Coherent Optical-to-Microwave Link Using an Integrated Microcomb

Microcombs are advancing optical frequency comb technology towards a chip-integrable form. Here, we characterize a microwave signal source based upon the two-point optical frequency division (2P-OFD) technique. The system uses a frequency microcomb to transfer relative frequency stability of two low-noise optical oscillators to the microcomb repetition rate tone. The two optical oscillators are based on semiconductor lasers jointly stabilized to an ultra-stable Fabry–Pérot cavity. The coherence of the comb spectrum is confirmed through multiple stability comparisons between its repetition rate and comb line spectrum. The results underscore the excellent performance of microcombs as coherent links between optical and microwave frequencies, and how they enable simplified, miniaturized architectures for optical frequency division.

Recently, an OFC architecture for transference of stability from optical to microwave rates has been demonstrated that provides significant system simplification in exchange for some reduction of performance.Rather than using conventional OFC self-referencing, two comb lines with optical span typically much less than an octave are stabilized to an optical reference cavity [24].In turn, this transfers the relative stability of the reference cavity to the comb repetition rate.Because the method, called 2-point optical frequency division (2P-OFD), does not require an octave span comb, it simplifies the system architecture considerably and also relaxes requirements on the frequency comb, itself.While first implemented using electro-optic combs through the method of electro-optical frequency division [24], it has more recently been implemented using microcombs stabilized to compact optical references [25], [26], [27].
Here, we study additional details of the 2P-OFD process implemented using a microcomb stabilized to a compact reference cavity.The study uses two continuous wave (CW) lasers locked to the reference cavity at a series of different relative spectral spans.At each span, the lasers are used to stabilize two microcomb lines, thereby implementing 2P-OFD at a series of optical division ratios.The relative phase noise of the two CW lasers is measured and compared with the phase noise of the microwave repetition rate tone at each division ratio.Under conditions of maximum optical frequency division, the phase noise of the generated 20 GHz tone is as low as −95 dBc/Hz (−133 dBc/Hz) at 100 Hz (10 kHz) offset frequencies, which is comparable to the result in [26]), while the fractional Allan deviation is 1.3 × 10 −12 at 80ms.Moreover, the effect of varying the optical frequency division ratio is observed in the microwave phase noise spectrum.

A. 2P-OFD Architecture
The operating principle of the 2P-OFD system is depicted in Fig. 1.Two CW lasers (at optical frequencies ν 1 and ν 2 ) are is stabilized to a local oscillator.By feeding back to the microcomb, the above scheme stabilizes the repetition rate of the microcomb, which is photo detected to generate a high-stability microwave signal.(b), Experimental setup of the 2P-OFD system.Two semiconductor lasers are stabilized to the Fabry-Pérot resonator by PDH locking (dashed gray box).As described in panel (a), mixing of these signals with corresponding comb lines is used to generate an error signal for servo control of the microcomb repetition rate by adjustment to the comb pump laser current.The microcomb is generated by directly pumping a pair of Si 3 N 4 coupled microring resonators (dashed orange box).The microcomb output is collected by a lensed fiber and isolated by an optical isolator followed by optical amplification (EDFA).The two comb lines are extracted via two notch filters (FBG), while the other comb output is detected by a fast photo detector and generates a microwave tone f rep .
Pound-Drever-Hall (PDH) stabilized to the same high-finesse Fabry-Pérot cavity.Details on the cavity are provided below.The CW laser signals are combined with two microcomb lines (at optical frequencies ν m and ν n ) and detected by two photo detectors, thereby generating electrical beatnotes f 1 = ν m − ν 1 and f 2 = −ν n + ν 2 .The two beatnotes are mixed by a frequency mixer to produce an intermediate frequency f I = f 1 + f 2 .To implement 2P-OFD, this intermediate frequency is then stabilized to a local oscillator (LO, whose frequency is f LO ) via a phase lock loop that servo controls the microcomb repetition rate.Since the frequencies of the mth and nth comb lines are denoted by ν m = f o + mf rep and ν n = f o + nf rep , where f o is the central frequency of the comb, and f rep is the comb repetition rate.Under the servo locking of f I , the optical-to-microwave link is established by, Generally, the noise in f LO , which is determined by a radiofrequency source, contributes negligible uncertainty within the bandwidth of the stabilizing phase lock loop.By using eqn.(1) to relate frequency fluctuations (instead of absolute frequency), spectral densities can be formed, resulting in the following relationship, where S φ rep (f ) is the single sideband (SSB) phase noise of the comb's microwave repetition rate, S φ 12 (f ) is the relative phase noise of the two CW lasers at ν 1 and ν 2 , and noise contributions from f LO have been neglected.In what follows, an out-of-loop comparison between S φ rep (f ) and S φ 12 (f )/(n − m) 2 confirms the coherent link between the microwave and optical domains.

