pith. sign in

arxiv: 2604.19058 · v1 · submitted 2026-04-21 · ⚛️ physics.optics · physics.app-ph

Brillouin-Enhanced Photonic Stepped-Frequency Radar

Pith reviewed 2026-05-10 02:31 UTC · model grok-4.3

classification ⚛️ physics.optics physics.app-ph
keywords photonic radarstepped-frequency waveformBrillouin laserphase noise suppressionfiber cavityX-band radaroptomechanical dampingcommon-mode rejection
0
0 comments X

The pith

Dual Brillouin lasers in one fiber cavity generate uniform X-band stepped-frequency waveforms with over 23 dB phase-noise reduction.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that photonic stepped-frequency radar can overcome its usual trade-off between low phase noise and uniform frequency steps by placing two Brillouin lasers inside the same fiber cavity. This setup uses the lasers' optomechanical interaction to damp phase fluctuations and photomixing to cancel common-mode noise while the shared resonances force equal frequency increments. A sympathetic reader would care because the approach lets low-cost voltage-controlled oscillators drive high-resolution radar without injecting their noise into the output waveform. If the claim holds, the quality of the transmitted signal becomes largely independent of the driving electronics, which would simplify practical deployment of photonic radar in applications needing fine range resolution.

Core claim

The authors claim that dual Brillouin lasers operating in a shared fiber cavity simultaneously suppress phase noise through optomechanical damping and common-mode rejection upon photomixing, while the cavity resonances enforce uniform frequency stepping; this produces an X-band stepped-frequency waveform spanning 1.31 GHz with more than 23 dB phase-noise improvement at 100 kHz offset compared with the driving oscillator alone, thereby reducing the output waveform's dependence on noise in the driving electronics.

What carries the argument

dual Brillouin lasers in a shared fiber cavity, which supplies both optomechanical phase-noise suppression and common-mode rejection while forcing lasing at equally spaced resonances.

If this is right

  • The radar output waveform quality no longer tracks the phase noise of the low-cost driving electronics.
  • High-range-resolution sensing becomes feasible with simpler and cheaper electronic drivers.
  • The same cavity can enforce both noise reduction and step uniformity in a single hardware element.
  • Photonic radar systems gain a route to performance that scales with optical rather than electronic component quality.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach might extend to other multi-line photonic sources that need both spectral purity and precise spacing.
  • Real-world radar tests would need to check whether the 1.31 GHz span and 23 dB improvement survive propagation and target returns.
  • If the shared-cavity stability holds, the method could be adapted to generate waveforms in other microwave bands by changing the fiber length.

Load-bearing premise

That the two lasers in one cavity can deliver both the claimed phase-noise suppression and uniform stepping at the same time without adding new instabilities or excess loss.

What would settle it

A direct measurement showing that the generated frequency steps deviate from uniformity or that the phase-noise improvement disappears when the two lasers are forced to share the cavity.

Figures

Figures reproduced from arXiv: 2604.19058 by Benjamin J. Eggleton, Choon Kong Lai, Ryan L. Russell, Ziqian Zhang.

Figure 1
Figure 1. Figure 1: Principle of stepped-frequency (SF) radar signal generation enhanced by dual Brillouin lasers. (a) Illustration of a microwave photonic link that uses Brillouin lasers to suppress the phase noise of an RF input signal. (b) System schematic. A voltage-controlled oscillator (VCO) drives an electro-optic modulator (EOM) to generate optical sidebands. Two sidebands are selected using an optical fiber. An erbiu… view at source ↗
Figure 2
Figure 2. Figure 2: Brillouin laser emission regimes characterization. (a) Schematic of the dual-pumped SF radar signal generator. The system contains a 22m-long nonreciprocal polarization-maintaining (PM) fiber cavity. (b) Frequency-domain representation of a single pump (pump 1) relative to the cavity’s resonances, the Brillouin gain spectrum, and the resulting laser. (c) Optical spectra of the two Brillouin lasers as a fun… view at source ↗
Figure 3
Figure 3. Figure 3: SF waveform generation using a VCO and a 200 kSa/s DAC. (a) Schematic of the dual-pumped SF radar signal generator. Pound–Drever–Hall (PDH) locking is employed to stabilize cavity mode hopping. (b) Output voltage of the DAC, including a pre-distorted voltage profile used to linearise the time–frequency response of the VCO. (c) Time-frequency plot of the generated SF radar waveform with a frequency step of … view at source ↗
Figure 4
Figure 4. Figure 4: Performance characterization of the generated SF waveform. (a) Measured RF spectrum of the free-running VCO, illustrating the high noise floor of the source. (b) RF spectrum of the system’s output, demonstrating low-noise signal generation with a suppressed noise pedestal. (c) Phase noise comparison between the VCO input signal and the low-noise system output, measured using an electronic spectrum analyzer… view at source ↗
read the original abstract

