the frequency shift of the AOM. When τc is greater than τd, the PSD will be the overlap of a beating signal and a Dirac function, as shown in Figure 6 (red line). However, considering the frequency fluctuation of lasers, the optical field can be expressed as

Equation 7

where Δω is the angular frequency fluctuation. For DSHI, an additional frequency shift is added. Figure 6 (blue line) shows the calculated PSD spectrum, where the optical frequency is linearly changed 10 kHz during the delay time. In contrast, when τc is less than τd, the Dirac function will be negligible, and our scheme can no longer measure the repetition rate fluctuation of DKSs. Our scheme is not suitable for the DKSs generated using a pump laser with a linewidth on the order of tens of kHz. Fortunately, a laser with a linewidth of less than 1 Hz has been commercialized, and locked fixed-frequency lasers with a linewidth of less than 40 mHz have been made20. Therefore, our scheme provides a simple rapid repetition rate instability measurement method for micro-comb performance evaluation in the future. 

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The authors declare that they have no competing financial interests.


This work was supported by the National Natural Science Foundation of China (NSFC) (Grant 62075238, 61675231) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB24030600).


Name Company Catalog Number Comments
6-axis coupling stage Suruga Seiki KXC620G
Contains 3 linear motorized translation states and 3 angular motorized rotational stages.
Linear state: Minimum stepping: 0.05 μm; Travel: 20mm; Max.speed: 25mm/s; Repeatability: +/-0.3 μm; Rotational stage:Travel: ±8°; Resolution/pulse: 0.003 degree; Repeatability:±0.005°
Abrasive powder Shenyang Kejing Auto-Instrument Co., LTD 2980002 Silicon carbide, granularity: 1.5 μm
Glue 3410 Electronic Materials Incorporated Optocast 3410 Optocast 3410 is an ultra violet light and heat curable epoxy suitable for opto-electronic assembly. It cures rapidly when exposed to U.V. light in the 320-380 nm.
High-index doped silica glass Home-made - The MRR is fabricated by a high index doped silica glass platform. The waveguide section is 2×3 μm and radius is 592.1 μm, corresponding to FSR of 49 GHz.
Pump laser NKT Photonics E15 It is a continuous wave fiber laser with linewidth of 100 Hz.
Ultrastable Laser Menlosystems ORS State-of-the-art linewidth (<1Hz) and stability (<2 x 10-15 Hz)



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Rapid Repetition Rate Fluctuation Measurement Soliton Crystals Microresonator Dissipative Kerr Soliton Chip-scale Coherent Light Source Soliton Physics Research Practical Applications Repetition Rate Fluctuation Micro-ring Resonator Packaging Soliton Generation On-chip Packaging Chip Fixture Six Axis Coupling Stage Fiber Array Optical Source Real-time Monitoring Coupling Efficiency Input Power Output Power Optical Power Meter Inset Loss Ultraviolet Curved Adhesive
Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
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Cite this Article

Xie, P., Wang, X., Wang, W., Zhang,More

Xie, P., Wang, X., Wang, W., Zhang, W., Lu, Z., Wang, Y., Zhao, W. Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator. J. Vis. Exp. (178), e60689, doi:10.3791/60689 (2021).

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