B. High-Finesse Reference Cavity
The high-coherence of the 2P-OFD system is derived from the compact, high-finesse Fabry-Pérot cavity.The cavity spacer and mirror substrates are made of ultra-low-expansion (ULE) glass.As shown in Fig. 2(a),(b), the spacer is 9.3 mm thick with a 50.8 mm outer-diameter and 13 mm inner diameter.The total cavity volume is 23 mL.The spacer has three, evenlydistributed vent holes with a diameter of 2 mm to evacuate the cavity.The mirror substrates (25.4 mm in diameter and 6.35 mm in thickness) have a radius of curvature of 1 m.The substrates with high reflective coating are optically contacted on the spacer to form resonance.Three counter-bored holes are evenly distributed on the spacer, with 20.95 mm to the center of the spacer, and three short Teflon rods are inserted into the holes to vertically support the cavity.To suppress vibration-induced frequency noise, we employ the vibration-immune design [29].Finite-element analysis (FEA) shows that vibration sensitivity of the cavity is minimized by adjusting the offset between the support surface of the Teflon rod and the top surface of the spacer.The offset is chosen to be 4.75 mm.FEA-simulated vertical vibration sensitivity is 1 × 10 −9 /g/mm (g = 9.8 m/s 2 ) where the distance refers to the offset, and horizontal vibration sensitivity is 2.75 × 10 −10 /g /mm where the distance refers to the transverse displacement of the beam from the cavity axis.To minimize the temperature-induced frequency noise, the cavity is installed in a multi-layer thermal shield (100 mm in diameter and 50 mm in height), consisting of two nested cup-shaped copper enclosures, and a ULE ring on which the three Teflon rods sit.The contact area between each part is minimized to provide low thermal conductivity.
The cavity finesse is determined by measuring the ringdown time in the reflected field (green data curve in Fig. 2(c)).The exponential fitting (red) gives a time constant of 4.4 μ s, corresponding to a finesse of 220,000.Pound-Drever-Hall locking of a CW laser near 1550 nm to a resonance of the Fabry-Pérot resonator stabilizes the laser.After removing linear drift of 4 Hz/s, the fractional-frequency-stability (FFS) versus averaging time τ (FFS, red data and red fit line in Fig. 2(d)) achieves a level of 9 × 10 −15 (green dashed line) for 0.1s< τ < .3s.This is limited by the coating Brownian noise [30].Additional details on the cavity characterization are provided in the Appendix.