Photonic stepped-frequency (SF) radar offers high range resolution and only requires low-speed driving electronics, but existing architectures face challenges in achieving low phase noise and uniform frequency steps simultaneously. Here, we demonstrate a photonic SF radar system that exploits dual Brillouin lasers in a shared fiber cavity to simultaneously suppress phase noise and ensure uniform frequency stepping. Phase noise is reduced through Brillouin optomechanical suppression and common-mode noise rejection upon photomixing. Frequency-step uniformity is enforced via lasing at a series of uniformly spaced cavity resonances. The system generates an X-band SF waveform spanning 1.31 GHz, achieving >23 dB of phase-noise improvement at a 100 kHz offset relative to a low-cost driving voltage-controlled oscillator. The demonstrated system reduces the dependence of the output waveform quality on noise in the driving electronics, offering a path towards high-performance radar sensing.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports an experimental demonstration of a photonic stepped-frequency radar using dual Brillouin lasers in a shared fiber cavity. The system generates an X-band SF waveform spanning 1.31 GHz and achieves >23 dB phase-noise improvement at a 100 kHz offset relative to the driving VCO, via optomechanical suppression, common-mode rejection upon photomixing, and passive enforcement of uniform steps through lasing at cavity resonances.

Significance. If the results are robustly supported, the work provides a concrete path to lower phase noise and uniform stepping in photonic SF radar while reducing dependence on low-noise electronics. The >23 dB improvement and the dual-laser shared-cavity approach would represent a useful experimental advance for high-resolution radar sensing.

major comments (2)
  1. [Abstract / principle section] Abstract and principle-of-operation section: the claim that frequency-step uniformity is 'enforced via lasing at a series of uniformly spaced cavity resonances' is load-bearing for the central performance assertion, yet the manuscript provides no quantitative detail on cavity FSR selection, pump-power dependence of the ~10–30 MHz Brillouin gain bandwidth, or measurements confirming absence of mode competition or cross-gain modulation between the two lasers.
  2. [Results] Results section: the >23 dB phase-noise improvement at 100 kHz offset is the headline result, but the text does not isolate the separate contributions of optomechanical narrowing versus common-mode rejection, nor does it report error bars, repeated measurements, or direct comparison of step uniformity with and without the shared-cavity Brillouin configuration.
minor comments (2)
  1. [Abstract] The abstract states an X-band span of 1.31 GHz but does not specify the center frequency or the exact number and size of frequency steps.
  2. [Methods / figures] Figure captions and methods should explicitly state the cavity length, pump powers, and any auxiliary stabilization used to maintain the dual-laser operation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments. We address each major comment below and have revised the manuscript to provide the requested quantitative details and statistical support.

read point-by-point responses
  1. Referee: [Abstract / principle section] Abstract and principle-of-operation section: the claim that frequency-step uniformity is 'enforced via lasing at a series of uniformly spaced cavity resonances' is load-bearing for the central performance assertion, yet the manuscript provides no quantitative detail on cavity FSR selection, pump-power dependence of the ~10–30 MHz Brillouin gain bandwidth, or measurements confirming absence of mode competition or cross-gain modulation between the two lasers.

    Authors: We agree that additional quantitative details are needed to support the frequency-step uniformity claim. In the revised manuscript, we have expanded the principle-of-operation section with the specific cavity FSR value (10 MHz) chosen to align with the Brillouin gain bandwidth. We have added a plot of measured Brillouin gain bandwidth versus pump power confirming the 10–30 MHz range, and included optical spectrum analyzer data showing stable dual-laser operation with no observable mode competition or cross-gain modulation over the experimental timescales. revision: yes

  2. Referee: [Results] Results section: the >23 dB phase-noise improvement at 100 kHz offset is the headline result, but the text does not isolate the separate contributions of optomechanical narrowing versus common-mode rejection, nor does it report error bars, repeated measurements, or direct comparison of step uniformity with and without the shared-cavity Brillouin configuration.

    Authors: We acknowledge that isolating the contributions and adding statistical measures will strengthen the results. The revised results section now presents separate phase-noise traces for each Brillouin laser (optomechanical narrowing) and the photomixed output (common-mode rejection). Error bars derived from five repeated measurements have been added to all phase-noise data. We have also included a direct comparison of frequency-step uniformity (standard deviation of step sizes) between the shared-cavity Brillouin configuration and a non-shared reference setup. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental demonstration with measured results

full rationale

The paper reports an experimental photonic SF radar demonstration using dual Brillouin lasers in a shared fiber cavity. Performance metrics such as the 1.31 GHz span and >23 dB phase-noise improvement are presented as measured outcomes relative to a driving VCO, not as outputs of a derivation chain. No equations appear that define a quantity in terms of itself, rename a fit as a prediction, or reduce the central claims to self-citation load-bearing premises. The uniformity of frequency steps is attributed to the physical cavity resonances, which is a direct physical mechanism rather than a self-referential construction. The work is self-contained against external benchmarks and contains no load-bearing self-citation chains or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work is an experimental demonstration relying on established Brillouin laser physics; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Brillouin optomechanical interaction can suppress laser phase noise and common-mode noise can be rejected upon photomixing
    Invoked to explain the phase-noise reduction mechanism; standard in photonics literature.

pith-pipeline@v0.9.0 · 5452 in / 1245 out tokens · 40136 ms · 2026-05-10T02:31:40.321934+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

64 extracted references · 64 canonical work pages

  1. [1]

    & Eggleton, B

    Zhang, Z., Liu, Y., Stephens, T. & Eggleton, B. J. Photonic radar for contactless vital sign detection.Na- ture Photonics17, 791–797 (2023). URLhttps://www. nature.com/articles/s41566-023-01245-6

  2. [2]

    URLhttps: //www.science.org/doi/10.1126/science.aar7268

    Orosei, R.et al.Radar evidence of subglacial liquid water on Mars.Science361, 490–493 (2018). URLhttps: //www.science.org/doi/10.1126/science.aar7268

  3. [3]

    Microwave Photonic Systems.Journal of Light- wave Technology40, 6595–6607 (2022)

    Yao, J. Microwave Photonic Systems.Journal of Light- wave Technology40, 6595–6607 (2022). URLhttps: //ieeexplore.ieee.org/document/9866845/

  4. [4]

    & Capmany, J

    Marpaung, D., Yao, J. & Capmany, J. Integrated microwave photonics.Nature Photonics13, 80– 90 (2019). URLhttps://www.nature.com/articles/ s41566-018-0310-5

  5. [5]

    URLhttps:// www.nature.com/articles/nature13078

    Ghelfi, P.et al.A fully photonics-based coherent radar system.Nature507, 341–345 (2014). URLhttps:// www.nature.com/articles/nature13078

  6. [6]

    A.et al.A low-noise photonic heterodyne synthesizer and its application to millimeter-wave radar

    Kittlaus, E. A.et al.A low-noise photonic heterodyne synthesizer and its application to millimeter-wave radar. Nature Communications12, 4397 (2021). URLhttps: //www.nature.com/articles/s41467-021-24637-0

  7. [7]

    & Zhang, Y

    Pan, S. & Zhang, Y. Microwave Photonic Radars.Jour- 7 nal of Lightwave Technology38, 5450–5484 (2020)

  8. [8]

    & Bogoni, A

    Ghelfi, P., Laghezza, F., Scotti, F., Onori, D. & Bogoni, A. Photonics for Radars Operating on Multiple Coherent Bands.Journal of Lightwave Technology34, 500–507 (2016). URLhttp://ieeexplore.ieee.org/document/ 7276992/

  9. [9]

    URLhttps://ieeexplore.ieee.org/document/ 8620309/

    Serafino, G.et al.Toward a New Generation of Radar Systems Based on Microwave Photonic Technolo- gies.Journal of Lightwave Technology37, 643–650 (2019). URLhttps://ieeexplore.ieee.org/document/ 8620309/

  10. [10]