C. Frequency Microcomb
The frequency microcomb is generated by directly pumping (i.e., without any intermediate components) a pair of coupledring Si 3 N 4 resonators using a DFB laser [28].The Si 3 N 4 Fig. 3. Typical measured optical spectrum of the microcomb.The measurement is made at the drop port of the coupled rings (see [28]).
resonators are fabricated at a CMOS foundry, and their dispersion is controlled using electrically-controlled thermal tuning of the individual coupled rings as described in ref. [31].Dispersion control, in turn, allows optimization of the comb spectral width.In this design, self-injection feedback stabilizes the pump laser to the Si 3 N 4 microcomb resonance [32], and generates mode-locked high-power-efficiency dark pulses at microwave repetition rates [10].A typical optical spectrum of the generated dark-pulse microcomb is shown in Fig. 3.
Referring to Fig. 1(b), additional details about the experiment are now discussed.Stabilization of the microcomb's repetition rate f rep to implement 2P-OFD requires fast actuation, which is provided by modulating the driving current the microcomb pump laser [28].To increase the signal-to-noise ratio (SNR) of the beatnotes f 1 and f 2 , the microcomb output is amplified by an Erbium-doped fiber amplifier (EDFA), and the comb lines at ν m and ν n are selected by two optical notch filters (FBG1 and FBG2).After photo detection (PD1 and PD2, Newport 1611), the SNRs are greater than 55 dB at an electrical resolution bandwidth of 100 kHz.The two beatnotes are electrically amplified and mixed using a frequency mixer to generate the intermediate beatnote at f I = f 1 + f 2 .The local electrical oscillator (R&S SMB100A) at f LO is mixed with the intermediate beatnote f I to generate the error signal, and sent to a laser servo (Vescent D2-125) to generate feedback signal.The servo output is applied to the DFB laser current supply (Vescent D2-105) and stabilizes the microcomb repetition rate via eqn.(1).After the 2P-OFD stabilization, the generated repetition rate tone is plotted in Fig. 4(a).

D. Phase Noise Vs. Optical Division Ratio
We measure the relative phase noise of the two CW lasers (S φ 12 (f )) and repetition rate phase noise of the microcomb (S φ rep (f )) for different OFD ratios (n − m).In the measurement of S φ 12 (f ), the two lasers are separated by one F SR of the Fabry-Pérot resonator, and their beating at 16 GHz is detected by a fast photodetector (Thorlabs) followed by characterization with an electrical signal analyzer (R&S FSWP).This relative phase noise of the optical reference is plotted as the upper (grey) curve in Fig. 4(b).Note that spurs are suppressed in this plot as discussed in the Appendix.
Next, the frequency of the laser at ν 1 (RIO PLANEX) is held fixed while the other laser at ν 2 (Toptica DLC pro) is tuned to other resonances of the Fabry-Pérot cavity.The microcomb is stabilized for each tuning via the aforementioned 2P-OFD scheme, and its detected repetition rate tone is characterized using the signal analyzer.The corresponding phase noise spectra are presented in Fig. 4(b) for a series of (n − m) values: 4, 8, 12, 33, 49.Here, the exact (n − m) values are chosen so that the frequency f I is lower than 1.5 GHz as required by the electronics used for signal processing.From 10 1 to 10 4 Hz in offset frequency, the microcomb-repetition-rate tone phase noise relative to the optical reference noise scales inversely with the square of the division ratio (n − m) 2 , as depicted in Fig. 4(c).The dashed lines in the plots are the theoretical phase-noise scaling.Each phase noise value is calculated by averaging the phase noise around 20 nearby points in the phase noise trace, with the error bar denoting standard deviation of the averaging.

III. DISCUSSION AND CONCLUSION
In conclusion, we analyzed optical and electrical phase noise in a 2P-OFD system and confirmed the optical frequency division process for a series of division ratios.The microcomb is directly pumped by a DFB laser thereby bypassing extra fiberoptic components, and representing a simplification relative to refs.[25], [27].Moreover, the two CW lasers are commercial semiconductor lasers, and directly actuated via current modulation.This removes the acoustic-opto modulator in ref. [26] used for laser locking.The current system also does not employ the spiral resonators used in ref. [26] to pre-stabilize the DFB laser.Both of these modifications reduce system complexity.For the limits of the current 2P-OFD approach, while quantum decoherence of the microcomb [33], [34], [35] fundamentally limits the phase noise, other technical noises set a practical limit, as discussed in the Appendix, e.g.projected phase noise of the two referenced lasers, or residual noise of the repetition rate locking.For the reduction of size, weight and power consumption (SWaP), heterogeneous integration [36], [37] of the III-V laser and Si 3 N 4 circuit is a possible direction.The optical reference lasers that are PDH-locked to the Fabry-Pérot cavity could also be locked to a monolithic resonator [38] and a self-injection locking mode could be employed for system simplification [39].
For comparison with other platforms, a survey can be found in the reference [26].Briefly, the current state-of-the-art low-noise microwaves are generated using a cabinet-sized OFD system [4], while electrical methods (e.g. a crystal-based oscillator) are typically with better SWaP [40].Overall, the system demonstrates features that could be useful in future portable microwave systems such as radar systems.They could also benefit the exploration of new physics.
We thank Henry Blauvelt at Emcore Corporation for supplying the DFB laser, as well as Frank Quinlan and Scott Diddams at NIST for helpful discussions.This work was supported by DARPA under the GRYPHON project (HR0011-22-2-0009).The research reported here performed by W. Z. and A.M. was carried out at the Jet Propulsion Laboratory at the California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004).