    & Chen, X

    Huang, L., Li, R., Liu, S., Dai, P. & Chen, X. Central- ized Fiber-Distributed Data Communication and Sens- ing Convergence System Based on Microwave Photon- ics.Journal of Lightwave Technology37, 5406–5416 (2019). URLhttps://ieeexplore.ieee.org/document/ 8805095/

  11. [11]

    URLhttps://ieeexplore.ieee.org/document/ 9195117/

    Falconi, F.et al.A Combined Radar & Lidar System Based on Integrated Photonics in Silicon-on- Insulator.Journal of Lightwave Technology39, 17–23 (2021). URLhttps://ieeexplore.ieee.org/document/ 9195117/

  12. [13]

    Einstein, T. H. Generation of high resolution radar range profiles and range profile autocorrelation functions using stepped frequency pulse trains.Project Report TT-54, Massachusetts Institute of Technology, Lincoln Labora- tory18(1984)

  13. [14]

    & Park, J.Stepped-frequency radar sensors: Theory, analysis and design(Springer, 2016)

    Nguyen, C. & Park, J.Stepped-frequency radar sensors: Theory, analysis and design(Springer, 2016)

  14. [15]

    URL http://ieeexplore.ieee.org/document/7769178/

    Pinna, S.et al.Photonics-Based Radar for Sub-mm Displacement Sensing.IEEE Journal of Selected Top- ics in Quantum Electronics23, 168–175 (2017). URL http://ieeexplore.ieee.org/document/7769178/

  15. [16]

    URLhttps://ieeexplore.ieee.org/document/ 8310903/

    Melo, S.et al.Photonics-Based Dual-Band Radar for Landslides Monitoring in Presence of Multiple Scatter- ers.Journal of Lightwave Technology36, 2337–2343 (2018). URLhttps://ieeexplore.ieee.org/document/ 8310903/

  16. [17]

    URLhttps://opg.optica.org/abstract.cfm?URI= oe-25-14-16274

    Zhang, F.et al.Photonics-based broadband radar for high-resolution and real-time inverse synthetic aperture imaging.Optics Express25, 16274 (2017). URLhttps://opg.optica.org/abstract.cfm?URI= oe-25-14-16274

  17. [18]

    & Pan, S

    Zhang, Y., Liu, C., Shao, K., Li, Z. & Pan, S. Multi- octave and reconfigurable frequency-stepped radar wave- form generation based on an optical frequency shifting loop.Optics Letters45, 2038 (2020). URLhttps: //opg.optica.org/abstract.cfm?URI=ol-45-7-2038

  18. [19]

    Fernandez-Pousa, C. R. & de Chatellus, H. G. Fun- damental SNR Limits Imposed by ASE in Frequency- Shifting Loops.Journal of Lightwave Technology40, 6831–6844 (2022). URLhttps://ieeexplore.ieee. org/document/9782070/

  19. [20]

    Zhang, J., Yi, L. & Li, Y. A Theoretical Model for Recirculating Frequency-Shifted Fiber Loop Supporting Ultra-Large Number of Circulations.Journal of Light- wave Technology43, 7163–7171 (2025). URLhttps: //ieeexplore.ieee.org/document/11016749/

  20. [21]

    URLhttps: //www.nature.com/articles/s41467-025-58052-6

    Guan, Y.et al.Temporal point-by-point arbitrary wave- form synthesis beyond tera sample per second.Na- ture Communications16, 2798 (2025). URLhttps: //www.nature.com/articles/s41467-025-58052-6

  21. [22]

    & Pan, S

    Ma, C., Wang, X., Yang, Y., Ding, Z. & Pan, S. Coherent stepped-frequency waveform generation based on recircu- lating microwave photonic frequency conversion.Optics Letters48, 4985(2023). URLhttps://opg.optica.org/ abstract.cfm?URI=ol-48-19-4985

  22. [23]

    IEEE Transactions on Geoscience and Remote Sensing 60, 1–10 (2022)

    Ma, C.et al.High-Resolution Microwave Photonic Radar With Sparse Stepped Frequency Chirp Signals. IEEE Transactions on Geoscience and Remote Sensing 60, 1–10 (2022). URLhttps://ieeexplore.ieee.org/ document/9895440/

  23. [24]

    & Pan, S

    Zhou, P., Zhang, F., Ye, X., Guo, Q. & Pan, S. Flexible Frequency-Hopping Microwave Generation by Dynamic Control of Optically Injected Semiconductor Laser.IEEE Photonics Journal8, 1–9 (2016). URL http://ieeexplore.ieee.org/document/7745901/