APPENDIX A CHARACTERIZATION DETAILS OF THE COMPACT FABRY-PÉROT RESONATOR
A continuous-wave (CW) laser at 1550 nm is frequencylocked to the compact ULE cavity by the Pound-Drever-Hall (PDH) technique [41].The output of the CW laser is split into two parts by a fiber coupler with a ratio of 99/1.The 99% output is used to generate the heterodyne signal with the microcomb.The other coupler port, with about 10 μ W output power, is used for PDH locking.Following the fiber coupler, a fiber-coupled electro-optic modulator (EOM) provides phase modulation at 9.6 MHz.The modulated laser signal is collimated and freespace coupled to the cavity with a 50% coupling efficiency.The reflection of the cavity is received by a photodetector and demodulated to generate the PDH error signal.The current modulation port of the CW laser is used for frequency locking with a 500 kHz feedback bandwidth.
To measure vibration sensitivity, the cavity with the enclosure is placed on an active vibration isolation table, which is driven by the modulation signal from a vector signal analyzer.An accelerometer measures the arbitrary vibration on the isolation table.The FP cavity stabilized laser is heterodyned with a reference laser (whose frequency stability is better than 2 × 10 −15 ), and the beatnote is detected using a photodetector.The heterodyned beatnote is analyzed using fast Fourier transform to obtain the frequency response.The vibration sensitivity of the compact cavity is derived to be 8 × 10 −10 /g along the gravitational direction and 5 × 10 −10 /g on the horizontal plane.The actual offset is 5.5 mm (Fig. 2(b)), as derived from the vertical vibration sensitivity measurement.Similarly, the beam position in experiment is 1.85 mm offset from the center of cavity geometry, which contributes to the measured horizontal sensitivity.Nevertheless, these measurements are consistent with the FEA simulation results and sufficient to suppress the vibration-induced frequency noise below the cavity thermal noise limit.
The temperature response of the compact cavity with the multi-layer thermal shield is measured by applying a stepchange on the temperature (∼ 0.5K) of the outer layer of the shield, and simultaneously recording the frequency change of the aforementioned heterodyned beatnote using a frequency counter.The exponential response of the beatnote, representing the thermal damping of the shield, shows a time constant > 2,000s.This enables the thermal shield to reduce the temperature-induced frequency noise below the cavity thermal noise when the temperature of the outer layer is actively stabilized on the level of mK.According to the FEA simulation, the zero-crossing of the coefficient of thermal expansion is about 297 K, with a slope of 1.4 × 10 −9 /K 2 .For applications in which long-term stability is a key consideration, the cavity can operate at this temperature to reduce linear drift to 0.1 Hz/s level.

APPENDIX B EXPERIMENTAL DETAILS OF 2P-OFD
Fabrication and assembly details of the microcomb module are described in previous works [28], [31].In the experiment, the drop port of the microcomb is used and a polarizationmaintaining lensed fiber collects more than 3dBm of optical power (optical spectrum in Fig. 3).After optical isolation, an Erbium-doped fiber amplifier is used to boost the optical power above 50mW.Referring to Fig. 1(b), after optical filtering, the two comb lines used for 2P-OFD each have higher than 100 μW at PD1 and PD2, while the power of the two CW lasers are ∼500 μW.Detectors PD1 and PD2 used to generate f 1 and f 2 are type New Focus 1611.The fast photo detector used to generate the 20 GHz repetition rate tone is a Thorlabs DXM30AF and and received incident optical power ∼ 8 mW.
Residual noise contribution of the 2P-OFD is summarized in Fig. 5(a).The blue line presents the phase noise corresponding to the division factor of 49.The phase noise is dominated by the beatnote phase noise of the two, reference-locked CW lasers up to 10kHz (yellow line).For the offset frequencies > 10 kHz, the residual noise of the repetition rate locking (gray line) makes the main contribution.Fractional Allan deviation is also measured for the 20 GHz repetition rate tone by sending the repetition rate tone to the R&S FSWP signal analyzer.Fractional Allan deviation reaches 1.3 × 10 −12 at 80ms (Fig. 5

(b)).
Qing-Xin Ji received the B.S. degree in physics from Peking University, Beijing, China, in 2020, and the M.S. degree from Caltech, Pasadena, CA, USA, in 2022.He is currently working toward the Ph.D. degree.He was a Research Assistant with Peking University in 2020.His research focuses on photonic integrated circuits for low-noise applications.Joel Guo (Member, IEEE) received the B.S. degree in electrical engineering from The University of Texas at Austin, Austin, TX, USA, in 2018, and the M.S. degree in electrical engineering in 2020 from the University of California, Santa Barbara, Santa Barbara, CA, USA, where he is currently working toward the Ph.D. degree.His research interests include InP/Si/Si3N4-based low-noise lasers, microcombs, and photonic integrated circuits heterogeneously integrated on silicon.
Avi Feshali is currently an experienced Executive with more than 15 years in silicon photonics fabrication&high-volume manufacturing of photonics devices and modules.At ANELLO, he is leading the product development from concept to engineering samples.At Intel, he was responsible for selecting, bringup and qualification of Intel's fab at Rio Rancho NM and and launch of the PSM4 and CWDM4 transceiver products.Prior to ANELLO, he was part of the camera&depth sensor team at Apple developing the LiDAR scanner found today in the iPad Pro and iPhone 12/13.Mario Paniccia (Fellow, IEEE) received the bachelor's degree in physics from the State University of New York at Binghamton, Binghamton, NY, USA, and the Ph.D. degree in solid state physics from Purdue University, West Lafayette, IN, USA.He is currently a Co-Founder and CEO of Anello Photonics, Santa Clara, CA, USA.Prior to Anello Photonics, he spent 22 years with Intel Corp., where he achieved the status of Intel Fellow, Chief Technology Officer, and GM for the Silicon Photonics Solutions Group.Dr. Paniccia is a Member of National Academy of Engineers, and is a SPIE and OSA Fellow.
John Bowers (Fellow, IEEE) holds the Fred Kavli Chair, and is the Director of the Institute for Energy Efficiency and a Distinguished Professor with the Electrical and Computer Engineering and Materials Departments, University of California, Santa Barbara, Santa Barbara, CA, USA.Dr. Bowers is a Member of the National Academy of Engineering and is an AAAS, OSA, and APS Fellow.He was the recipient of the IEEE Nishizawa Medal, IEEE Photonics, OSA/IEEE Tyndall, OSA Holonyak, and IEEE William Streifer Awards.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