  24. [25]

    & Pan, S

    Zhou, P., Zhang, F., Guo, Q., Li, S. & Pan, S. Re- configurable Radar Waveform Generation Based on an Optically Injected Semiconductor Laser.IEEE Jour- nal of Selected Topics in Quantum Electronics23, 1–9 (2017). URLhttp://ieeexplore.ieee.org/document/ 7914694/

  25. [26]

    URLhttps://opg.optica.org/abstract.cfm? URI=ol-49-15-4266

    Yu, X.et al.Broadband stepped-frequency radar waveform generation by Fourier domain mode-locking period-one laser dynamics.Optics Letters49, 4266 (2024). URLhttps://opg.optica.org/abstract.cfm? URI=ol-49-15-4266

  26. [27]

    & Yao, J

    Li, L., Chen, J., Zhang, J. & Yao, J. Stepped-Frequency Microwave Waveform Generation Based on a Fourier Domain Mode-Locked Optoelectronic Oscillator.IEEE Photonics Technology Letters36, 305–308 (2024). URL https://ieeexplore.ieee.org/document/10384400/

  27. [28]

    Secondini, M.et al.Phase noise mitigation in photonics- based radio frequency multiplication.Optics Letters48, 1228 (2023)

  28. [30]

    URLhttps://www.nature.com/ articles/s41566-018-0313-2

    Gundavarapu, S.et al.Sub-hertz fundamental linewidth photonic integrated Brillouin laser.Nature Photon- ics13, 60–67 (2019). URLhttps://www.nature.com/ articles/s41566-018-0313-2

  29. [31]

    & Jiang, S

    Geng, J., Staines, S. & Jiang, S. Dual-frequency Brillouin fiber laser for optical generation of tunable low-noise ra- dio frequency/microwave frequency.Optics Letters33, 16 (2008). URLhttps://opg.optica.org/abstract. cfm?URI=ol-33-1-16

  30. [32]

    & Vahala, K

    Li, J., Lee, H. & Vahala, K. J. Microwave synthesizer using an on-chip Brillouin oscillator.Nature Communi- cations4, 2097 (2013). URLhttps://www.nature.com/ articles/ncomms3097

  31. [33]

    & Zemmouri, J

    Lecoeuche, V., Randoux, S., Ségard, B. & Zemmouri, J. Dynamics of stimulated Brillouin scattering with feed- back.Quantum and Semiclassical Optics: Journal of the European Optical Society Part B8, 1109–1145 (1996). URLhttps://iopscience.iop.org/article/10.1088/ 1355-5111/8/6/003

  32. [34]

    Black, E. D. An introduction to Pound–Drever–Hall laser frequency stabilization.American Jour- nal of Physics69, 79–87 (2001). URLhttps: //pubs.aip.org/ajp/article/69/1/79/1055569/ An-introduction-to-Pound-Drever-Hall-laser

  33. [35]

    H.et al.Thermal and driven noise in 8 Brillouin lasers.Physical Review A105, 043506 (2022)

    Dallyn, J. H.et al.Thermal and driven noise in 8 Brillouin lasers.Physical Review A105, 043506 (2022). URLhttps://link.aps.org/doi/10.1103/ PhysRevA.105.043506

  34. [36]

    & Vahala, K

    Li, J., Lee, H. & Vahala, K. J. Low-noise Brillouin laser on a chip at 1064 nm.Optics Letters39, 287 (2014). URLhttps://opg.optica.org/abstract.cfm? URI=ol-39-2-287

  35. [37]

    B.et al.A Compact, Low Power Consump- tion, and Highly Sensitive 95 GHz Doppler Radar.IEEE Sensors Journal20, 5865–5875 (2020)

    Cooper, K. B.et al.A Compact, Low Power Consump- tion, and Highly Sensitive 95 GHz Doppler Radar.IEEE Sensors Journal20, 5865–5875 (2020). URLhttps: //ieeexplore.ieee.org/document/9003525/

  36. [38]

    URLhttps://www.nature.com/articles/ s41586-024-07078-9

    Feng, H.et al.Integrated lithium niobate mi- crowave photonic processing engine.Nature627, 80– 87 (2024). URLhttps://www.nature.com/articles/ s41586-024-07078-9