Fig. 1 .
Fig. 1. (a), Architecture of the two-point optical frequency division (2P-OFD) system.Two lasers are stabilized to two optical resonances (ν 1 and ν 2 ) of a high-finesse Fabry-Pérot resonator, separated by up to 1 THz.Two lines of a microcomb (at optical frequency ν m = f o + mf rep and ν n = f o + nf rep ) are mixed with the two lasers and generate two beats (f 1 = ν m − ν 1 and f 2 = −ν n + ν 2 ) via photo detection.The two beatnotes are mixed by a frequency mixer, and the output tone atf 1 + f 2 = (ν 2 − ν 1 ) − (n − m)f repis stabilized to a local oscillator.By feeding back to the microcomb, the above scheme stabilizes the repetition rate of the microcomb, which is photo detected to generate a high-stability microwave signal.(b), Experimental setup of the 2P-OFD system.Two semiconductor lasers are stabilized to the Fabry-Pérot resonator by PDH locking (dashed gray box).As described in panel (a), mixing of these signals with corresponding comb lines is used to generate an error signal for servo control of the microcomb repetition rate by adjustment to the comb pump laser current.The microcomb is generated by directly pumping a pair of Si 3 N 4 coupled microring resonators (dashed orange box).The microcomb output is collected by a lensed fiber and isolated by an optical isolator followed by optical amplification (EDFA).The two comb lines are extracted via two notch filters (FBG), while the other comb output is detected by a fast photo detector and generates a microwave tone f rep .

Fig. 2 .
Fig. 2. (a) Photograph of the compact Fabry-Pérot cavity, showing dimensions 9.3 mm (length) by 50.8 mm (diameter).(b) The section view of the cavity design, where t1 is the spacer thickness and t2 is the offset of the support position.(c) Ring-down measurement of the Fabry-Pérot cavity.The red curve denotes exponential decay fitting of 4.4 μs, yielding a finesse of 220 000.(d) Measured fractional frequency stability (red) of a laser when stabilized to the Fabry-Pérot reference cavity by PDH lock.For averaging time between 0.1 s to 0.3 s, the laser stability is limited by the cavity thermal noise (green) to about 9× 10 −15 .

Fig. 4 .
Fig. 4. Phase noise spectrum measurement of optical and microwave tones confirming the coherent optical-to-microwave link.(a) Representative microwave tone generated by photo detecting the output of the microcomb.The resolution bandwidth is 1 Hz.(b), Gray line: measured SSB phase noise of the relative phase noise of the two lasers.The other lines are measured phase noise of the generated 20 GHz microwave tone using the 2P-OFD.From top to bottom, the division ratio (n − m) is 4, 8, 12, 33, 49, respectively.(c) Measured phase noise versus the division ratio at different offset frequencies.From top to bottom, the frequency offset (whose color corresponds to the vertical dashed lines in panel (b)) is 100 Hz, 300 Hz, 1 kHz, 2 kHz, 5 kHz, and 10 kHz.The dashed line denotes the theoretical predictions from (2).

Fig. 5 .
Fig. 5. (a) Residual phase noise contribution of the optical-to-microwave link.(b) Measured fractional Allan deviation of the 20 GHz repetition rate tone.
Wei Zhang (Member, IEEE) received the Ph.D. degree from the Institute of Physics, Chinese Academy of Sciences, Beijing, China, in 2009.From 2009 to 2012, he was with SYRTE, Observatoire de Paris, Paris, France, for low phase noise microwave generation by optics-to-microwave frequency division with ultrastable laser and fiber-based frequency comb.From 2012 to 2019, he was with the JILA, University of Colorado at Boulder and Time and Frequency Division, NIST to develop several ultrastable lasers for high precision measurements.Since 2020, he has been a Member of technical staff with Jet Propulsion Laboratory.His research focuses on optical oscillators.Lue Wu received the B.S. degree in precision instrument and mechanical engineering from Tsinghua University, Beijng, China, in 2016, and the M.S. and Ph.D. degrees in applied physics from Caltech, Pasadena, CA, USA, in 2020 and 2024, respectively.He has been an Engineer with Apple Inc., Cupertino, CA, since 2023.He is the author of 27 peer reviewed articles.His research interests include the technology to make optical microresonators on a silicon chip with ultrahigh Q factor, and the uses of these microresonator devices for high-performance applications in nonlinear optics, integrated photonics, lasers and microwave oscillators.Warren Jin received the B.S. degree in computer engineering from Brown University, Providence, RI, USA, and the Ph.D. degree from the Electrical Engineering Department, University of California, Santa Barbara, Santa Barbara, CA, USA.He is currently an Engineer with Anello Photonics, Cupertino, CA.