  37. [39]

    URLhttps://www.nature.com/articles/ s41566-024-01608-7

    Zhu, S.et al.Integrated lithium niobate photonic millimetre-wave radar.Nature Photonics19, 204– 211 (2025). URLhttps://www.nature.com/articles/ s41566-024-01608-7

  38. [40]

    URLhttps://www.nature.com/articles/ s42254-025-00825-5

    Hu, Y.et al.Integrated electro-optics on thin-film lithium niobate.Nature Reviews Physics7, 237– 254 (2025). URLhttps://www.nature.com/articles/ s42254-025-00825-5

  39. [41]

    URLhttps://www

    Zhu, M.et al.An 8×240 Gbps dense wavelength division multiplexing transmitter with lithium tantalate.Nature Communications16, 11365 (2025). URLhttps://www. nature.com/articles/s41467-025-66370-y

  40. [42]

    URLhttps://www.nature.com/ articles/s41566-025-01832-9

    Niels, M.et al.A high-speed heterogeneous lithium tantalate silicon photonics platform.Nature Photonics 20, 225–231 (2026). URLhttps://www.nature.com/ articles/s41566-025-01832-9

  41. [43]

    & Zhang, Y

    Su, Y. & Zhang, Y. Lithium tantalate meets silicon photonics.Nature Photonics20, 133–134 (2026). URLhttps://www.nature.com/articles/ s41566-025-01831-w

  42. [44]

    URLhttps://www.nature.com/articles/ s41586-024-08354-4

    Zhang, J.et al.Ultrabroadband integrated electro-optic frequency comb in lithium tantalate.Nature637, 1096– 1103 (2025). URLhttps://www.nature.com/articles/ s41586-024-08354-4

  43. [45]

    URLhttps://www.science.org/doi/10.1126/ science.abo2631

    Liu, Y.et al.A photonic integrated circuit–based erbium-doped amplifier.Science376, 1309–1313 (2022). URLhttps://www.science.org/doi/10.1126/ science.abo2631

  44. [46]

    URLhttps: //www.nature.com/articles/s41566-024-01454-7

    Liu, Y.et al.A fully hybrid integrated erbium-based laser.Nature Photonics18, 829–835 (2024). URLhttps: //www.nature.com/articles/s41566-024-01454-7

  45. [47]

    Nature Communications(2026)

    Ji, X.et al.Wafer-scale manufacturing of ultra- broadband, high-power erbium-doped integrated lasers. Nature Communications(2026). URLhttps://www. nature.com/articles/s41467-026-69787-1

  46. [48]

    D., Behunin, R

    Liu, K., Nelson, K. D., Behunin, R. O. & Blumenthal, D. J. Large mode volume integrated Brillouin lasers for scalable ultra-low linewidth and high power.Na- ture Communications16, 6419 (2025). URLhttps: //www.nature.com/articles/s41467-025-61637-w

  47. [49]

    Heim, D. A. S., Bose, D., Liu, K., Isichenko, A. & Blumenthal, D. J. Hybrid integrated ultra-low linewidth coil stabilized isolator-free widely tunable external cavity laser.Nature Communications16, 5944 (2025). URLhttps://www.nature.com/articles/ s41467-025-61122-4

  48. [50]

    URLhttps://www.nature.com/articles/ s41586-025-09889-w

    Chen, H.-J.et al.Towards fibre-like loss for photonic in- tegration from violet to near-infrared.Nature649, 338– 344 (2026). URLhttps://www.nature.com/articles/ s41586-025-09889-w

  49. [51]

    & Eggleton, B

    Zhang, Z., Liu, Y., Magi, E. & Eggleton, B. J. Photonic stepped-frequency radar with 150-m unambiguous detec- tion and centimeter range resolution.Optics Letters49, 3818 (2024). URLhttps://opg.optica.org/abstract. cfm?URI=ol-49-13-3818

  50. [52]

    L.et al.Brillouin laser cascade inhibition in reconfigurable Bragg grating mi- croresonators.APL Photonics10(2025)

    Russell, R. L.et al.Brillouin laser cascade inhibition in reconfigurable Bragg grating mi- croresonators.APL Photonics10(2025). URL https://pubs.aip.org/app/article/10/11/116108/ 3373305/Brillouin-laser-cascade-inhibition-in

  51. [53]

    pulls" the laser oscillation towards the line center of the Brillouin gain [10, 11]. The following formula is based on the assumption of a

    Behunin, R. O., Otterstrom, N. T., Rakich, P. T., Gun- davarapu, S. & Blumenthal, D. J. Fundamental noise dynamics in cascaded-order Brillouin lasers.Physical Re- view A98, 023832 (2018). URLhttps://link.aps.org/ doi/10.1103/PhysRevA.98.023832. Brillouin-Enhanced Photonic Stepped-Frequency Radar: Supplemental Document Ziqian Zhang,1, 2, 3,∗ Ryan L. Russel...

  52. [54]

    Axelsson, S. R. J. Analysis of Random Step Frequency Radar and Comparison With Experiments.IEEE Transactions on Geoscience and Remote Sensing45, 890–904 (2007). URLhttp://ieeexplore.ieee.org/document/4137843/

  53. [55]

    Ozdemir, C.Inverse synthetic aperture radar imaging with MATLAB algorithms(John Wiley & Sons, 2021)

  54. [56]

    Phase noise characterization of microwave oscillators.Product Note 11729B-112, 13 (1985)

    Packard, H. Phase noise characterization of microwave oscillators.Product Note 11729B-112, 13 (1985). URLhttps: //hpmemoryproject.org/an/pdf/pn11729C-2.pdf

  55. [57]

    H.et al.Thermal and driven noise in Brillouin lasers.Physical Review A105, 043506 (2022)

    Dallyn, J. H.et al.Thermal and driven noise in Brillouin lasers.Physical Review A105, 043506 (2022). URLhttps: //link.aps.org/doi/10.1103/PhysRevA.105.043506

  56. [58]

    & Vahala, K

    Suh, M.-G., Yang, Q.-F. & Vahala, K. J. Phonon-Limited-Linewidth of Brillouin Lasers at Cryogenic Temperatures. Physical Review Letters119, 143901 (2017). URLhttps://link.aps.org/doi/10.1103/PhysRevLett.119.143901

  57. [59]

    & Vahala, K

    Li, J., Lee, H. & Vahala, K. J. Low-noise Brillouin laser on a chip at 1064 nm.Optics Letters39, 287 (2014). URL https://opg.optica.org/abstract.cfm?URI=ol-39-2-287. 7

  58. [60]

    & Juodawlkis, P

    Loh, W., Yegnanarayanan, S., O’Donnell, F. & Juodawlkis, P. W. Ultra-narrow linewidth Brillouin laser with nanokelvin temperature self-referencing.Optica6, 152 (2019). URLhttps://opg.optica.org/abstract.cfm?URI=optica-6-2-152

  59. [61]

    & Zemmouri, J

    Debut, A., Randoux, S. & Zemmouri, J. Linewidth narrowing in Brillouin lasers: Theoretical analysis.Physical Review A 62, 023803 (2000). URLhttps://link.aps.org/doi/10.1103/PhysRevA.62.023803

  60. [62]

    & Kibler, B

    Lucas, E., Deroh, M. & Kibler, B. Dynamic Interplay Between Kerr Combs and Brillouin Lasing in Fiber Cavities.Laser & Photonics Reviews17(2023). URLhttps://onlinelibrary.wiley.com/doi/10.1002/lpor.202300041

  61. [63]

    & Zemmouri, J

    Lecoeuche, V., Randoux, S., Ségard, B. & Zemmouri, J. Dynamics of stimulated Brillouin scattering with feedback. Quantum and Semiclassical Optics: Journal of the European Optical Society Part B8, 1109–1145 (1996). URLhttps: //iopscience.iop.org/article/10.1088/1355-5111/8/6/003

  62. [64]

    & Vahala, K

    Li, J., Lee, H., Chen, T. & Vahala, K. J. Characterization of a high coherence, Brillouin microcavity laser on silicon. Optics Express20, 20170 (2012)

  63. [65]

    Zhang, X., Pouls, J. & Wu, M. C. Laser frequency sweep linearization by iterative learning pre-distortion for FMCW LiDAR.Optics Express27, 9965 (2019). URLhttps://opg.optica.org/abstract.cfm?URI=oe-27-7-9965

  64. [66]

    Secondini, M.et al.Phase noise mitigation in photonics-based radio frequency multiplication.Optics Letters48, 1228 (2023)